%------------------------------------------------------------------------------
% File     : ITP001_1 : TPTP v8.2.0. Released v8.1.0.
% Domain   : Interactive Theorem Proving
% Problem  : SMT-LIB Gauss_Jordan Linear_Maps 00893_043693
% Version  : [Des21] axioms.
% English  :

% Refs     : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% Source   : [Des21]
% Names    : Gauss_Jordan-0025_Linear_Maps-prob_00893_043693 [Des21]

% Status   : Theorem
% Rating   : 1.00 v8.1.0
% Syntax   : Number of formulae    : 1608 ( 493 unt; 696 typ;   0 def)
%            Number of atoms       : 2045 (1120 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives : 1272 ( 139   ~;  24   |; 405   &)
%                                         ( 162 <=>; 542  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   5 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number arithmetic     :  351 ( 144 atm;   2 fun;  62 num; 143 var)
%            Number of types       :  112 ( 110 usr;   1 ari)
%            Number of type conns  :  964 ( 510   >; 454   *;   0   +;   0  <<)
%            Number of predicates  :   55 (  50 usr;   3 prp; 0-3 aty)
%            Number of functors    :  538 ( 536 usr;  76 con; 0-4 aty)
%            Number of variables   : 2670 (2617   !;  53   ?;2670   :)
% SPC      : TF0_THM_EQU_ARI

% Comments : Translated from SMT format using smttotptp 0.9.10. See
%            https://bitbucket.org/peba123/smttotptp/src/master/
%          : SMT-LIB AUFLIA logic
%------------------------------------------------------------------------------
%% Types:
tff('Nat_set_set$',type,
    'Nat_set_set$': $tType ).

tff('N_n_fun_n_vec$',type,
    'N_n_fun_n_vec$': $tType ).

tff('A_n_n_fun_vec$',type,
    'A_n_n_fun_vec$': $tType ).

tff('Nat_n_prod_set$',type,
    'Nat_n_prod_set$': $tType ).

tff('N_n_a_n_vec_fun_fun$',type,
    'N_n_a_n_vec_fun_fun$': $tType ).

tff('Int_bool_fun$',type,
    'Int_bool_fun$': $tType ).

tff('Nat_n_n_fun_a_fun_fun$',type,
    'Nat_n_n_fun_a_fun_fun$': $tType ).

tff('N_option_set$',type,
    'N_option_set$': $tType ).

tff('N_a_n_vec_fun_bool_fun$',type,
    'N_a_n_vec_fun_bool_fun$': $tType ).

tff('N_n_a_fun_fun$',type,
    'N_n_a_fun_fun$': $tType ).

tff('Nat_nat_bool_fun_fun$',type,
    'Nat_nat_bool_fun_fun$': $tType ).

tff('N_nat_prod_set$',type,
    'N_nat_prod_set$': $tType ).

tff('N_a_n_vec_a_n_vec_fun_fun$',type,
    'N_a_n_vec_a_n_vec_fun_fun$': $tType ).

tff('A_n_n_fun_vec_n_vec$',type,
    'A_n_n_fun_vec_n_vec$': $tType ).

tff('N_nat_a_n_vec_fun_fun$',type,
    'N_nat_a_n_vec_fun_fun$': $tType ).

tff('A_nat_fun$',type,
    'A_nat_fun$': $tType ).

tff('Nat_a_fun$',type,
    'Nat_a_fun$': $tType ).

tff('A_set_set$',type,
    'A_set_set$': $tType ).

tff('Nat_nat_fun_set$',type,
    'Nat_nat_fun_set$': $tType ).

tff('A_n_fun$',type,
    'A_n_fun$': $tType ).

tff('A_a_n_vec_fun$',type,
    'A_a_n_vec_fun$': $tType ).

tff('A_n_vec_n_n_fun_vec$',type,
    'A_n_vec_n_n_fun_vec$': $tType ).

tff('A_n_vec_set$',type,
    'A_n_vec_set$': $tType ).

tff('Nat_nat_nat_fun_fun$',type,
    'Nat_nat_nat_fun_fun$': $tType ).

tff('N_a_fun_set$',type,
    'N_a_fun_set$': $tType ).

tff('A_n_vec_a_fun$',type,
    'A_n_vec_a_fun$': $tType ).

tff('A_n_vec_n_vec_bool_fun$',type,
    'A_n_vec_n_vec_bool_fun$': $tType ).

tff('Nat_n_sum_set$',type,
    'Nat_n_sum_set$': $tType ).

tff('N_a_n_vec_fun$',type,
    'N_a_n_vec_fun$': $tType ).

tff('Int_set$',type,
    'Int_set$': $tType ).

tff('Int_int_fun$',type,
    'Int_int_fun$': $tType ).

tff('N_n_vec$',type,
    'N_n_vec$': $tType ).

tff('N_n_sum_set$',type,
    'N_n_sum_set$': $tType ).

tff('A_n_vec_n_vec_a_fun$',type,
    'A_n_vec_n_vec_a_fun$': $tType ).

tff('N_nat_fun$',type,
    'N_nat_fun$': $tType ).

tff('N_set$',type,
    'N_set$': $tType ).

tff('Nat_nat_prod_set$',type,
    'Nat_nat_prod_set$': $tType ).

tff('A_n_vec_n_vec$',type,
    'A_n_vec_n_vec$': $tType ).

tff('N_a_n_vec_bool_fun_fun$',type,
    'N_a_n_vec_bool_fun_fun$': $tType ).

tff('Nat_n_fun$',type,
    'Nat_n_fun$': $tType ).

tff('N_nat_sum_set$',type,
    'N_nat_sum_set$': $tType ).

tff('A_n_vec_nat_fun$',type,
    'A_n_vec_nat_fun$': $tType ).

tff('N_a_n_vec_n_vec_bool_fun_fun$',type,
    'N_a_n_vec_n_vec_bool_fun_fun$': $tType ).

tff('A_n_vec_a_n_vec_bool_fun_fun$',type,
    'A_n_vec_a_n_vec_bool_fun_fun$': $tType ).

tff('N_n_fun_a_n_vec_fun$',type,
    'N_n_fun_a_n_vec_fun$': $tType ).

tff('Nat_nat_fun$',type,
    'Nat_nat_fun$': $tType ).

tff('N_a_n_vec_n_vec_fun_set$',type,
    'N_a_n_vec_n_vec_fun_set$': $tType ).

tff('Nat_n_vec_n_vec$',type,
    'Nat_n_vec_n_vec$': $tType ).

tff('Nat$',type,
    'Nat$': $tType ).

tff('N_nat_fun_set$',type,
    'N_nat_fun_set$': $tType ).

tff('A_n_vec_n_vec_set$',type,
    'A_n_vec_n_vec_set$': $tType ).

tff('N_int_fun$',type,
    'N_int_fun$': $tType ).

tff('N$',type,
    'N$': $tType ).

tff('A_a_n_vec_a_n_vec_fun_fun$',type,
    'A_a_n_vec_a_n_vec_fun_fun$': $tType ).

tff('N_a_fun_bool_fun$',type,
    'N_a_fun_bool_fun$': $tType ).

tff('N_nat_fun_bool_fun$',type,
    'N_nat_fun_bool_fun$': $tType ).

tff('N_n_fun_bool_fun$',type,
    'N_n_fun_bool_fun$': $tType ).

tff('N_a_set_fun$',type,
    'N_a_set_fun$': $tType ).

tff('N_n_fun_set$',type,
    'N_n_fun_set$': $tType ).

tff('N_n_fun_a_fun$',type,
    'N_n_fun_a_fun$': $tType ).

tff('Nat_n_a_fun_fun$',type,
    'Nat_n_a_fun_fun$': $tType ).

tff('Nat_nat_sum_set$',type,
    'Nat_nat_sum_set$': $tType ).

tff(tlbool,type,
    tlbool: $tType ).

tff('A_a_bool_fun_fun$',type,
    'A_a_bool_fun_fun$': $tType ).

tff('N_n_fun_n_a_fun_fun$',type,
    'N_n_fun_n_a_fun_fun$': $tType ).

tff('N_nat_a_fun_fun$',type,
    'N_nat_a_fun_fun$': $tType ).

tff('A_a_n_vec_n_vec_fun$',type,
    'A_a_n_vec_n_vec_fun$': $tType ).

tff('N_a_n_vec_fun_set$',type,
    'N_a_n_vec_fun_set$': $tType ).

tff('N_n_prod_set$',type,
    'N_n_prod_set$': $tType ).

tff('N_a_bool_fun_fun$',type,
    'N_a_bool_fun_fun$': $tType ).

tff('A_bool_fun$',type,
    'A_bool_fun$': $tType ).

tff('A_set$',type,
    'A_set$': $tType ).

tff('N_a_fun$',type,
    'N_a_fun$': $tType ).

tff('Nat_nat_fun_n_vec$',type,
    'Nat_nat_fun_n_vec$': $tType ).

tff('N_a_n_vec_n_vec_n_vec_fun$',type,
    'N_a_n_vec_n_vec_n_vec_fun$': $tType ).

tff('Nat_nat_set_fun$',type,
    'Nat_nat_set_fun$': $tType ).

tff('N_n_a_set_fun_fun$',type,
    'N_n_a_set_fun_fun$': $tType ).

tff('A$',type,
    'A$': $tType ).

tff('N_n_n_fun_a_fun_fun$',type,
    'N_n_n_fun_a_fun_fun$': $tType ).

tff('N_n_fun$',type,
    'N_n_fun$': $tType ).

tff('Nat_n_vec$',type,
    'Nat_n_vec$': $tType ).

tff('A_n_vec$',type,
    'A_n_vec$': $tType ).

tff('A_a_a_fun_fun$',type,
    'A_a_a_fun_fun$': $tType ).

tff('Nat_a_set_fun$',type,
    'Nat_a_set_fun$': $tType ).

tff('Nat_option_set$',type,
    'Nat_option_set$': $tType ).

tff('A_n_vec_a_n_vec_fun$',type,
    'A_n_vec_a_n_vec_fun$': $tType ).

tff('N_n_fun_nat_a_fun_fun$',type,
    'N_n_fun_nat_a_fun_fun$': $tType ).

tff('A_n_vec_n_vec_n_vec_n_vec$',type,
    'A_n_vec_n_vec_n_vec_n_vec$': $tType ).

tff('A_a_fun$',type,
    'A_a_fun$': $tType ).

tff('Nat_ennreal_fun$',type,
    'Nat_ennreal_fun$': $tType ).

tff('A_n_vec_n_vec_n_vec$',type,
    'A_n_vec_n_vec_n_vec$': $tType ).

tff('Int_int_bool_fun_fun$',type,
    'Int_int_bool_fun_fun$': $tType ).

tff('N_nat_bool_fun_fun$',type,
    'N_nat_bool_fun_fun$': $tType ).

tff('Nat_nat_fun_bool_fun$',type,
    'Nat_nat_fun_bool_fun$': $tType ).

tff('Nat_bool_fun$',type,
    'Nat_bool_fun$': $tType ).

tff('Ennreal$',type,
    'Ennreal$': $tType ).

tff('N_set_set$',type,
    'N_set_set$': $tType ).

tff('N_a_n_vec_set_fun$',type,
    'N_a_n_vec_set_fun$': $tType ).

tff('Nat_n_a_n_vec_fun_fun$',type,
    'Nat_n_a_n_vec_fun_fun$': $tType ).

tff('A_n_vec_bool_fun$',type,
    'A_n_vec_bool_fun$': $tType ).

tff('Nat_set$',type,
    'Nat_set$': $tType ).

tff('N_a_n_vec_n_vec_fun_bool_fun$',type,
    'N_a_n_vec_n_vec_fun_bool_fun$': $tType ).

tff('N_n_bool_fun_fun$',type,
    'N_n_bool_fun_fun$': $tType ).

tff('Nat_nat_a_fun_fun$',type,
    'Nat_nat_a_fun_fun$': $tType ).

tff('Int_n_vec$',type,
    'Int_n_vec$': $tType ).

tff('Nat_n_bool_fun_fun$',type,
    'Nat_n_bool_fun_fun$': $tType ).

tff('N_bool_fun$',type,
    'N_bool_fun$': $tType ).

tff('A_n_n_fun_vec_n_n_fun_vec$',type,
    'A_n_n_fun_vec_n_n_fun_vec$': $tType ).

tff('Nat_a_n_vec_fun$',type,
    'Nat_a_n_vec_fun$': $tType ).

tff('N_a_n_vec_n_vec_fun$',type,
    'N_a_n_vec_n_vec_fun$': $tType ).

%% Declarations:
tff('van$',type,
    'van$': ( 'A_n_vec_n_vec$' * 'N$' * 'A$' ) > 'N_a_n_vec_fun$' ).

tff('plus$a',type,
    'plus$a': 'A$' > 'A_a_fun$' ).

tff('vdw$',type,
    'vdw$': ( 'A_n_vec_n_vec$' * 'N$' * 'N$' * 'A$' ) > 'N_n_a_fun_fun$' ).

tff('vcz$',type,
    'vcz$': ( 'N_set$' * 'N_n_a_n_vec_fun_fun$' * 'N_a_n_vec_fun$' * 'N_n_fun$' ) > 'N_a_n_vec_fun$' ).

tff('prod$b',type,
    'prod$b': ( 'Nat_ennreal_fun$' * 'Nat_set$' ) > 'Ennreal$' ).

tff('sum$n',type,
    'sum$n': ( 'A_a_fun$' * 'A_set$' ) > 'A$' ).

tff('vee$',type,
    'vee$': ( 'A_n_vec_n_vec$' * 'A_n_vec$' * 'N$' ) > 'N_n_a_fun_fun$' ).

tff('plus$b',type,
    'plus$b': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).

tff('fun_app$u',type,
    'fun_app$u': ( 'A_bool_fun$' * 'A$' ) > $o ).

tff('finite$m',type,
    'finite$m': 'N_nat_prod_set$' > $o ).

tff('uvl$',type,
    'uvl$': 'N_n_fun_set$' > 'N_n_fun_bool_fun$' ).

tff('vec_lambda$c',type,
    'vec_lambda$c': 'N_a_n_vec_n_vec_fun$' > 'A_n_vec_n_vec_n_vec$' ).

tff('set_of_vector$e',type,
    'set_of_vector$e': 'Nat_n_vec$' > 'Nat_set$' ).

tff('uvr$',type,
    'uvr$': ( 'A$' * 'Nat_a_fun$' ) > 'Nat_a_fun$' ).

tff('top$v',type,
    'top$v': 'N_n_sum_set$' ).

tff('transpose_row$b',type,
    'transpose_row$b': 'A_n_vec_n_vec_n_vec$' > 'N_a_n_vec_n_vec_fun$' ).

tff('uyo$',type,
    'uyo$': 'N_n_n_fun_a_fun_fun$' > 'N_n_fun_n_a_fun_fun$' ).

tff('trace$a',type,
    'trace$a': 'A_n_n_fun_vec_n_n_fun_vec$' > 'A$' ).

tff('map_matrix$h',type,
    'map_matrix$h': ( 'A_n_vec_n_vec_a_fun$' * 'A_n_vec_n_vec_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).

tff('uwc$',type,
    'uwc$': 'A_bool_fun$' ).

tff('top$w',type,
    'top$w': 'Nat_option_set$' ).

tff('sum$a',type,
    'sum$a': ( 'N_a_fun$' * 'N_set$' ) > 'A$' ).

tff('vaf$',type,
    'vaf$': ( 'A_n_vec_n_vec$' * 'N$' * 'A$' ) > 'N_n_a_fun_fun$' ).

tff('span$',type,
    'span$': ( 'A_a_n_vec_a_n_vec_fun_fun$' * 'A_n_vec_set$' ) > 'A_n_vec_set$' ).

tff('linear$b',type,
    'linear$b': ( 'A_a_n_vec_a_n_vec_fun_fun$' * 'A_a_a_fun_fun$' * 'A_n_vec_a_fun$' ) > $o ).

tff('fun_app$ay',type,
    'fun_app$ay': ( 'N_a_n_vec_n_vec_fun_bool_fun$' * 'N_a_n_vec_n_vec_fun$' ) > $o ).

tff('fun_app$ab',type,
    'fun_app$ab': ( 'Nat_nat_a_fun_fun$' * 'Nat$' ) > 'Nat_a_fun$' ).

tff('uud$',type,
    'uud$': 'N_a_n_vec_fun$' ).

tff('h$',type,
    'h$': 'N_a_fun$' ).

tff('vcu$',type,
    'vcu$': ( 'Nat_bool_fun$' * 'Nat_nat_fun$' ) > 'Nat_bool_fun$' ).

tff('vam$',type,
    'vam$': ( 'A_n_vec_n_vec$' * 'N$' * 'N$' ) > 'N_n_a_fun_fun$' ).

tff('uwk$',type,
    'uwk$': ( 'A_n_vec$' * 'A_n_vec$' ) > 'N_a_fun$' ).

tff('vaz$',type,
    'vaz$': 'A_a_fun$' ).

tff('fun_app$ao',type,
    'fun_app$ao': ( 'Nat_nat_nat_fun_fun$' * 'Nat$' ) > 'Nat_nat_fun$' ).

tff('det$',type,
    'det$': 'A_n_vec_n_vec_a_fun$' ).

tff('uzh$',type,
    'uzh$': ( 'Nat_n_vec_n_vec$' * 'Nat_n_vec$' * 'N$' ) > 'N_nat_fun$' ).

tff('vcp$',type,
    'vcp$': 'Nat_bool_fun$' > 'Nat_bool_fun$' ).

tff('uwl$',type,
    'uwl$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' * 'A_n_vec_a_n_vec_fun$' ) > 'N_n_a_n_vec_fun_fun$' ).

tff('top$a',type,
    'top$a': 'N_a_n_vec_n_vec_fun_set$' ).

tff('uuy$',type,
    'uuy$': 'N_a_fun_bool_fun$' ).

tff('vbw$',type,
    'vbw$': ( 'Nat_set$' * 'Nat_n_a_fun_fun$' * 'Nat_n_bool_fun_fun$' ) > 'N_a_fun$' ).

tff('coord$',type,
    'coord$': 'A_n_vec_n_vec$' > 'A_n_vec_a_n_vec_fun$' ).

tff('vdf$',type,
    'vdf$': ( 'N_a_fun$' * 'N_a_n_vec_fun$' ) > 'N_a_n_vec_fun$' ).

tff('uus$',type,
    'uus$': ( tlbool * 'N_a_fun$' * 'N_a_fun$' ) > 'N_a_fun_bool_fun$' ).

tff('vbv$',type,
    'vbv$': ( 'N_set$' * 'Nat_n_a_fun_fun$' * 'Nat_n_bool_fun_fun$' ) > 'Nat_a_fun$' ).

tff('uzi$',type,
    'uzi$': ( 'A_n_n_fun_vec_n_vec$' * 'A_n_n_fun_vec$' ) > 'N_n_n_fun_a_fun_fun$' ).

tff('fun_app$bc',type,
    'fun_app$bc': ( 'A_nat_fun$' * 'A$' ) > 'Nat$' ).

tff('vdr$',type,
    'vdr$': ( 'A_n_vec_a_n_vec_fun$' * 'A_n_vec_a_n_vec_fun$' ) > 'A_n_vec_a_n_vec_fun$' ).

tff('vcs$',type,
    'vcs$': ( 'Nat_bool_fun$' * 'Nat_bool_fun$' ) > 'Nat_bool_fun$' ).

tff('uyj$',type,
    'uyj$': ( 'Nat_nat_a_fun_fun$' * 'Nat_set$' ) > 'Nat_a_fun$' ).

tff('fun_app$av',type,
    'fun_app$av': ( 'Nat_n_bool_fun_fun$' * 'Nat$' ) > 'N_bool_fun$' ).

tff('finite$a',type,
    'finite$a': 'A_n_vec_set$' > $o ).

tff('member$d',type,
    'member$d': ( 'N_n_fun$' * 'N_n_fun_set$' ) > $o ).

tff('uve$',type,
    'uve$': 'A_n_vec_n_vec_n_vec$' > 'N_a_n_vec_fun$' ).

tff('uzv$',type,
    'uzv$': ( 'A_n_vec$' * 'A_n_vec_n_vec$' ) > 'N_a_n_vec_fun$' ).

tff('row_add$',type,
    'row_add$': ( 'A_n_vec_n_vec$' * 'N$' * 'N$' ) > 'A_a_n_vec_n_vec_fun$' ).

tff('vae$',type,
    'vae$': ( 'A_n_vec_n_vec$' * 'N$' * 'A$' ) > 'N_n_a_fun_fun$' ).

tff('ved$',type,
    'ved$': ( 'Nat_nat_fun$' * 'Nat_bool_fun$' ) > 'Nat_bool_fun$' ).

tff('map_matrix$i',type,
    'map_matrix$i': ( 'A_a_n_vec_n_vec_fun$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec_n_vec_n_vec$' ).

tff('collect$d',type,
    'collect$d': 'A_n_vec_bool_fun$' > 'A_n_vec_set$' ).

tff('uvo$',type,
    'uvo$': ( 'Nat_a_fun$' * 'A$' ) > 'Nat_a_fun$' ).

tff('y$',type,
    'y$': 'A_n_vec_n_vec$' ).

tff('vcx$',type,
    'vcx$': 'N_nat_fun$' > 'Nat_bool_fun$' ).

tff('top$aa',type,
    'top$aa': 'Nat_nat_prod_set$' ).

tff('uyv$',type,
    'uyv$': ( 'N_n_fun_n_a_fun_fun$' * 'N_n_fun_set$' ) > 'N_a_fun$' ).

tff('top$s',type,
    'top$s': 'Nat_nat_sum_set$' ).

tff('vef$',type,
    'vef$': ( 'A_n_vec_n_vec$' * 'A_n_vec$' ) > 'N_n_a_n_vec_fun_fun$' ).

tff('vdn$',type,
    'vdn$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'N_a_n_vec_fun$' ).

tff('vdm$',type,
    'vdm$': ( 'N$' * 'N_a_fun$' ) > 'N_a_fun$' ).

tff('uxi$',type,
    'uxi$': ( 'N_n_fun_a_fun$' * 'N_a_fun$' * 'N_set$' ) > 'N_n_fun_a_fun$' ).

tff('matrix_scalar_mult$',type,
    'matrix_scalar_mult$': ( 'A$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).

tff('fun_app$ai',type,
    'fun_app$ai': ( 'Nat_n_a_fun_fun$' * 'Nat$' ) > 'N_a_fun$' ).

tff('mult_row$',type,
    'mult_row$': ( 'A_n_vec_n_vec$' * 'N$' ) > 'A_a_n_vec_n_vec_fun$' ).

tff('uxj$',type,
    'uxj$': ( 'N_n_fun_a_fun$' * 'Nat_a_fun$' ) > 'N_n_fun_nat_a_fun_fun$' ).

tff('collect$a',type,
    'collect$a': 'Nat_bool_fun$' > 'Nat_set$' ).

tff('uws$',type,
    'uws$': ( 'N_a_n_vec_fun$' * 'A_n_vec$' ) > 'N_a_n_vec_fun$' ).

tff('columnvector_row$a',type,
    'columnvector_row$a': ( 'Nat_n_vec$' * 'N$' ) > 'Nat_n_vec$' ).

tff('finite$j',type,
    'finite$j': 'N_set_set$' > $o ).

tff('uvp$',type,
    'uvp$': ( 'N_n_fun_a_fun$' * 'A$' ) > 'N_n_fun_a_fun$' ).

tff('zero$',type,
    'zero$': 'A_n_vec$' ).

tff('scalar_product$d',type,
    'scalar_product$d': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec$' ).

tff('top$d',type,
    'top$d': 'N_a_fun_set$' ).

tff('vaw$',type,
    'vaw$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'N_a_n_vec_fun$' ).

tff('uut$',type,
    'uut$': ( 'A_n_vec$' * 'N_a_n_vec_n_vec_fun$' ) > 'N_a_n_vec_n_vec_fun$' ).

tff('fun_app$c',type,
    'fun_app$c': ( 'A_a_n_vec_a_n_vec_fun_fun$' * 'A$' ) > 'A_n_vec_a_n_vec_fun$' ).

tff('uzk$',type,
    'uzk$': ( 'A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'N_n_a_n_vec_fun_fun$' ).

tff('fun_app$aq',type,
    'fun_app$aq': ( 'Int_int_fun$' * $int ) > $int ).

tff('vdv$',type,
    'vdv$': 'A_n_vec_a_n_vec_fun$' ).

tff('vbx$',type,
    'vbx$': ( 'Nat_set$' * 'N_nat_bool_fun_fun$' ) > 'N_nat_bool_fun_fun$' ).

tff('vbs$',type,
    'vbs$': 'Nat_n_a_n_vec_fun_fun$' > 'N_nat_a_n_vec_fun_fun$' ).

tff('times$j',type,
    'times$j': ( 'N_a_fun_set$' * 'N_a_fun_set$' ) > 'N_a_fun_set$' ).

tff('fun_app$m',type,
    'fun_app$m': ( 'Nat_bool_fun$' * 'Nat$' ) > $o ).

tff('uum$',type,
    'uum$': 'N_a_fun$' > 'N_a_fun_bool_fun$' ).

tff('mult_row_row$',type,
    'mult_row_row$': ( 'A_n_vec_n_vec$' * 'N$' * 'A$' ) > 'N_a_n_vec_fun$' ).

tff('collect$c',type,
    'collect$c': 'N_a_fun_bool_fun$' > 'N_a_fun_set$' ).

tff('vec_nth$e',type,
    'vec_nth$e': ( 'Nat_n_vec_n_vec$' * 'N$' ) > 'Nat_n_vec$' ).

tff('matrix_vector_mult$c',type,
    'matrix_vector_mult$c': ( 'A_n_vec_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$' ) > 'A_n_vec_n_vec_n_vec$' ).

tff('collect$f',type,
    'collect$f': 'N_n_fun_bool_fun$' > 'N_n_fun_set$' ).

tff('prod$a',type,
    'prod$a': ( 'N_a_n_vec_fun$' * 'N_set$' ) > 'A_n_vec$' ).

tff('uxe$',type,
    'uxe$': ( 'N_a_fun$' * 'N_n_fun_a_fun$' * 'N_n_fun_set$' ) > 'N_a_fun$' ).

tff('val$',type,
    'val$': ( 'A_n_vec_n_vec$' * 'N$' * 'N$' ) > 'N_n_a_fun_fun$' ).

tff('member$a',type,
    'member$a': ( 'Nat$' * 'Nat_set$' ) > $o ).

tff('top$m',type,
    'top$m': 'N_n_fun_bool_fun$' ).

tff('uwa$',type,
    'uwa$': 'N_a_n_vec_fun_bool_fun$' ).

tff('uwh$',type,
    'uwh$': ( 'A_n_n_fun_vec$' * 'A_n_n_fun_vec$' ) > 'N_n_fun_a_fun$' ).

tff('times$c',type,
    'times$c': 'Nat_nat_nat_fun_fun$' ).

tff('vbj$',type,
    'vbj$': ( 'N$' * 'A_n_vec$' * 'A_n_vec_n_vec$' ) > 'N_a_n_vec_fun$' ).

tff('matrix_vector_mult$',type,
    'matrix_vector_mult$': 'A_n_vec_n_vec$' > 'A_n_vec_a_n_vec_fun$' ).

tff('uun$',type,
    'uun$': ( 'Nat_a_fun$' * 'A_n_vec$' ) > 'Nat_a_n_vec_fun$' ).

tff('vbd$',type,
    'vbd$': ( 'N_a_n_vec_a_n_vec_fun_fun$' * 'A_n_vec$' ) > 'N_a_n_vec_fun$' ).

tff('fun_app$q',type,
    'fun_app$q': ( 'Nat_nat_fun_bool_fun$' * 'Nat_nat_fun$' ) > $o ).

tff('columnvector_row$',type,
    'columnvector_row$': 'A_n_vec_n_vec_n_vec$' > 'N_a_n_vec_n_vec_n_vec_fun$' ).

tff('matrix_change_of_basis$',type,
    'matrix_change_of_basis$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).

tff('zero$a',type,
    'zero$a': 'A$' ).

tff('uwt$',type,
    'uwt$': ( 'N_a_fun$' * 'N_a_fun$' ) > 'N_n_a_fun_fun$' ).

tff('cart_basis$',type,
    'cart_basis$': 'A_n_vec_n_vec$' ).

tff('vay$',type,
    'vay$': ( 'A_n_vec_a_fun$' * 'A_n_vec$' ) > 'A_n_vec_a_n_vec_fun$' ).

tff('fun_app$y',type,
    'fun_app$y': ( 'N_n_fun$' * 'N$' ) > 'N$' ).

tff('finite$c',type,
    'finite$c': 'Nat_nat_sum_set$' > $o ).

tff('less$a',type,
    'less$a': ( 'N_set$' * 'N_set$' ) > $o ).

tff('uxh$',type,
    'uxh$': ( 'N_n_fun_a_fun$' * 'N_a_fun$' ) > 'N_n_fun_n_a_fun_fun$' ).

tff('comp$',type,
    'comp$': ( 'A_n_vec_a_fun$' * 'N_a_n_vec_fun$' ) > 'N_a_fun$' ).

tff('vbf$',type,
    'vbf$': ( 'A_n_vec_a_n_vec_fun$' * 'N_a_n_vec_fun$' ) > 'N_a_n_vec_fun$' ).

tff('x$a',type,
    'x$a': 'N$' ).

tff('uuk$',type,
    'uuk$': 'N_a_n_vec_fun$' > 'N_n_a_fun_fun$' ).

tff('vector_scalar_mult$c',type,
    'vector_scalar_mult$c': ( 'Nat$' * 'Nat_n_vec$' ) > 'Nat_n_vec$' ).

tff('uuj$',type,
    'uuj$': 'N_a_n_vec_n_vec_fun$' > 'N_n_a_n_vec_fun_fun$' ).

tff('vdg$',type,
    'vdg$': ( 'N$' * 'N$' * 'A_n_vec_n_vec$' * 'A$' ) > 'N_a_n_vec_fun$' ).

tff('fun_app$an',type,
    'fun_app$an': ( 'N_n_a_set_fun_fun$' * 'N$' ) > 'N_a_set_fun$' ).

tff('scalar_product$c',type,
    'scalar_product$c': ( 'A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).

tff('uyx$',type,
    'uyx$': 'N_n_fun_nat_a_fun_fun$' > 'Nat_n_n_fun_a_fun_fun$' ).

tff('uxv$',type,
    'uxv$': ( 'N_n_a_fun_fun$' * 'N_set$' ) > 'N_a_fun$' ).

tff('vdx$',type,
    'vdx$': ( 'A_n_vec_n_vec$' * 'N$' * 'N$' * 'A$' ) > 'N_n_a_fun_fun$' ).

tff('vec$b',type,
    'vec$b': 'A_n_vec$' > 'A_n_vec_n_vec$' ).

tff('times$',type,
    'times$': 'A_a_a_fun_fun$' ).

tff('times$e',type,
    'times$e': ( 'A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$' ) > 'A_n_vec_n_vec_n_vec$' ).

tff('columnvector_row$c',type,
    'columnvector_row$c': 'A_n_vec$' > 'N_a_n_vec_fun$' ).

tff('times$p',type,
    'times$p': ( 'Nat_set_set$' * 'Nat_set_set$' ) > 'Nat_set_set$' ).

tff('times$n',type,
    'times$n': ( 'A_set$' * 'A_set$' ) > 'A_set$' ).

tff('uwm$',type,
    'uwm$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'N_n_a_n_vec_fun_fun$' ).

tff('sum$c',type,
    'sum$c': ( 'N_n_fun_a_fun$' * 'N_n_fun_set$' ) > 'A$' ).

tff('interchange_columns_row$',type,
    'interchange_columns_row$': ( 'A_n_vec_n_vec$' * 'N$' ) > 'N_n_a_n_vec_fun_fun$' ).

tff('fun_app$j',type,
    'fun_app$j': ( 'A_n_vec_a_fun$' * 'A_n_vec$' ) > 'A$' ).

tff('less$',type,
    'less$': ( 'Ennreal$' * 'Ennreal$' ) > $o ).

tff('top$',type,
    'top$': 'N_set$' ).

tff('vcc$',type,
    'vcc$': ( 'N_set$' * 'N_n_bool_fun_fun$' ) > 'N_n_bool_fun_fun$' ).

tff('map_matrix$a',type,
    'map_matrix$a': ( 'A_a_n_vec_fun$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec_n_vec$' ).

tff('collect$h',type,
    'collect$h': 'A_n_vec_n_vec_bool_fun$' > 'A_n_vec_n_vec_set$' ).

tff('times$a',type,
    'times$a': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).

tff('uup$',type,
    'uup$': ( 'N_a_fun$' * 'A_n_vec$' ) > 'N_a_n_vec_fun$' ).

tff('uwu$',type,
    'uwu$': ( 'N_a_fun$' * 'N_a_fun$' * 'N_set$' ) > 'N_a_fun$' ).

tff('uzo$',type,
    'uzo$': 'A_n_vec$' > 'A_a_n_vec_fun$' ).

tff('vde$',type,
    'vde$': ( 'N_set$' * 'N_a_set_fun$' ) > 'A_bool_fun$' ).

tff('fun_app$z',type,
    'fun_app$z': ( 'N_n_a_n_vec_fun_fun$' * 'N$' ) > 'N_a_n_vec_fun$' ).

tff('times$o',type,
    'times$o': ( 'A_set_set$' * 'A_set_set$' ) > 'A_set_set$' ).

tff('of_nat$',type,
    'of_nat$': 'Nat$' > $int ).

tff('top$j',type,
    'top$j': 'N_n_fun_set$' ).

tff('finite$f',type,
    'finite$f': 'N_n_sum_set$' > $o ).

tff('uvw$',type,
    'uvw$': ( 'A_n_vec_n_vec$' * 'N_a_fun$' ) > 'N_a_n_vec_fun$' ).

tff('fun_app$ba',type,
    'fun_app$ba': ( 'N_a_n_vec_n_vec_bool_fun_fun$' * 'N$' ) > 'A_n_vec_n_vec_bool_fun$' ).

tff('columnvector_row$b',type,
    'columnvector_row$b': 'A_n_vec_n_vec$' > 'N_a_n_vec_n_vec_fun$' ).

tff('vac$',type,
    'vac$': ( 'A_n_vec_n_vec$' * 'A_n_vec$' ) > 'N_a_n_vec_fun$' ).

tff('fun_app$bh',type,
    'fun_app$bh': ( 'Nat_a_set_fun$' * 'Nat$' ) > 'A_set$' ).

tff('finite$k',type,
    'finite$k': 'Nat_nat_prod_set$' > $o ).

tff('uxr$',type,
    'uxr$': 'A_n_vec_n_vec_n_vec$' > 'A_n_vec_n_vec_bool_fun$' ).

tff('vaj$',type,
    'vaj$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'N_a_n_vec_fun$' ).

tff('mat_row$a',type,
    'mat_row$a': 'A$' > 'N_a_n_vec_fun$' ).

tff('fun_app$bg',type,
    'fun_app$bg': ( 'Nat_n_fun$' * 'Nat$' ) > 'N$' ).

tff('map_matrix$d',type,
    'map_matrix$d': ( 'A_nat_fun$' * 'A_n_vec_n_vec$' ) > 'Nat_n_vec_n_vec$' ).

tff('sum$b',type,
    'sum$b': ( 'N_a_n_vec_n_vec_fun$' * 'N_set$' ) > 'A_n_vec_n_vec$' ).

tff('uub$',type,
    'uub$': 'N_a_n_vec_fun$' ).

tff('vdt$',type,
    'vdt$': ( 'N_a_n_vec_fun$' * 'N_bool_fun$' ) > 'N_a_n_vec_fun$' ).

tff('vec_nth$a',type,
    'vec_nth$a': 'A_n_vec$' > 'N_a_fun$' ).

tff('uzg$',type,
    'uzg$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'N_n_a_fun_fun$' ).

tff('veb$',type,
    'veb$': 'Nat_nat_bool_fun_fun$' ).

tff('vec_nth$c',type,
    'vec_nth$c': 'A_n_vec_n_vec_n_vec_n_vec$' > 'N_a_n_vec_n_vec_n_vec_fun$' ).

tff('vdq$',type,
    'vdq$': ( 'N_a_fun$' * 'N_a_fun$' ) > 'N_a_fun$' ).

tff('vector_scalar_mult$b',type,
    'vector_scalar_mult$b': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$' ) > 'A_n_vec_n_vec_n_vec$' ).

tff('fun_app$am',type,
    'fun_app$am': ( 'N_a_set_fun$' * 'N$' ) > 'A_set$' ).

tff('vec_nth$',type,
    'vec_nth$': 'A_n_vec_n_vec$' > 'N_a_n_vec_fun$' ).

tff('vah$',type,
    'vah$': ( 'N$' * 'A_n_vec_n_vec$' ) > 'N_a_fun$' ).

tff('vdo$',type,
    'vdo$': ( 'A_n_vec$' * 'A_n_vec$' ) > 'N_a_fun$' ).

tff('vba$',type,
    'vba$': ( 'A_n_vec_a_n_vec_fun$' * 'A$' ) > 'A_n_vec_a_n_vec_fun$' ).

tff('prod$c',type,
    'prod$c': ( 'Nat_nat_fun$' * 'Nat_set$' ) > 'Nat$' ).

tff('vdp$',type,
    'vdp$': ( 'N_a_n_vec_fun$' * 'N_a_n_vec_fun$' ) > 'N_a_n_vec_fun$' ).

tff('fun_app$ak',type,
    'fun_app$ak': ( 'N_n_fun_n_a_fun_fun$' * 'N_n_fun$' ) > 'N_a_fun$' ).

tff('uxm$',type,
    'uxm$': ( 'N_n_fun_a_fun$' * 'N_n_fun_a_fun$' * 'N_n_fun_set$' ) > 'N_n_fun_a_fun$' ).

tff('finite$b',type,
    'finite$b': 'Nat_set$' > $o ).

tff('member$i',type,
    'member$i': ( 'N_nat_fun$' * 'N_nat_fun_set$' ) > $o ).

tff('vbr$',type,
    'vbr$': ( 'N_set$' * 'Nat_n_a_n_vec_fun_fun$' * 'Nat_n_bool_fun_fun$' ) > 'Nat_a_n_vec_fun$' ).

tff('g$',type,
    'g$': 'N_a_fun$' ).

tff('linear$',type,
    'linear$': ( 'A_a_n_vec_a_n_vec_fun_fun$' * 'A_a_n_vec_a_n_vec_fun_fun$' * 'A_n_vec_a_n_vec_fun$' ) > $o ).

tff('fun_app$bl',type,
    'fun_app$bl': ( 'Int_bool_fun$' * $int ) > $o ).

tff('uxt$',type,
    'uxt$': 'A_n_vec_n_vec$' > 'A_n_vec_bool_fun$' ).

tff('times$f',type,
    'times$f': ( 'Nat_n_vec$' * 'Nat_n_vec$' ) > 'Nat_n_vec$' ).

tff('fun_app$ar',type,
    'fun_app$ar': ( 'N_n_fun_a_n_vec_fun$' * 'N_n_fun$' ) > 'A_n_vec$' ).

tff('vcl$',type,
    'vcl$': ( 'N$' * 'N_n_a_n_vec_fun_fun$' * 'N_a_n_vec_fun$' ) > 'N_n_a_n_vec_fun_fun$' ).

tff('fun_app$v',type,
    'fun_app$v': ( 'Nat_nat_fun$' * 'Nat$' ) > 'Nat$' ).

tff('vec_nth$m',type,
    'vec_nth$m': 'A_n_vec_n_n_fun_vec$' > 'N_n_fun_a_n_vec_fun$' ).

tff('finite$e',type,
    'finite$e': 'N_nat_sum_set$' > $o ).

tff('vdh$',type,
    'vdh$': 'N_a_n_vec_fun$' ).

tff('map_matrix$g',type,
    'map_matrix$g': ( 'A_n_vec_a_n_vec_fun$' * 'A_n_vec_n_vec_n_vec$' ) > 'A_n_vec_n_vec_n_vec$' ).

tff('top$f',type,
    'top$f': 'A_set$' ).

tff('fun_app$ah',type,
    'fun_app$ah': ( 'N_nat_a_fun_fun$' * 'N$' ) > 'Nat_a_fun$' ).

tff('uyy$',type,
    'uyy$': ( 'N_n_fun_nat_a_fun_fun$' * 'N_n_fun_set$' ) > 'Nat_a_fun$' ).

tff('uww$',type,
    'uww$': ( 'N_a_n_vec_fun$' * 'N_a_n_vec_fun$' * 'N_set$' ) > 'N_a_n_vec_fun$' ).

tff('vec$',type,
    'vec$': 'Nat_nat_fun$' > 'Nat_bool_fun$' ).

tff('transpose_row$c',type,
    'transpose_row$c': 'A_n_vec_n_vec$' > 'N_a_n_vec_fun$' ).

tff('vbk$',type,
    'vbk$': ( 'A$' * 'A_n_vec_n_vec$' ) > 'N_n_a_fun_fun$' ).

tff('span$a',type,
    'span$a': ( 'A_a_a_fun_fun$' * 'A_set$' ) > 'A_set$' ).

tff('uwj$',type,
    'uwj$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'N_a_n_vec_fun$' ).

tff('sum$q',type,
    'sum$q': ( 'Nat_nat_set_fun$' * 'Nat_set$' ) > 'Nat_set$' ).

tff('fun_app$ac',type,
    'fun_app$ac': ( 'N_n_fun_nat_a_fun_fun$' * 'N_n_fun$' ) > 'Nat_a_fun$' ).

tff('uxp$',type,
    'uxp$': 'N_n_fun_n_vec$' > 'N_n_fun_bool_fun$' ).

tff('top$ab',type,
    'top$ab': 'Nat_n_prod_set$' ).

tff('uya$',type,
    'uya$': ( 'N_n_a_n_vec_fun_fun$' * 'N_set$' ) > 'N_a_n_vec_fun$' ).

tff('vdy$',type,
    'vdy$': 'A_a_fun$' ).

tff('uxa$',type,
    'uxa$': ( 'Nat_a_fun$' * 'N_a_fun$' * 'N_set$' ) > 'Nat_a_fun$' ).

tff('vak$',type,
    'vak$': ( 'A_n_vec_n_vec$' * 'N$' * 'A$' ) > 'N_a_n_vec_fun$' ).

tff('prod$',type,
    'prod$': ( 'N_a_fun$' * 'N_set$' ) > 'A$' ).

tff('uyi$',type,
    'uyi$': 'Nat_nat_a_fun_fun$' > 'Nat_nat_a_fun_fun$' ).

tff('uyp$',type,
    'uyp$': ( 'N_n_n_fun_a_fun_fun$' * 'N_set$' ) > 'N_n_fun_a_fun$' ).

tff('mat_row$',type,
    'mat_row$': 'A_n_vec$' > 'N_a_n_vec_n_vec_fun$' ).

tff('uzn$',type,
    'uzn$': 'A_n_vec$' > 'A_n_vec_a_n_vec_fun$' ).

tff('vcy$',type,
    'vcy$': ( 'N_set$' * 'N_set$' * 'N_n_a_n_vec_fun_fun$' * 'N_a_n_vec_fun$' ) > 'N_a_n_vec_fun$' ).

tff('uua$',type,
    'uua$': 'N_a_fun_bool_fun$' ).

tff('uzy$',type,
    'uzy$': ( 'N_a_n_vec_fun$' * 'N_set$' ) > 'N_a_fun$' ).

tff('vbn$',type,
    'vbn$': ( 'N_n_a_n_vec_fun_fun$' * 'N_n_fun$' ) > 'N_a_n_vec_fun$' ).

tff('veg$',type,
    'veg$': ( 'A_n_vec_n_vec$' * 'A_n_vec$' ) > 'N_a_fun$' ).

tff('fun_app$w',type,
    'fun_app$w': ( 'A_n_vec_n_vec_a_fun$' * 'A_n_vec_n_vec$' ) > 'A$' ).

tff('fun_app$au',type,
    'fun_app$au': ( 'N_a_n_vec_set_fun$' * 'N$' ) > 'A_n_vec_set$' ).

tff(tltrue,type,
    tltrue: tlbool ).

tff('uxc$',type,
    'uxc$': ( 'Nat_a_fun$' * 'Nat_a_fun$' * 'Nat_set$' ) > 'Nat_a_fun$' ).

tff('finite$l',type,
    'finite$l': 'Nat_n_prod_set$' > $o ).

tff('uvh$',type,
    'uvh$': 'N_a_fun_set$' > 'N_a_fun_bool_fun$' ).

tff('vdc$',type,
    'vdc$': ( 'Nat_set$' * 'Nat_nat_set_fun$' ) > 'Nat_bool_fun$' ).

tff('comp$d',type,
    'comp$d': ( 'A_n_vec_a_n_vec_fun$' * 'N_a_n_vec_fun$' ) > 'N_a_n_vec_fun$' ).

tff('vector_scalar_mult$a',type,
    'vector_scalar_mult$a': ( 'A_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).

tff('vec_lambda$',type,
    'vec_lambda$': 'N_a_fun$' > 'A_n_vec$' ).

tff('times$d',type,
    'times$d': $int > 'Int_int_fun$' ).

tff('matrix$',type,
    'matrix$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' * 'A_n_vec_a_n_vec_fun$' ) > 'A_n_vec_n_vec$' ).

tff('map_matrix$',type,
    'map_matrix$': ( 'A_a_fun$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).

tff('map_matrix$e',type,
    'map_matrix$e': ( 'Nat_a_n_vec_fun$' * 'Nat_n_vec_n_vec$' ) > 'A_n_vec_n_vec_n_vec$' ).

tff('top$x',type,
    'top$x': 'N_option_set$' ).

tff('vbe$',type,
    'vbe$': ( 'N_set$' * 'N_a_n_vec_a_n_vec_fun_fun$' ) > 'A_n_vec_a_n_vec_fun$' ).

tff('fun_app$x',type,
    'fun_app$x': ( 'A_n_vec_n_vec_bool_fun$' * 'A_n_vec_n_vec$' ) > $o ).

tff('x$',type,
    'x$': 'A_n_vec_n_vec$' ).

tff('uzq$',type,
    'uzq$': ( 'A_n_vec_n_vec$' * 'N_a_n_vec_fun$' ) > 'N_a_n_vec_fun$' ).

tff('vag$',type,
    'vag$': 'A_n_vec_n_vec$' > 'N_a_n_vec_fun$' ).

tff('fun_app$bj',type,
    'fun_app$bj': ( 'A_n_vec_a_n_vec_bool_fun_fun$' * 'A_n_vec$' ) > 'A_n_vec_bool_fun$' ).

tff('uyd$',type,
    'uyd$': ( 'N_nat_a_fun_fun$' * 'N_set$' ) > 'Nat_a_fun$' ).

tff('uvb$',type,
    'uvb$': 'Nat_n_vec_n_vec$' > 'N_nat_fun$' ).

tff('linear$c',type,
    'linear$c': ( 'A_a_a_fun_fun$' * 'A_a_n_vec_a_n_vec_fun_fun$' * 'A_a_n_vec_fun$' ) > $o ).

tff('top$c',type,
    'top$c': 'N_a_n_vec_fun_set$' ).

tff('set_of_vector$f',type,
    'set_of_vector$f': 'A_n_vec$' > 'A_set$' ).

tff('uwz$',type,
    'uwz$': ( 'Nat_a_fun$' * 'N_a_fun$' ) > 'Nat_n_a_fun_fun$' ).

tff('sum$j',type,
    'sum$j': ( 'N_a_n_vec_set_fun$' * 'N_set$' ) > 'A_n_vec_set$' ).

tff('vcv$',type,
    'vcv$': ( 'Nat_bool_fun$' * 'Nat_bool_fun$' * 'Nat_nat_nat_fun_fun$' ) > 'Nat_bool_fun$' ).

tff('trace$d',type,
    'trace$d': 'A_n_vec_n_vec_a_fun$' ).

tff('sum$i',type,
    'sum$i': ( 'N_a_n_vec_n_vec_n_vec_fun$' * 'N_set$' ) > 'A_n_vec_n_vec_n_vec$' ).

tff('collect$e',type,
    'collect$e': 'A_bool_fun$' > 'A_set$' ).

tff('uxq$',type,
    'uxq$': 'Nat_nat_fun_n_vec$' > 'Nat_nat_fun_bool_fun$' ).

tff('vbi$',type,
    'vbi$': ( 'A_n_vec$' * 'A_n_vec_n_vec$' ) > 'N_a_n_vec_fun$' ).

tff('uvj$',type,
    'uvj$': 'A_n_vec_set$' > 'A_n_vec_bool_fun$' ).

tff('fun_app$at',type,
    'fun_app$at': ( 'Nat_nat_set_fun$' * 'Nat$' ) > 'Nat_set$' ).

tff('vbt$',type,
    'vbt$': ( 'Nat_set$' * 'Nat_n_bool_fun_fun$' ) > 'N_nat_bool_fun_fun$' ).

tff('row_add_row$',type,
    'row_add_row$': ( 'A_n_vec_n_vec$' * 'N$' * 'N$' * 'A$' ) > 'N_a_n_vec_fun$' ).

tff('vds$',type,
    'vds$': ( 'N_set$' * 'N_bool_fun$' ) > 'N_bool_fun$' ).

tff('vbu$',type,
    'vbu$': ( 'Nat_set$' * 'Nat_n_a_n_vec_fun_fun$' * 'Nat_n_bool_fun_fun$' ) > 'N_a_n_vec_fun$' ).

tff('vce$',type,
    'vce$': ( 'N_set$' * 'N_n_bool_fun_fun$' ) > 'N_n_bool_fun_fun$' ).

tff('uuc$',type,
    'uuc$': 'N$' > 'N_a_fun_bool_fun$' ).

tff('uyc$',type,
    'uyc$': 'N_nat_a_fun_fun$' > 'Nat_n_a_fun_fun$' ).

tff('fun_app$b',type,
    'fun_app$b': ( 'A_n_vec_a_n_vec_fun$' * 'A_n_vec$' ) > 'A_n_vec$' ).

tff('uxn$',type,
    'uxn$': 'A_n_vec_n_vec$' > 'A_n_vec_bool_fun$' ).

tff('finite$d',type,
    'finite$d': 'Nat_n_sum_set$' > $o ).

tff('vbg$',type,
    'vbg$': ( 'N$' * 'A$' * 'N_a_n_vec_fun$' * 'N_a_n_vec_fun$' ) > 'N_a_n_vec_fun$' ).

tff('uur$',type,
    'uur$': 'A_n_vec_a_fun$' > 'N_a_n_vec_fun$' ).

tff('uxx$',type,
    'uxx$': ( 'N_n_a_fun_fun$' * 'N_set$' ) > 'N_a_fun$' ).

tff('top$n',type,
    'top$n': 'Nat_nat_fun_set$' ).

tff('w$',type,
    'w$': 'N_a_fun$' ).

tff('uxy$',type,
    'uxy$': ( 'N_n_a_n_vec_fun_fun$' * 'N_set$' ) > 'N_a_n_vec_fun$' ).

tff('fun_app$s',type,
    'fun_app$s': ( 'N_n_fun_bool_fun$' * 'N_n_fun$' ) > $o ).

tff('fun_app$as',type,
    'fun_app$as': ( 'N_a_n_vec_bool_fun_fun$' * 'N$' ) > 'A_n_vec_bool_fun$' ).

tff('vec_nth$d',type,
    'vec_nth$d': 'Nat_n_vec$' > 'N_nat_fun$' ).

tff('uzp$',type,
    'uzp$': 'A$' > 'A_a_fun$' ).

tff('uwf$',type,
    'uwf$': ( 'Int_n_vec$' * 'Int_n_vec$' ) > 'N_int_fun$' ).

tff('vec_nth$i',type,
    'vec_nth$i': ( 'N_n_fun_n_vec$' * 'N$' ) > 'N_n_fun$' ).

tff('uxw$',type,
    'uxw$': 'N_n_a_fun_fun$' > 'N_n_a_fun_fun$' ).

tff('top$h',type,
    'top$h': $o ).

tff('set_of_vector$c',type,
    'set_of_vector$c': 'Nat_nat_fun_n_vec$' > 'Nat_nat_fun_set$' ).

tff('row$',type,
    'row$': ( 'N$' * 'A_n_vec_n_vec$' ) > 'A_n_vec$' ).

tff('uxs$',type,
    'uxs$': 'Nat_n_vec$' > 'Nat_bool_fun$' ).

tff('uvi$',type,
    'uvi$': 'N_set$' > 'N_bool_fun$' ).

tff('sum$p',type,
    'sum$p': ( 'Nat_ennreal_fun$' * 'Nat_set$' ) > 'Ennreal$' ).

tff('uzw$',type,
    'uzw$': ( 'A$' * 'A_n_vec$' ) > 'N_a_fun$' ).

tff('uyr$',type,
    'uyr$': 'Nat_n_n_fun_a_fun_fun$' > 'N_n_fun_nat_a_fun_fun$' ).

tff('uzs$',type,
    'uzs$': ( 'A_n_vec_n_vec$' * 'A_n_vec$' ) > 'N_a_fun$' ).

tff('top$b',type,
    'top$b': 'N_nat_fun_set$' ).

tff('uuo$',type,
    'uuo$': ( 'N_n_fun_a_fun$' * 'A_n_vec$' ) > 'N_n_fun_a_n_vec_fun$' ).

tff('vector_matrix_mult$c',type,
    'vector_matrix_mult$c': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).

tff('vdi$',type,
    'vdi$': 'N_a_fun$' ).

tff('fun_app$i',type,
    'fun_app$i': ( 'N_n_fun_a_fun$' * 'N_n_fun$' ) > 'A$' ).

tff('var$',type,
    'var$': ( 'N$' * 'A_n_vec_n_vec$' * 'A_n_vec$' ) > 'N_a_n_vec_fun$' ).

tff('vav$',type,
    'vav$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'N_n_a_n_vec_fun_fun$' ).

tff('matrix_vector_mult$b',type,
    'matrix_vector_mult$b': ( 'A_n_n_fun_vec_n_vec$' * 'A_n_n_fun_vec$' ) > 'A_n_vec$' ).

tff('vbq$',type,
    'vbq$': ( 'N_set$' * 'Nat_n_bool_fun_fun$' ) > 'Nat_n_bool_fun_fun$' ).

tff('uwn$',type,
    'uwn$': ( 'A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$' * 'N$' ) > 'N_n_a_n_vec_fun_fun$' ).

tff('mat_mult_row$a',type,
    'mat_mult_row$a': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'N_a_n_vec_fun$' ).

tff('vai$',type,
    'vai$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'N_n_a_fun_fun$' ).

tff('uvu$',type,
    'uvu$': 'A_n_vec_a_fun$' > 'A_n_vec_a_n_vec_fun$' ).

tff('vec_lambda$b',type,
    'vec_lambda$b': 'N_nat_fun$' > 'Nat_n_vec$' ).

tff('vax$',type,
    'vax$': 'A$' > 'A_a_fun$' ).

tff('uym$',type,
    'uym$': ( 'N_n_a_set_fun_fun$' * 'N_set$' ) > 'N_a_set_fun$' ).

tff('fun_app$bi',type,
    'fun_app$bi': ( 'Nat_ennreal_fun$' * 'Nat$' ) > 'Ennreal$' ).

tff('member$f',type,
    'member$f': ( 'N$' * 'N_set$' ) > $o ).

tff('column_add$',type,
    'column_add$': ( 'A_n_vec_n_vec$' * 'N$' * 'N$' ) > 'A_a_n_vec_n_vec_fun$' ).

tff('uvs$',type,
    'uvs$': ( 'A$' * 'N_n_fun_a_fun$' ) > 'N_n_fun_a_fun$' ).

tff('vdd$',type,
    'vdd$': ( 'N_set$' * 'N_a_n_vec_set_fun$' ) > 'A_n_vec_bool_fun$' ).

tff('fun_app$bk',type,
    'fun_app$bk': ( 'A_a_bool_fun_fun$' * 'A$' ) > 'A_bool_fun$' ).

tff('divide$',type,
    'divide$': 'A$' > 'A_a_fun$' ).

tff('vec_nth$j',type,
    'vec_nth$j': 'N_n_vec$' > 'N_n_fun$' ).

tff('f$',type,
    'f$': 'N_a_fun$' ).

tff('uuh$',type,
    'uuh$': 'N_n_fun_a_n_vec_fun$' > 'N_n_n_fun_a_fun_fun$' ).

tff('mat_mult_row$',type,
    'mat_mult_row$': ( 'A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$' ) > 'N_a_n_vec_n_vec_fun$' ).

tff('fun_app$af',type,
    'fun_app$af': ( 'N_nat_a_n_vec_fun_fun$' * 'N$' ) > 'Nat_a_n_vec_fun$' ).

tff('member$m',type,
    'member$m': ( $int * 'Int_set$' ) > $o ).

tff('uzf$',type,
    'uzf$': ( 'A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$' ) > 'N_n_a_n_vec_fun_fun$' ).

tff('sum$m',type,
    'sum$m': ( 'N_int_fun$' * 'N_set$' ) > $int ).

tff('uuv$',type,
    'uuv$': 'N_a_fun$' > 'N_a_n_vec_fun$' ).

tff('finite$i',type,
    'finite$i': 'Nat_set_set$' > $o ).

tff('uvz$',type,
    'uvz$': 'Nat_nat_fun_bool_fun$' ).

tff('finite$',type,
    'finite$': 'N_set$' > $o ).

tff('uzr$',type,
    'uzr$': 'A_n_vec_n_vec$' > 'N_n_a_fun_fun$' ).

tff('finite$g',type,
    'finite$g': 'Nat_option_set$' > $o ).

tff('vbb$',type,
    'vbb$': 'A_n_vec_a_n_vec_fun$' ).

tff('uyf$',type,
    'uyf$': 'Nat_n_a_fun_fun$' > 'N_nat_a_fun_fun$' ).

tff('vda$',type,
    'vda$': ( 'N_set$' * 'N_n_a_n_vec_fun_fun$' * 'N_a_n_vec_fun$' ) > 'N_n_fun_a_fun$' ).

tff('vco$',type,
    'vco$': 'Nat_nat_bool_fun_fun$' > 'Nat_nat_bool_fun_fun$' ).

tff('uue$',type,
    'uue$': 'N_a_fun$' > 'N_a_n_vec_fun$' ).

tff('trace$b',type,
    'trace$b': 'A_n_vec_n_vec_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).

tff('top$ac',type,
    'top$ac': 'N_nat_prod_set$' ).

tff('matrix$a',type,
    'matrix$a': 'A_n_vec_a_n_vec_fun$' > 'A_n_vec_n_vec$' ).

tff('vcj$',type,
    'vcj$': ( 'N_set$' * 'N_n_a_fun_fun$' * 'N_n_bool_fun_fun$' ) > 'N_a_fun$' ).

tff('uzz$',type,
    'uzz$': ( 'A_n_vec_n_vec$' * 'A_n_vec$' ) > 'N_a_fun_bool_fun$' ).

tff('scalar_product$b',type,
    'scalar_product$b': ( 'A_n_n_fun_vec$' * 'A_n_n_fun_vec$' ) > 'A$' ).

tff('uva$',type,
    'uva$': 'N_a_fun_bool_fun$' ).

tff('top$i',type,
    'top$i': 'N_bool_fun$' ).

tff('uzu$',type,
    'uzu$': ( 'A_n_vec$' * 'A_n_vec_n_vec$' ) > 'N_a_fun$' ).

tff('finite$n',type,
    'finite$n': 'N_n_prod_set$' > $o ).

tff('uux$',type,
    'uux$': 'N_a_fun$' > 'N_n_a_fun_fun$' ).

tff('uvf$',type,
    'uvf$': 'A_n_vec_n_vec$' > 'N_a_fun$' ).

tff('uuw$',type,
    'uuw$': 'N_n_a_fun_fun$' ).

tff('vab$',type,
    'vab$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' * 'A_n_vec_a_n_vec_fun$' ) > 'N_a_n_vec_fun$' ).

tff('fun_app$ap',type,
    'fun_app$ap': ( 'N_int_fun$' * 'N$' ) > $int ).

tff('vdl$',type,
    'vdl$': ( 'N$' * 'N_a_n_vec_fun$' ) > 'N_a_n_vec_fun$' ).

tff('uvc$',type,
    'uvc$': 'A_n_n_fun_vec_n_n_fun_vec$' > 'N_n_fun_a_fun$' ).

tff('matrix_matrix_mult$',type,
    'matrix_matrix_mult$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).

tff('uwg$',type,
    'uwg$': ( 'Nat_n_vec$' * 'Nat_n_vec$' ) > 'N_nat_fun$' ).

tff('vcb$',type,
    'vcb$': ( 'N_set$' * 'N_nat_a_n_vec_fun_fun$' * 'N_nat_bool_fun_fun$' ) > 'Nat_a_n_vec_fun$' ).

tff('vby$',type,
    'vby$': ( 'Nat_set$' * 'N_nat_a_n_vec_fun_fun$' * 'N_nat_bool_fun_fun$' ) > 'N_a_n_vec_fun$' ).

tff('vcn$',type,
    'vcn$': ( 'Nat_bool_fun$' * 'Nat_nat_bool_fun_fun$' ) > 'Nat_bool_fun$' ).

tff('vct$',type,
    'vct$': ( 'Nat_set$' * 'Nat_nat_bool_fun_fun$' ) > 'Nat_nat_bool_fun_fun$' ).

tff('trace$',type,
    'trace$': 'Nat_n_vec_n_vec$' > 'Nat$' ).

tff('transpose$',type,
    'transpose$': 'A_n_vec_n_vec$' > 'A_n_vec_n_vec$' ).

tff('mult_column$',type,
    'mult_column$': ( 'A_n_vec_n_vec$' * 'N$' ) > 'A_a_n_vec_n_vec_fun$' ).

tff('fun_app$ad',type,
    'fun_app$ad': ( 'Nat_n_n_fun_a_fun_fun$' * 'Nat$' ) > 'N_n_fun_a_fun$' ).

tff('vcm$',type,
    'vcm$': ( 'N$' * 'N_n_a_n_vec_fun_fun$' * 'N_a_n_vec_fun$' ) > 'N_a_fun$' ).

tff('uzj$',type,
    'uzj$': ( 'A_n_vec_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$' * 'N$' ) > 'N_a_n_vec_n_vec_fun$' ).

tff('times$g',type,
    'times$g': ( 'N_a_n_vec_fun$' * 'N_a_n_vec_fun$' ) > 'N_a_n_vec_fun$' ).

tff('fun_app$h',type,
    'fun_app$h': ( 'N_nat_fun$' * 'N$' ) > 'Nat$' ).

tff('finite$h',type,
    'finite$h': 'N_option_set$' > $o ).

tff('top$o',type,
    'top$o': 'Nat_nat_fun_bool_fun$' ).

tff('vector_matrix_mult$d',type,
    'vector_matrix_mult$d': ( 'A_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec$' ).

tff('fun_app$aa',type,
    'fun_app$aa': ( 'Nat_a_fun$' * 'Nat$' ) > 'A$' ).

tff('map_matrix$f',type,
    'map_matrix$f': ( 'A_n_vec_nat_fun$' * 'A_n_vec_n_vec_n_vec$' ) > 'Nat_n_vec_n_vec$' ).

tff('uza$',type,
    'uza$': ( 'Nat_n_vec$' * 'Nat_n_vec_n_vec$' * 'N$' ) > 'N_nat_fun$' ).

tff('vector_scalar_mult$',type,
    'vector_scalar_mult$': 'A_a_n_vec_a_n_vec_fun_fun$' ).

tff('fun_app$a',type,
    'fun_app$a': ( 'N_a_n_vec_fun$' * 'N$' ) > 'A_n_vec$' ).

tff('vaq$',type,
    'vaq$': ( 'N$' * 'A_n_vec_n_vec$' * 'A_n_vec$' ) > 'N_n_a_fun_fun$' ).

tff('uyk$',type,
    'uyk$': ( 'N_n_a_set_fun_fun$' * 'N_set$' ) > 'N_a_set_fun$' ).

tff('uzc$',type,
    'uzc$': ( 'A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec_n_vec$' * 'N$' ) > 'N_a_n_vec_n_vec_fun$' ).

tff('is_basis$',type,
    'is_basis$': 'A_n_vec_set$' > $o ).

tff('uvq$',type,
    'uvq$': ( 'N_a_fun$' * 'A$' ) > 'N_a_fun$' ).

tff('power$',type,
    'power$': 'A$' > 'Nat_a_fun$' ).

tff('vec_nth$f',type,
    'vec_nth$f': 'A_n_n_fun_vec$' > 'N_n_fun_a_fun$' ).

tff('column$',type,
    'column$': ( 'N$' * 'A_n_vec_n_vec$' ) > 'A_n_vec$' ).

tff('fun_app$f',type,
    'fun_app$f': ( 'N_a_n_vec_n_vec_fun$' * 'N$' ) > 'A_n_vec_n_vec$' ).

tff('uyl$',type,
    'uyl$': 'N_n_a_set_fun_fun$' > 'N_n_a_set_fun_fun$' ).

tff('uxf$',type,
    'uxf$': ( 'Nat_a_fun$' * 'N_n_fun_a_fun$' ) > 'Nat_n_n_fun_a_fun_fun$' ).

tff('uxl$',type,
    'uxl$': ( 'N_n_fun_a_fun$' * 'N_n_fun_a_fun$' * 'N_n_fun$' ) > 'N_n_fun_a_fun$' ).

tff('finite$o',type,
    'finite$o': 'Nat_nat_fun_set$' > $o ).

tff('times$m',type,
    'times$m': ( 'A_n_vec_n_vec_set$' * 'A_n_vec_n_vec_set$' ) > 'A_n_vec_n_vec_set$' ).

tff('uvn$',type,
    'uvn$': 'Nat_set$' > 'Nat_bool_fun$' ).

tff('vci$',type,
    'vci$': ( 'N_set$' * 'N_n_a_fun_fun$' * 'N_n_bool_fun_fun$' ) > 'N_a_fun$' ).

tff('fun_app$be',type,
    'fun_app$be': ( 'A_a_n_vec_n_vec_fun$' * 'A$' ) > 'A_n_vec_n_vec$' ).

tff('uxo$',type,
    'uxo$': 'N_n_vec$' > 'N_bool_fun$' ).

tff('vdz$',type,
    'vdz$': ( 'A_n_vec_n_vec$' * 'N$' * 'N$' * 'A$' ) > 'N_a_n_vec_fun$' ).

tff('vej$',type,
    'vej$': 'A_n_vec_n_vec$' > 'N_a_n_vec_bool_fun_fun$' ).

tff('uul$',type,
    'uul$': 'N_a_fun$' > 'N_a_fun_bool_fun$' ).

tff('vbz$',type,
    'vbz$': 'N_nat_a_n_vec_fun_fun$' > 'Nat_n_a_n_vec_fun_fun$' ).

tff('uxb$',type,
    'uxb$': ( 'Nat_a_fun$' * 'Nat_a_fun$' ) > 'Nat_nat_a_fun_fun$' ).

tff('sum$k',type,
    'sum$k': ( 'N_nat_fun$' * 'N_set$' ) > 'Nat$' ).

tff('vdb$',type,
    'vdb$': ( 'N_set$' * 'N_set$' ) > 'N_n_fun_bool_fun$' ).

tff('times$i',type,
    'times$i': ( 'N_a_fun$' * 'N_a_fun$' ) > 'N_a_fun$' ).

tff('vca$',type,
    'vca$': ( 'N_set$' * 'N_nat_bool_fun_fun$' ) > 'Nat_n_bool_fun_fun$' ).

tff('matrix_vector_mult$a',type,
    'matrix_vector_mult$a': ( 'Nat_n_vec_n_vec$' * 'Nat_n_vec$' ) > 'Nat_n_vec$' ).

tff('uuz$',type,
    'uuz$': 'N_a_fun$' > 'N_n_a_fun_fun$' ).

tff('scalar_product$a',type,
    'scalar_product$a': ( 'Nat_n_vec$' * 'Nat_n_vec$' ) > 'Nat$' ).

tff('vau$',type,
    'vau$': ( 'A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$' ) > 'N_a_n_vec_n_vec_fun$' ).

tff('interchange_columns$',type,
    'interchange_columns$': ( 'A_n_vec_n_vec$' * 'N$' ) > 'N_a_n_vec_n_vec_fun$' ).

tff('fun_app$bd',type,
    'fun_app$bd': ( 'A_n_vec_nat_fun$' * 'A_n_vec$' ) > 'Nat$' ).

tff('times$q',type,
    'times$q': ( 'Int_set$' * 'Int_set$' ) > 'Int_set$' ).

tff('fun_app$bb',type,
    'fun_app$bb': ( 'N_a_bool_fun_fun$' * 'N$' ) > 'A_bool_fun$' ).

tff('member$j',type,
    'member$j': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec_set$' ) > $o ).

tff('vbm$',type,
    'vbm$': ( 'N_set$' * 'N_n_a_n_vec_fun_fun$' ) > 'N_a_n_vec_fun$' ).

tff('uze$',type,
    'uze$': ( 'A_n_vec$' * 'A_n_vec_n_vec$' ) > 'N_n_a_fun_fun$' ).

tff('fun_app$k',type,
    'fun_app$k': ( 'A_a_fun$' * 'A$' ) > 'A$' ).

tff('fun_app$n',type,
    'fun_app$n': ( 'Nat_nat_bool_fun_fun$' * 'Nat$' ) > 'Nat_bool_fun$' ).

tff('sum$d',type,
    'sum$d': ( 'Nat_a_fun$' * 'Nat_set$' ) > 'A$' ).

tff('vbo$',type,
    'vbo$': 'N_n_a_n_vec_fun_fun$' > 'N_n_fun_a_fun$' ).

tff('uwb$',type,
    'uwb$': 'N_a_fun_bool_fun$' ).

tff('uug$',type,
    'uug$': 'Nat_a_n_vec_fun$' > 'N_nat_a_fun_fun$' ).

tff('collect$',type,
    'collect$': 'N_bool_fun$' > 'N_set$' ).

tff('zero$b',type,
    'zero$b': 'A_n_vec_n_vec$' ).

tff('collect$g',type,
    'collect$g': 'Nat_nat_fun_bool_fun$' > 'Nat_nat_fun_set$' ).

tff('top$z',type,
    'top$z': 'N_set_set$' ).

tff('vad$',type,
    'vad$': ( 'A_n_vec_n_vec$' * 'A_n_vec$' ) > 'N_a_n_vec_fun$' ).

tff('uvx$',type,
    'uvx$': 'A_n_vec_bool_fun$' ).

tff('vec_nth$l',type,
    'vec_nth$l': ( 'A_n_n_fun_vec_n_vec$' * 'N$' ) > 'A_n_n_fun_vec$' ).

tff('fun_app$ax',type,
    'fun_app$ax': ( 'N_n_bool_fun_fun$' * 'N$' ) > 'N_bool_fun$' ).

tff('sum$f',type,
    'sum$f': ( 'Nat_nat_fun$' * 'Nat_set$' ) > 'Nat$' ).

tff('vbl$',type,
    'vbl$': ( 'A$' * 'A_n_vec_n_vec$' ) > 'N_a_n_vec_fun$' ).

tff('uxd$',type,
    'uxd$': ( 'N_a_fun$' * 'N_n_fun_a_fun$' ) > 'N_n_n_fun_a_fun_fun$' ).

tff('uwx$',type,
    'uwx$': ( 'N_a_fun$' * 'Nat_a_fun$' ) > 'N_nat_a_fun_fun$' ).

tff(tlfalse,type,
    tlfalse: tlbool ).

tff('uuf$',type,
    'uuf$': 'N_a_n_vec_fun$' ).

tff('map_matrix$b',type,
    'map_matrix$b': ( 'A_n_vec_a_fun$' * 'A_n_vec_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).

tff('scalar_product$',type,
    'scalar_product$': ( 'Int_n_vec$' * 'Int_n_vec$' ) > $int ).

tff('nat$',type,
    'nat$': $int > 'Nat$' ).

tff('top$l',type,
    'top$l': 'A_n_vec_bool_fun$' ).

tff('uwr$',type,
    'uwr$': ( 'N_a_n_vec_n_vec_fun$' * 'A_n_vec_n_vec$' ) > 'N_a_n_vec_n_vec_fun$' ).

tff('vaa$',type,
    'vaa$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' * 'A_n_vec_a_n_vec_fun$' ) > 'N_n_a_fun_fun$' ).

tff('vcw$',type,
    'vcw$': ( 'Nat_set$' * 'Nat_set$' * 'Nat$' ) > 'Nat_nat_fun_bool_fun$' ).

tff('fun_app$d',type,
    'fun_app$d': ( 'N_a_fun$' * 'N$' ) > 'A$' ).

tff('map_matrix$c',type,
    'map_matrix$c': ( 'Nat_a_fun$' * 'Nat_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).

tff('set_of_vector$',type,
    'set_of_vector$': 'A_n_vec_n_vec$' > 'A_n_vec_set$' ).

tff('fun_app$az',type,
    'fun_app$az': ( 'N_nat_fun_bool_fun$' * 'N_nat_fun$' ) > $o ).

tff('column_add_row$',type,
    'column_add_row$': ( 'A_n_vec_n_vec$' * 'N$' * 'N$' * 'A$' ) > 'N_a_n_vec_fun$' ).

tff('det$a',type,
    'det$a': 'A_n_vec_n_vec_n_vec$' > 'A_n_vec$' ).

tff('uwp$',type,
    'uwp$': ( 'A_n_vec_n_vec$' * 'N_a_n_vec_n_vec_fun$' ) > 'N_a_n_vec_n_vec_fun$' ).

tff('member$',type,
    'member$': ( 'A_n_vec$' * 'A_n_vec_set$' ) > $o ).

tff('uxz$',type,
    'uxz$': 'N_n_a_n_vec_fun_fun$' > 'N_n_a_n_vec_fun_fun$' ).

tff('fun_app$ae',type,
    'fun_app$ae': ( 'Nat_a_n_vec_fun$' * 'Nat$' ) > 'A_n_vec$' ).

tff('vbp$',type,
    'vbp$': 'N_set$' > 'N_n_fun_bool_fun$' ).

tff('uwi$',type,
    'uwi$': ( 'A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$' ) > 'N_a_n_vec_n_vec_fun$' ).

tff('fun_app$r',type,
    'fun_app$r': ( 'N_a_n_vec_fun_bool_fun$' * 'N_a_n_vec_fun$' ) > $o ).

tff('set_of_vector$b',type,
    'set_of_vector$b': 'N_n_fun_n_vec$' > 'N_n_fun_set$' ).

tff('uwo$',type,
    'uwo$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' * 'N$' ) > 'N_n_a_fun_fun$' ).

tff('vec_lambda$a',type,
    'vec_lambda$a': 'N_a_n_vec_fun$' > 'A_n_vec_n_vec$' ).

tff('vec_nth$b',type,
    'vec_nth$b': 'A_n_vec_n_vec_n_vec$' > 'N_a_n_vec_n_vec_fun$' ).

tff('fun_app$aw',type,
    'fun_app$aw': ( 'N_nat_bool_fun_fun$' * 'N$' ) > 'Nat_bool_fun$' ).

tff('uye$',type,
    'uye$': ( 'Nat_n_a_fun_fun$' * 'N_set$' ) > 'Nat_a_fun$' ).

tff('member$h',type,
    'member$h': ( 'N_a_n_vec_n_vec_fun$' * 'N_a_n_vec_n_vec_fun_set$' ) > $o ).

tff('uyu$',type,
    'uyu$': 'N_n_fun_n_a_fun_fun$' > 'N_n_n_fun_a_fun_fun$' ).

tff('vea$',type,
    'vea$': ( 'A_n_vec_n_vec$' * 'N$' * 'N$' * 'A$' ) > 'N_a_n_vec_fun$' ).

tff('member$c',type,
    'member$c': ( 'N_a_n_vec_fun$' * 'N_a_n_vec_fun_set$' ) > $o ).

tff('set_of_vector$d',type,
    'set_of_vector$d': 'A_n_vec_n_vec_n_vec$' > 'A_n_vec_n_vec_set$' ).

tff('veh$',type,
    'veh$': ( 'N_a_fun$' * 'A$' ) > 'N_a_fun$' ).

tff('sum$h',type,
    'sum$h': ( 'N_n_fun_a_n_vec_fun$' * 'N_n_fun_set$' ) > 'A_n_vec$' ).

tff('top$ad',type,
    'top$ad': 'N_n_prod_set$' ).

tff('vector_matrix_mult$b',type,
    'vector_matrix_mult$b': ( 'A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec_n_vec$' ) > 'A_n_vec_n_vec_n_vec$' ).

tff('uyg$',type,
    'uyg$': ( 'Nat_n_a_fun_fun$' * 'Nat_set$' ) > 'N_a_fun$' ).

tff('top$e',type,
    'top$e': 'Nat_set$' ).

tff('uyt$',type,
    'uyt$': ( 'N_n_fun_n_a_fun_fun$' * 'N_set$' ) > 'N_n_fun_a_fun$' ).

tff('times$h',type,
    'times$h': ( 'N_a_n_vec_fun_set$' * 'N_a_n_vec_fun_set$' ) > 'N_a_n_vec_fun_set$' ).

tff('vcf$',type,
    'vcf$': ( 'N_set$' * 'N_n_a_n_vec_fun_fun$' * 'N_n_bool_fun_fun$' ) > 'N_a_n_vec_fun$' ).

tff('fun_app$l',type,
    'fun_app$l': ( 'A_a_a_fun_fun$' * 'A$' ) > 'A_a_fun$' ).

tff('matrix_vector_mult$d',type,
    'matrix_vector_mult$d': ( 'A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'A_n_vec_n_vec$' ).

tff('fun_app$p',type,
    'fun_app$p': ( 'A_n_vec_bool_fun$' * 'A_n_vec$' ) > $o ).

tff('interchange_rows_row$',type,
    'interchange_rows_row$': ( 'A_n_vec_n_vec$' * 'N$' ) > 'N_n_a_n_vec_fun_fun$' ).

tff('uuu$',type,
    'uuu$': ( 'A$' * 'N_a_n_vec_fun$' ) > 'N_a_n_vec_fun$' ).

tff('uxk$',type,
    'uxk$': ( 'N_n_fun_a_fun$' * 'Nat_a_fun$' * 'Nat_set$' ) > 'N_n_fun_a_fun$' ).

tff('vector_matrix_mult$a',type,
    'vector_matrix_mult$a': ( 'A_n_n_fun_vec$' * 'A_n_vec_n_n_fun_vec$' ) > 'A_n_vec$' ).

tff('uzm$',type,
    'uzm$': 'A$' > 'A_n_vec_a_fun$' ).

tff('uys$',type,
    'uys$': ( 'Nat_n_n_fun_a_fun_fun$' * 'Nat_set$' ) > 'N_n_fun_a_fun$' ).

tff('set_of_vector$a',type,
    'set_of_vector$a': 'N_n_vec$' > 'N_set$' ).

tff('fun_app$e',type,
    'fun_app$e': ( 'N_n_a_fun_fun$' * 'N$' ) > 'N_a_fun$' ).

tff('sum$e',type,
    'sum$e': ( 'N_a_set_fun$' * 'N_set$' ) > 'A_set$' ).

tff('vcq$',type,
    'vcq$': 'N_bool_fun$' > 'N_bool_fun$' ).

tff('top$r',type,
    'top$r': 'A_bool_fun$' ).

tff('top$u',type,
    'top$u': 'N_nat_sum_set$' ).

tff('fun_app$bm',type,
    'fun_app$bm': ( 'Int_int_bool_fun_fun$' * $int ) > 'Int_bool_fun$' ).

tff('uzl$',type,
    'uzl$': ( 'A_n_vec_n_vec$' * 'A_n_vec$' ) > 'N_n_a_fun_fun$' ).

tff('top$t',type,
    'top$t': 'Nat_n_sum_set$' ).

tff('uxg$',type,
    'uxg$': ( 'Nat_a_fun$' * 'N_n_fun_a_fun$' * 'N_n_fun_set$' ) > 'Nat_a_fun$' ).

tff('fun_app$aj',type,
    'fun_app$aj': ( 'N_n_n_fun_a_fun_fun$' * 'N$' ) > 'N_n_fun_a_fun$' ).

tff('sum$g',type,
    'sum$g': ( 'Nat_a_n_vec_fun$' * 'Nat_set$' ) > 'A_n_vec$' ).

tff('vck$',type,
    'vck$': ( 'N_set$' * 'N$' * 'N_n_a_n_vec_fun_fun$' * 'N_a_n_vec_fun$' ) > 'N_a_n_vec_fun$' ).

tff('vei$',type,
    'vei$': ( 'Nat_a_fun$' * 'Nat_a_fun$' ) > 'Nat_a_fun$' ).

tff('uvy$',type,
    'uvy$': 'N_n_fun_bool_fun$' ).

tff('uwe$',type,
    'uwe$': 'N_bool_fun$' ).

tff('member$e',type,
    'member$e': ( 'N_a_fun$' * 'N_a_fun_set$' ) > $o ).

tff('uvg$',type,
    'uvg$': 'N_a_n_vec_fun_set$' > 'N_a_n_vec_fun_bool_fun$' ).

tff('member$l',type,
    'member$l': ( 'Nat_set$' * 'Nat_set_set$' ) > $o ).

tff('v$',type,
    'v$': 'A_n_vec$' ).

tff('vek$',type,
    'vek$': ( 'A_n_vec$' * 'A_n_vec_n_vec$' ) > 'N_n_a_n_vec_fun_fun$' ).

tff('top$ae',type,
    'top$ae': 'Ennreal$' ).

tff('fun_app$bf',type,
    'fun_app$bf': ( 'A_n_fun$' * 'A$' ) > 'N$' ).

tff('uvd$',type,
    'uvd$': 'A_n_vec_n_vec_n_vec_n_vec$' > 'N_a_n_vec_n_vec_fun$' ).

tff('top$k',type,
    'top$k': 'A_n_vec_set$' ).

tff('vec$a',type,
    'vec$a': 'A_a_n_vec_fun$' ).

tff('member$g',type,
    'member$g': ( 'A$' * 'A_set$' ) > $o ).

tff('top$y',type,
    'top$y': 'Nat_set_set$' ).

tff('vbh$',type,
    'vbh$': ( 'N$' * 'N_a_n_vec_fun$' * 'N_a_n_vec_fun$' ) > 'N_a_n_vec_fun$' ).

tff('times$l',type,
    'times$l': ( 'A_n_vec_set$' * 'A_n_vec_set$' ) > 'A_n_vec_set$' ).

tff('comp$b',type,
    'comp$b': ( 'A_a_n_vec_fun$' * 'N_a_fun$' ) > 'N_a_n_vec_fun$' ).

tff('sum$',type,
    'sum$': ( 'N_a_n_vec_fun$' * 'N_set$' ) > 'A_n_vec$' ).

tff('uyz$',type,
    'uyz$': ( 'A_n_vec_n_vec$' * 'A_n_vec_a_fun$' ) > 'N_a_n_vec_fun$' ).

tff('vcr$',type,
    'vcr$': ( 'Nat_bool_fun$' * 'Nat_bool_fun$' ) > 'Nat_bool_fun$' ).

tff('the$',type,
    'the$': 'N_a_fun_bool_fun$' > 'N_a_fun$' ).

tff('collect$b',type,
    'collect$b': 'N_a_n_vec_fun_bool_fun$' > 'N_a_n_vec_fun_set$' ).

tff('vec_nth$g',type,
    'vec_nth$g': ( 'A_n_n_fun_vec_n_n_fun_vec$' * 'N_n_fun$' ) > 'A_n_n_fun_vec$' ).

tff('vec_nth$h',type,
    'vec_nth$h': ( 'Nat_nat_fun_n_vec$' * 'N$' ) > 'Nat_nat_fun$' ).

tff('vdk$',type,
    'vdk$': ( 'N$' * 'N_a_fun$' ) > 'N_a_fun$' ).

tff('member$k',type,
    'member$k': ( 'A_set$' * 'A_set_set$' ) > $o ).

tff('t$',type,
    't$': 'N_n_a_fun_fun$' ).

tff('uyq$',type,
    'uyq$': ( 'Nat_n_n_fun_a_fun_fun$' * 'N_n_fun_set$' ) > 'Nat_a_fun$' ).

tff('uzd$',type,
    'uzd$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$' ) > 'N_n_a_n_vec_fun_fun$' ).

tff('fun_app$o',type,
    'fun_app$o': ( 'A_a_n_vec_fun$' * 'A$' ) > 'A_n_vec$' ).

tff('times$b',type,
    'times$b': 'A_n_vec$' > 'A_n_vec_a_n_vec_fun$' ).

tff('uwy$',type,
    'uwy$': ( 'N_a_fun$' * 'Nat_a_fun$' * 'Nat_set$' ) > 'N_a_fun$' ).

tff('transpose_row$a',type,
    'transpose_row$a': ( 'Nat_n_vec_n_vec$' * 'N$' ) > 'Nat_n_vec$' ).

tff('matrix_matrix_mult$a',type,
    'matrix_matrix_mult$a': ( 'A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$' ) > 'A_n_vec_n_vec_n_vec$' ).

tff('uxu$',type,
    'uxu$': 'A_n_vec$' > 'A_bool_fun$' ).

tff('uvt$',type,
    'uvt$': ( 'A$' * 'N_a_fun$' ) > 'N_a_fun$' ).

tff('vdj$',type,
    'vdj$': ( 'N$' * 'N_a_n_vec_fun$' ) > 'N_a_n_vec_fun$' ).

tff('times$k',type,
    'times$k': ( 'Nat_set$' * 'Nat_set$' ) > 'Nat_set$' ).

tff('trace$c',type,
    'trace$c': 'A_n_vec_n_vec_n_vec$' > 'A_n_vec$' ).

tff('uwq$',type,
    'uwq$': ( 'A_n_vec$' * 'N_a_n_vec_fun$' ) > 'N_a_n_vec_fun$' ).

tff('interchange_rows$',type,
    'interchange_rows$': ( 'A_n_vec_n_vec$' * 'N$' ) > 'N_a_n_vec_n_vec_fun$' ).

tff('uyw$',type,
    'uyw$': ( 'N_n_fun_nat_a_fun_fun$' * 'Nat_set$' ) > 'N_n_fun_a_fun$' ).

tff('uzt$',type,
    'uzt$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$' ) > 'N_a_n_vec_fun$' ).

tff('uvm$',type,
    'uvm$': 'Nat_nat_fun_set$' > 'Nat_nat_fun_bool_fun$' ).

tff('vec_nth$k',type,
    'vec_nth$k': ( 'Int_n_vec$' * 'N$' ) > $int ).

tff('vas$',type,
    'vas$': ( 'A_n_vec_n_vec$' * 'N$' ) > 'N_n_a_n_vec_fun_fun$' ).

tff('vdu$',type,
    'vdu$': ( 'N_a_fun$' * 'N_bool_fun$' ) > 'N_a_fun$' ).

tff('comp$c',type,
    'comp$c': ( 'A_a_fun$' * 'N_a_fun$' ) > 'N_a_fun$' ).

tff('zero$c',type,
    'zero$c': 'Ennreal$' ).

tff('uwv$',type,
    'uwv$': ( 'N_a_n_vec_fun$' * 'N_a_n_vec_fun$' ) > 'N_n_a_n_vec_fun_fun$' ).

tff('uvk$',type,
    'uvk$': 'A_set$' > 'A_bool_fun$' ).

tff('uyh$',type,
    'uyh$': ( 'Nat_nat_a_fun_fun$' * 'Nat_set$' ) > 'Nat_a_fun$' ).

tff('vcg$',type,
    'vcg$': ( 'Nat_set$' * 'N_nat_a_fun_fun$' * 'N_nat_bool_fun_fun$' ) > 'N_a_fun$' ).

tff('uui$',type,
    'uui$': ( 'N_a_n_vec_n_vec_n_vec_fun$' * 'N$' ) > 'N_a_n_vec_n_vec_fun$' ).

tff('top$g',type,
    'top$g': 'Nat_bool_fun$' ).

tff('vch$',type,
    'vch$': ( 'N_set$' * 'N_nat_a_fun_fun$' * 'N_nat_bool_fun_fun$' ) > 'Nat_a_fun$' ).

tff('fun_app$al',type,
    'fun_app$al': ( 'N_a_n_vec_a_n_vec_fun_fun$' * 'N$' ) > 'A_n_vec_a_n_vec_fun$' ).

tff('uu$',type,
    'uu$': 'N_a_fun$' > 'N_a_n_vec_fun$' ).

tff('fun_app$t',type,
    'fun_app$t': ( 'N_bool_fun$' * 'N$' ) > $o ).

tff('fun_app$',type,
    'fun_app$': ( 'N_a_fun_bool_fun$' * 'N_a_fun$' ) > $o ).

tff('plus$',type,
    'plus$': 'A_n_vec$' > 'A_n_vec_a_n_vec_fun$' ).

tff('vap$',type,
    'vap$': ( 'A_n_vec_n_vec$' * 'A_n_vec_n_vec$' ) > 'N_a_n_vec_fun$' ).

tff('sum$l',type,
    'sum$l': ( 'A_n_vec_a_n_vec_fun$' * 'A_n_vec_set$' ) > 'A_n_vec$' ).

tff('uzb$',type,
    'uzb$': ( 'A_n_n_fun_vec$' * 'A_n_vec_n_n_fun_vec$' ) > 'N_n_n_fun_a_fun_fun$' ).

tff('top$p',type,
    'top$p': 'N_a_n_vec_fun_bool_fun$' ).

tff('vao$',type,
    'vao$': ( 'A_n_vec_n_vec$' * 'N$' ) > 'N_n_a_n_vec_fun_fun$' ).

tff('uyn$',type,
    'uyn$': ( 'N_n_n_fun_a_fun_fun$' * 'N_n_fun_set$' ) > 'N_a_fun$' ).

tff('sum$o',type,
    'sum$o': ( 'Nat_a_set_fun$' * 'Nat_set$' ) > 'A_set$' ).

tff('member$b',type,
    'member$b': ( 'Nat_nat_fun$' * 'Nat_nat_fun_set$' ) > $o ).

tff('comp$a',type,
    'comp$a': ( 'A_n_vec_a_n_vec_fun$' * 'A_n_vec_a_n_vec_fun$' ) > 'A_n_vec_a_n_vec_fun$' ).

tff('linear$a',type,
    'linear$a': ( 'A_a_a_fun_fun$' * 'A_a_a_fun_fun$' * 'A_a_fun$' ) > $o ).

tff('uyb$',type,
    'uyb$': ( 'N_nat_a_fun_fun$' * 'Nat_set$' ) > 'N_a_fun$' ).

tff('uuq$',type,
    'uuq$': 'A_n_vec$' > 'N_a_n_vec_fun$' ).

tff('top$q',type,
    'top$q': 'N_a_fun_bool_fun$' ).

tff('vat$',type,
    'vat$': ( 'A_n_vec_n_vec_n_vec$' * 'A_n_vec_n_vec_n_vec$' * 'N$' ) > 'N_a_n_vec_n_vec_fun$' ).

tff('plus$c',type,
    'plus$c': ( 'Nat_set$' * 'Nat_set$' ) > 'Nat_set$' ).

tff('uzx$',type,
    'uzx$': ( 'N_a_n_vec_n_vec_fun$' * 'N_set$' ) > 'N_a_n_vec_fun$' ).

tff('vbc$',type,
    'vbc$': 'A_n_vec$' > 'A_a_n_vec_fun$' ).

tff('mult_column_row$',type,
    'mult_column_row$': ( 'A_n_vec_n_vec$' * 'N$' * 'A$' ) > 'N_a_n_vec_fun$' ).

tff('transpose_row$',type,
    'transpose_row$': 'A_n_vec_n_vec_n_vec_n_vec$' > 'N_a_n_vec_n_vec_n_vec_fun$' ).

tff('uwd$',type,
    'uwd$': 'Nat_bool_fun$' ).

tff('uvv$',type,
    'uvv$': ( 'A_n_vec_n_vec$' * 'A_n_vec_a_fun$' ) > 'N_a_n_vec_fun$' ).

tff('scalar_product$e',type,
    'scalar_product$e': 'A_n_vec$' > 'A_n_vec_a_fun$' ).

tff('vector_matrix_mult$',type,
    'vector_matrix_mult$': ( 'Nat_n_vec$' * 'Nat_n_vec_n_vec$' ) > 'Nat_n_vec$' ).

tff('fun_app$g',type,
    'fun_app$g': ( 'N_a_n_vec_n_vec_n_vec_fun$' * 'N$' ) > 'A_n_vec_n_vec_n_vec$' ).

tff('vcd$',type,
    'vcd$': ( 'N_set$' * 'N_n_a_n_vec_fun_fun$' * 'N_n_bool_fun_fun$' ) > 'N_a_n_vec_fun$' ).

tff('fun_app$ag',type,
    'fun_app$ag': ( 'Nat_n_a_n_vec_fun_fun$' * 'Nat$' ) > 'N_a_n_vec_fun$' ).

%% Assertions:
%% ∀ ?v0:N_a_fun$ (fun_app$(uua$, ?v0) = (fun_app$a(vec_nth$(x$), x$a) = sum$(uu$(?v0), top$)))
tff(axiom0,axiom,
    ! [A__questionmark_v0: 'N_a_fun$'] :
      ( 'fun_app$'('uua$',A__questionmark_v0)
    <=> ( 'fun_app$a'('vec_nth$'('x$'),'x$a') = 'sum$'('uu$'(A__questionmark_v0),'top$') ) ) ).

%% ∀ ?v0:N$ (fun_app$a(uub$, ?v0) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$d(h$, ?v0)), fun_app$a(vec_nth$(y$), ?v0)))
tff(axiom1,axiom,
    ! [A__questionmark_v0: 'N$'] : 'fun_app$a'('uub$',A__questionmark_v0) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$d'('h$',A__questionmark_v0)),'fun_app$a'('vec_nth$'('y$'),A__questionmark_v0)) ).

%% ∀ ?v0:N$ (fun_app$a(uuf$, ?v0) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$d(g$, ?v0)), fun_app$a(vec_nth$(x$), ?v0)))
tff(axiom2,axiom,
    ! [A__questionmark_v0: 'N$'] : 'fun_app$a'('uuf$',A__questionmark_v0) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$d'('g$',A__questionmark_v0)),'fun_app$a'('vec_nth$'('x$'),A__questionmark_v0)) ).

%% ∀ ?v0:N$ (fun_app$a(uud$, ?v0) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$d(f$, ?v0)), fun_app$a(vec_nth$(y$), ?v0)))
tff(axiom3,axiom,
    ! [A__questionmark_v0: 'N$'] : 'fun_app$a'('uud$',A__questionmark_v0) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$d'('f$',A__questionmark_v0)),'fun_app$a'('vec_nth$'('y$'),A__questionmark_v0)) ).

%% ∀ ?v0:N_a_fun$ (fun_app$(uva$, ?v0) = ∀ ?v1:N$ (fun_app$d(vec_nth$a(v$), ?v1) = sum$a(fun_app$e(uuz$(?v0), ?v1), top$)))
tff(axiom4,axiom,
    ! [A__questionmark_v0: 'N_a_fun$'] :
      ( 'fun_app$'('uva$',A__questionmark_v0)
    <=> ! [A__questionmark_v1: 'N$'] : 'fun_app$d'('vec_nth$a'('v$'),A__questionmark_v1) = 'sum$a'('fun_app$e'('uuz$'(A__questionmark_v0),A__questionmark_v1),'top$') ) ).

%% ∀ ?v0:N_a_fun$ (fun_app$(uuy$, ?v0) = ∀ ?v1:N$ (fun_app$d(vec_nth$a(v$), ?v1) = sum$a(fun_app$e(uux$(?v0), ?v1), top$)))
tff(axiom5,axiom,
    ! [A__questionmark_v0: 'N_a_fun$'] :
      ( 'fun_app$'('uuy$',A__questionmark_v0)
    <=> ! [A__questionmark_v1: 'N$'] : 'fun_app$d'('vec_nth$a'('v$'),A__questionmark_v1) = 'sum$a'('fun_app$e'('uux$'(A__questionmark_v0),A__questionmark_v1),'top$') ) ).

%% ∀ ?v0:A_n_vec$ ?v1:N$ (fun_app$a(uuq$(?v0), ?v1) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$d(vec_nth$a(?v0), ?v1)), fun_app$a(vec_nth$(cart_basis$), ?v1)))
tff(axiom6,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'N$'] : 'fun_app$a'('uuq$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$d'('vec_nth$a'(A__questionmark_v0),A__questionmark_v1)),'fun_app$a'('vec_nth$'('cart_basis$'),A__questionmark_v1)) ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec_n_vec$ ?v1:N$ (fun_app$f(uvd$(?v0), ?v1) = fun_app$f(vec_nth$b(fun_app$g(vec_nth$c(?v0), ?v1)), ?v1))
tff(axiom7,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec_n_vec$',A__questionmark_v1: 'N$'] : 'fun_app$f'('uvd$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$f'('vec_nth$b'('fun_app$g'('vec_nth$c'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v1) ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ ?v1:N$ (fun_app$a(uve$(?v0), ?v1) = fun_app$a(vec_nth$(fun_app$f(vec_nth$b(?v0), ?v1)), ?v1))
tff(axiom8,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$',A__questionmark_v1: 'N$'] : 'fun_app$a'('uve$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$a'('vec_nth$'('fun_app$f'('vec_nth$b'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v1) ).

%% ∀ ?v0:Nat_n_vec_n_vec$ ?v1:N$ (fun_app$h(uvb$(?v0), ?v1) = fun_app$h(vec_nth$d(vec_nth$e(?v0, ?v1)), ?v1))
tff(axiom9,axiom,
    ! [A__questionmark_v0: 'Nat_n_vec_n_vec$',A__questionmark_v1: 'N$'] : 'fun_app$h'('uvb$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$h'('vec_nth$d'('vec_nth$e'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v1) ).

%% ∀ ?v0:A_n_n_fun_vec_n_n_fun_vec$ ?v1:N_n_fun$ (fun_app$i(uvc$(?v0), ?v1) = fun_app$i(vec_nth$f(vec_nth$g(?v0, ?v1)), ?v1))
tff(axiom10,axiom,
    ! [A__questionmark_v0: 'A_n_n_fun_vec_n_n_fun_vec$',A__questionmark_v1: 'N_n_fun$'] : 'fun_app$i'('uvc$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$i'('vec_nth$f'('vec_nth$g'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v1) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ (fun_app$d(uvf$(?v0), ?v1) = fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v1)), ?v1))
tff(axiom11,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$'] : 'fun_app$d'('uvf$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v1) ).

%% ∀ ?v0:N$ ?v1:N_a_fun$ (fun_app$(uuc$(?v0), ?v1) = (fun_app$a(vec_nth$(x$), ?v0) = sum$(uu$(?v1), top$)))
tff(axiom12,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'N_a_fun$'] :
      ( 'fun_app$'('uuc$'(A__questionmark_v0),A__questionmark_v1)
    <=> ( 'fun_app$a'('vec_nth$'('x$'),A__questionmark_v0) = 'sum$'('uu$'(A__questionmark_v1),'top$') ) ) ).

%% ∀ ?v0:A_n_vec_a_fun$ ?v1:N$ (fun_app$a(uur$(?v0), ?v1) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$j(?v0, fun_app$a(vec_nth$(cart_basis$), ?v1))), fun_app$a(vec_nth$(cart_basis$), ?v1)))
tff(axiom13,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_fun$',A__questionmark_v1: 'N$'] : 'fun_app$a'('uur$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$j'(A__questionmark_v0,'fun_app$a'('vec_nth$'('cart_basis$'),A__questionmark_v1))),'fun_app$a'('vec_nth$'('cart_basis$'),A__questionmark_v1)) ).

%% ∀ ?v0:N_a_fun$ ?v1:N$ (fun_app$a(uu$(?v0), ?v1) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$d(?v0, ?v1)), fun_app$a(vec_nth$(y$), ?v1)))
tff(axiom14,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N$'] : 'fun_app$a'('uu$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$d'(A__questionmark_v0,A__questionmark_v1)),'fun_app$a'('vec_nth$'('y$'),A__questionmark_v1)) ).

%% ∀ ?v0:N_a_fun$ ?v1:N$ (fun_app$a(uue$(?v0), ?v1) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$d(?v0, ?v1)), fun_app$a(vec_nth$(x$), ?v1)))
tff(axiom15,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N$'] : 'fun_app$a'('uue$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$d'(A__questionmark_v0,A__questionmark_v1)),'fun_app$a'('vec_nth$'('x$'),A__questionmark_v1)) ).

%% ∀ ?v0:N_a_fun$ ?v1:N$ (fun_app$a(uuv$(?v0), ?v1) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$d(?v0, ?v1)), fun_app$a(vec_nth$(cart_basis$), ?v1)))
tff(axiom16,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N$'] : 'fun_app$a'('uuv$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$d'(A__questionmark_v0,A__questionmark_v1)),'fun_app$a'('vec_nth$'('cart_basis$'),A__questionmark_v1)) ).

%% ∀ ?v0:A_n_vec_a_fun$ ?v1:A_n_vec$ (fun_app$b(uvu$(?v0), ?v1) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$j(?v0, ?v1)), ?v1))
tff(axiom17,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_fun$',A__questionmark_v1: 'A_n_vec$'] : 'fun_app$b'('uvu$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$j'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v1) ).

%% ∀ ?v0:N$ ?v1:N$ (fun_app$d(fun_app$e(uuw$, ?v0), ?v1) = fun_app$k(fun_app$l(times$, fun_app$d(g$, ?v1)), fun_app$d(fun_app$e(t$, ?v1), ?v0)))
tff(axiom18,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'N$'] : 'fun_app$d'('fun_app$e'('uuw$',A__questionmark_v0),A__questionmark_v1) = 'fun_app$k'('fun_app$l'('times$','fun_app$d'('g$',A__questionmark_v1)),'fun_app$d'('fun_app$e'('t$',A__questionmark_v1),A__questionmark_v0)) ).

%% ∀ ?v0:Nat$ ?v1:Nat$ (fun_app$m(fun_app$n(veb$, ?v0), ?v1) = (of_nat$(?v1) < of_nat$(?v0)))
tff(axiom19,axiom,
    ! [A__questionmark_v0: 'Nat$',A__questionmark_v1: 'Nat$'] :
      ( 'fun_app$m'('fun_app$n'('veb$',A__questionmark_v0),A__questionmark_v1)
    <=> $less('of_nat$'(A__questionmark_v1),'of_nat$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:A_n_vec$ ?v1:A$ (fun_app$o(vbc$(?v0), ?v1) = fun_app$b(fun_app$c(vector_scalar_mult$, ?v1), ?v0))
tff(axiom20,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A$'] : 'fun_app$o'('vbc$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v1),A__questionmark_v0) ).

%% ∀ ?v0:A$ ?v1:A$ (fun_app$k(vax$(?v0), ?v1) = fun_app$k(fun_app$l(times$, ?v1), ?v0))
tff(axiom21,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$'] : 'fun_app$k'('vax$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v1),A__questionmark_v0) ).

%% ∀ ?v0:A_n_vec_set$ ?v1:A_n_vec$ (fun_app$p(uvj$(?v0), ?v1) = member$(?v1, ?v0))
tff(axiom22,axiom,
    ! [A__questionmark_v0: 'A_n_vec_set$',A__questionmark_v1: 'A_n_vec$'] :
      ( 'fun_app$p'('uvj$'(A__questionmark_v0),A__questionmark_v1)
    <=> 'member$'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat$ (fun_app$m(uvn$(?v0), ?v1) = member$a(?v1, ?v0))
tff(axiom23,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat$'] :
      ( 'fun_app$m'('uvn$'(A__questionmark_v0),A__questionmark_v1)
    <=> 'member$a'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:Nat_nat_fun_set$ ?v1:Nat_nat_fun$ (fun_app$q(uvm$(?v0), ?v1) = member$b(?v1, ?v0))
tff(axiom24,axiom,
    ! [A__questionmark_v0: 'Nat_nat_fun_set$',A__questionmark_v1: 'Nat_nat_fun$'] :
      ( 'fun_app$q'('uvm$'(A__questionmark_v0),A__questionmark_v1)
    <=> 'member$b'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:N_a_n_vec_fun_set$ ?v1:N_a_n_vec_fun$ (fun_app$r(uvg$(?v0), ?v1) = member$c(?v1, ?v0))
tff(axiom25,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun_set$',A__questionmark_v1: 'N_a_n_vec_fun$'] :
      ( 'fun_app$r'('uvg$'(A__questionmark_v0),A__questionmark_v1)
    <=> 'member$c'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:N_n_fun_set$ ?v1:N_n_fun$ (fun_app$s(uvl$(?v0), ?v1) = member$d(?v1, ?v0))
tff(axiom26,axiom,
    ! [A__questionmark_v0: 'N_n_fun_set$',A__questionmark_v1: 'N_n_fun$'] :
      ( 'fun_app$s'('uvl$'(A__questionmark_v0),A__questionmark_v1)
    <=> 'member$d'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:N_a_fun_set$ ?v1:N_a_fun$ (fun_app$(uvh$(?v0), ?v1) = member$e(?v1, ?v0))
tff(axiom27,axiom,
    ! [A__questionmark_v0: 'N_a_fun_set$',A__questionmark_v1: 'N_a_fun$'] :
      ( 'fun_app$'('uvh$'(A__questionmark_v0),A__questionmark_v1)
    <=> 'member$e'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:N_set$ ?v1:N$ (fun_app$t(uvi$(?v0), ?v1) = member$f(?v1, ?v0))
tff(axiom28,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N$'] :
      ( 'fun_app$t'('uvi$'(A__questionmark_v0),A__questionmark_v1)
    <=> 'member$f'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:A_set$ ?v1:A$ (fun_app$u(uvk$(?v0), ?v1) = member$g(?v1, ?v0))
tff(axiom29,axiom,
    ! [A__questionmark_v0: 'A_set$',A__questionmark_v1: 'A$'] :
      ( 'fun_app$u'('uvk$'(A__questionmark_v0),A__questionmark_v1)
    <=> 'member$g'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_a_fun$ (fun_app$(uum$(?v0), ?v1) = (?v0 = ?v1))
tff(axiom30,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_a_fun$'] :
      ( 'fun_app$'('uum$'(A__questionmark_v0),A__questionmark_v1)
    <=> ( A__questionmark_v0 = A__questionmark_v1 ) ) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_a_fun$ (fun_app$(uul$(?v0), ?v1) = (?v1 = ?v0))
tff(axiom31,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_a_fun$'] :
      ( 'fun_app$'('uul$'(A__questionmark_v0),A__questionmark_v1)
    <=> ( A__questionmark_v1 = A__questionmark_v0 ) ) ).

%% ∀ ?v0:Nat_nat_fun$ ?v1:Nat$ (fun_app$m(vec$(?v0), ?v1) = (0 < of_nat$(fun_app$v(?v0, ?v1))))
tff(axiom32,axiom,
    ! [A__questionmark_v0: 'Nat_nat_fun$',A__questionmark_v1: 'Nat$'] :
      ( 'fun_app$m'('vec$'(A__questionmark_v0),A__questionmark_v1)
    <=> $less(0,'of_nat$'('fun_app$v'(A__questionmark_v0,A__questionmark_v1))) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ (fun_app$a(vag$(?v0), ?v1) = vec_lambda$(fun_app$e(uzr$(?v0), ?v1)))
tff(axiom33,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$'] : 'fun_app$a'('vag$'(A__questionmark_v0),A__questionmark_v1) = 'vec_lambda$'('fun_app$e'('uzr$'(A__questionmark_v0),A__questionmark_v1)) ).

%% ∀ ?v0:Nat_bool_fun$ ?v1:Nat$ (fun_app$m(vcp$(?v0), ?v1) = ¬fun_app$m(?v0, ?v1))
tff(axiom34,axiom,
    ! [A__questionmark_v0: 'Nat_bool_fun$',A__questionmark_v1: 'Nat$'] :
      ( 'fun_app$m'('vcp$'(A__questionmark_v0),A__questionmark_v1)
    <=> ~ 'fun_app$m'(A__questionmark_v0,A__questionmark_v1) ) ).

%% ∀ ?v0:N_bool_fun$ ?v1:N$ (fun_app$t(vcq$(?v0), ?v1) = ¬fun_app$t(?v0, ?v1))
tff(axiom35,axiom,
    ! [A__questionmark_v0: 'N_bool_fun$',A__questionmark_v1: 'N$'] :
      ( 'fun_app$t'('vcq$'(A__questionmark_v0),A__questionmark_v1)
    <=> ~ 'fun_app$t'(A__questionmark_v0,A__questionmark_v1) ) ).

%% ∀ ?v0:N_n_a_n_vec_fun_fun$ ?v1:N_n_fun$ (fun_app$i(vbo$(?v0), ?v1) = fun_app$w(det$, vec_lambda$a(vbn$(?v0, ?v1))))
tff(axiom36,axiom,
    ! [A__questionmark_v0: 'N_n_a_n_vec_fun_fun$',A__questionmark_v1: 'N_n_fun$'] : 'fun_app$i'('vbo$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$w'('det$','vec_lambda$a'('vbn$'(A__questionmark_v0,A__questionmark_v1))) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec$ (fun_app$p(uxn$(?v0), ?v1) = ∃ ?v2:N_a_fun$ (sum$(uvw$(?v0, ?v2), top$) = ?v1))
tff(axiom37,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec$'] :
      ( 'fun_app$p'('uxn$'(A__questionmark_v0),A__questionmark_v1)
    <=> ? [A__questionmark_v2: 'N_a_fun$'] : 'sum$'('uvw$'(A__questionmark_v0,A__questionmark_v2),'top$') = A__questionmark_v1 ) ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ (fun_app$x(uxr$(?v0), ?v1) = ∃ ?v2:N$ ((?v1 = fun_app$f(vec_nth$b(?v0), ?v2)) ∧ member$f(?v2, top$)))
tff(axiom38,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$'] :
      ( 'fun_app$x'('uxr$'(A__questionmark_v0),A__questionmark_v1)
    <=> ? [A__questionmark_v2: 'N$'] :
          ( ( A__questionmark_v1 = 'fun_app$f'('vec_nth$b'(A__questionmark_v0),A__questionmark_v2) )
          & 'member$f'(A__questionmark_v2,'top$') ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec$ (fun_app$p(uxt$(?v0), ?v1) = ∃ ?v2:N$ ((?v1 = fun_app$a(vec_nth$(?v0), ?v2)) ∧ member$f(?v2, top$)))
tff(axiom39,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec$'] :
      ( 'fun_app$p'('uxt$'(A__questionmark_v0),A__questionmark_v1)
    <=> ? [A__questionmark_v2: 'N$'] :
          ( ( A__questionmark_v1 = 'fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v2) )
          & 'member$f'(A__questionmark_v2,'top$') ) ) ).

%% ∀ ?v0:Nat_n_vec$ ?v1:Nat$ (fun_app$m(uxs$(?v0), ?v1) = ∃ ?v2:N$ ((?v1 = fun_app$h(vec_nth$d(?v0), ?v2)) ∧ member$f(?v2, top$)))
tff(axiom40,axiom,
    ! [A__questionmark_v0: 'Nat_n_vec$',A__questionmark_v1: 'Nat$'] :
      ( 'fun_app$m'('uxs$'(A__questionmark_v0),A__questionmark_v1)
    <=> ? [A__questionmark_v2: 'N$'] :
          ( ( A__questionmark_v1 = 'fun_app$h'('vec_nth$d'(A__questionmark_v0),A__questionmark_v2) )
          & 'member$f'(A__questionmark_v2,'top$') ) ) ).

%% ∀ ?v0:Nat_nat_fun_n_vec$ ?v1:Nat_nat_fun$ (fun_app$q(uxq$(?v0), ?v1) = ∃ ?v2:N$ ((?v1 = vec_nth$h(?v0, ?v2)) ∧ member$f(?v2, top$)))
tff(axiom41,axiom,
    ! [A__questionmark_v0: 'Nat_nat_fun_n_vec$',A__questionmark_v1: 'Nat_nat_fun$'] :
      ( 'fun_app$q'('uxq$'(A__questionmark_v0),A__questionmark_v1)
    <=> ? [A__questionmark_v2: 'N$'] :
          ( ( A__questionmark_v1 = 'vec_nth$h'(A__questionmark_v0,A__questionmark_v2) )
          & 'member$f'(A__questionmark_v2,'top$') ) ) ).

%% ∀ ?v0:N_n_fun_n_vec$ ?v1:N_n_fun$ (fun_app$s(uxp$(?v0), ?v1) = ∃ ?v2:N$ ((?v1 = vec_nth$i(?v0, ?v2)) ∧ member$f(?v2, top$)))
tff(axiom42,axiom,
    ! [A__questionmark_v0: 'N_n_fun_n_vec$',A__questionmark_v1: 'N_n_fun$'] :
      ( 'fun_app$s'('uxp$'(A__questionmark_v0),A__questionmark_v1)
    <=> ? [A__questionmark_v2: 'N$'] :
          ( ( A__questionmark_v1 = 'vec_nth$i'(A__questionmark_v0,A__questionmark_v2) )
          & 'member$f'(A__questionmark_v2,'top$') ) ) ).

%% ∀ ?v0:N_n_vec$ ?v1:N$ (fun_app$t(uxo$(?v0), ?v1) = ∃ ?v2:N$ ((?v1 = fun_app$y(vec_nth$j(?v0), ?v2)) ∧ member$f(?v2, top$)))
tff(axiom43,axiom,
    ! [A__questionmark_v0: 'N_n_vec$',A__questionmark_v1: 'N$'] :
      ( 'fun_app$t'('uxo$'(A__questionmark_v0),A__questionmark_v1)
    <=> ? [A__questionmark_v2: 'N$'] :
          ( ( A__questionmark_v1 = 'fun_app$y'('vec_nth$j'(A__questionmark_v0),A__questionmark_v2) )
          & 'member$f'(A__questionmark_v2,'top$') ) ) ).

%% ∀ ?v0:A_n_vec$ ?v1:A$ (fun_app$u(uxu$(?v0), ?v1) = ∃ ?v2:N$ ((?v1 = fun_app$d(vec_nth$a(?v0), ?v2)) ∧ member$f(?v2, top$)))
tff(axiom44,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A$'] :
      ( 'fun_app$u'('uxu$'(A__questionmark_v0),A__questionmark_v1)
    <=> ? [A__questionmark_v2: 'N$'] :
          ( ( A__questionmark_v1 = 'fun_app$d'('vec_nth$a'(A__questionmark_v0),A__questionmark_v2) )
          & 'member$f'(A__questionmark_v2,'top$') ) ) ).

%% ∀ ?v0:N_nat_fun$ ?v1:Nat$ (fun_app$m(vcx$(?v0), ?v1) = ∃ ?v2:N$ ((?v1 = fun_app$h(?v0, ?v2)) ∧ member$f(?v2, top$)))
tff(axiom45,axiom,
    ! [A__questionmark_v0: 'N_nat_fun$',A__questionmark_v1: 'Nat$'] :
      ( 'fun_app$m'('vcx$'(A__questionmark_v0),A__questionmark_v1)
    <=> ? [A__questionmark_v2: 'N$'] :
          ( ( A__questionmark_v1 = 'fun_app$h'(A__questionmark_v0,A__questionmark_v2) )
          & 'member$f'(A__questionmark_v2,'top$') ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_n_fun$ (fun_app$s(vbp$(?v0), ?v1) = ∀ ?v2:N$ member$f(fun_app$y(?v1, ?v2), ?v0))
tff(axiom46,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_n_fun$'] :
      ( 'fun_app$s'('vbp$'(A__questionmark_v0),A__questionmark_v1)
    <=> ! [A__questionmark_v2: 'N$'] : 'member$f'('fun_app$y'(A__questionmark_v1,A__questionmark_v2),A__questionmark_v0) ) ).

%% ∀ ?v0:N$ ?v1:N_a_n_vec_fun$ ?v2:N$ (fun_app$a(vdj$(?v0, ?v1), ?v2) = (if (?v0 = ?v2) fun_app$a(?v1, ?v2) else zero$))
tff(axiom47,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N$'] :
      ( ( ( A__questionmark_v0 = A__questionmark_v2 )
       => ( 'fun_app$a'('vdj$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$a'(A__questionmark_v1,A__questionmark_v2) ) )
      & ( ( A__questionmark_v0 != A__questionmark_v2 )
       => ( 'fun_app$a'('vdj$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'zero$' ) ) ) ).

%% ∀ ?v0:N$ ?v1:N_a_fun$ ?v2:N$ (fun_app$d(vdk$(?v0, ?v1), ?v2) = (if (?v0 = ?v2) fun_app$d(?v1, ?v2) else zero$a))
tff(axiom48,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N$'] :
      ( ( ( A__questionmark_v0 = A__questionmark_v2 )
       => ( 'fun_app$d'('vdk$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$d'(A__questionmark_v1,A__questionmark_v2) ) )
      & ( ( A__questionmark_v0 != A__questionmark_v2 )
       => ( 'fun_app$d'('vdk$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'zero$a' ) ) ) ).

%% ∀ ?v0:N$ ?v1:N_a_n_vec_fun$ ?v2:N$ (fun_app$a(vdl$(?v0, ?v1), ?v2) = (if (?v2 = ?v0) fun_app$a(?v1, ?v2) else zero$))
tff(axiom49,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N$'] :
      ( ( ( A__questionmark_v2 = A__questionmark_v0 )
       => ( 'fun_app$a'('vdl$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$a'(A__questionmark_v1,A__questionmark_v2) ) )
      & ( ( A__questionmark_v2 != A__questionmark_v0 )
       => ( 'fun_app$a'('vdl$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'zero$' ) ) ) ).

%% ∀ ?v0:N$ ?v1:N_a_fun$ ?v2:N$ (fun_app$d(vdm$(?v0, ?v1), ?v2) = (if (?v2 = ?v0) fun_app$d(?v1, ?v2) else zero$a))
tff(axiom50,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N$'] :
      ( ( ( A__questionmark_v2 = A__questionmark_v0 )
       => ( 'fun_app$d'('vdm$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$d'(A__questionmark_v1,A__questionmark_v2) ) )
      & ( ( A__questionmark_v2 != A__questionmark_v0 )
       => ( 'fun_app$d'('vdm$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'zero$a' ) ) ) ).

%% ∀ ?v0:N_a_n_vec_fun$ ?v1:N_bool_fun$ ?v2:N$ (fun_app$a(vdt$(?v0, ?v1), ?v2) = (if fun_app$t(?v1, ?v2) fun_app$a(?v0, ?v2) else zero$))
tff(axiom51,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$',A__questionmark_v1: 'N_bool_fun$',A__questionmark_v2: 'N$'] :
      ( ( 'fun_app$t'(A__questionmark_v1,A__questionmark_v2)
       => ( 'fun_app$a'('vdt$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$a'(A__questionmark_v0,A__questionmark_v2) ) )
      & ( ~ 'fun_app$t'(A__questionmark_v1,A__questionmark_v2)
       => ( 'fun_app$a'('vdt$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'zero$' ) ) ) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_bool_fun$ ?v2:N$ (fun_app$d(vdu$(?v0, ?v1), ?v2) = (if fun_app$t(?v1, ?v2) fun_app$d(?v0, ?v2) else zero$a))
tff(axiom52,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_bool_fun$',A__questionmark_v2: 'N$'] :
      ( ( 'fun_app$t'(A__questionmark_v1,A__questionmark_v2)
       => ( 'fun_app$d'('vdu$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$d'(A__questionmark_v0,A__questionmark_v2) ) )
      & ( ~ 'fun_app$t'(A__questionmark_v1,A__questionmark_v2)
       => ( 'fun_app$d'('vdu$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'zero$a' ) ) ) ).

%% ∀ ?v0:N_n_a_n_vec_fun_fun$ ?v1:N_n_fun$ ?v2:N$ (fun_app$a(vbn$(?v0, ?v1), ?v2) = fun_app$a(fun_app$z(?v0, ?v2), fun_app$y(?v1, ?v2)))
tff(axiom53,axiom,
    ! [A__questionmark_v0: 'N_n_a_n_vec_fun_fun$',A__questionmark_v1: 'N_n_fun$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vbn$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$a'('fun_app$z'(A__questionmark_v0,A__questionmark_v2),'fun_app$y'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:Nat_nat_bool_fun_fun$ ?v1:Nat$ ?v2:Nat$ (fun_app$m(fun_app$n(vco$(?v0), ?v1), ?v2) = fun_app$m(fun_app$n(?v0, ?v2), ?v1))
tff(axiom54,axiom,
    ! [A__questionmark_v0: 'Nat_nat_bool_fun_fun$',A__questionmark_v1: 'Nat$',A__questionmark_v2: 'Nat$'] :
      ( 'fun_app$m'('fun_app$n'('vco$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2)
    <=> 'fun_app$m'('fun_app$n'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ) ).

%% ∀ ?v0:Nat_nat_a_fun_fun$ ?v1:Nat$ ?v2:Nat$ (fun_app$aa(fun_app$ab(uyi$(?v0), ?v1), ?v2) = fun_app$aa(fun_app$ab(?v0, ?v2), ?v1))
tff(axiom55,axiom,
    ! [A__questionmark_v0: 'Nat_nat_a_fun_fun$',A__questionmark_v1: 'Nat$',A__questionmark_v2: 'Nat$'] : 'fun_app$aa'('fun_app$ab'('uyi$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$aa'('fun_app$ab'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:Nat_n_n_fun_a_fun_fun$ ?v1:N_n_fun$ ?v2:Nat$ (fun_app$aa(fun_app$ac(uyr$(?v0), ?v1), ?v2) = fun_app$i(fun_app$ad(?v0, ?v2), ?v1))
tff(axiom56,axiom,
    ! [A__questionmark_v0: 'Nat_n_n_fun_a_fun_fun$',A__questionmark_v1: 'N_n_fun$',A__questionmark_v2: 'Nat$'] : 'fun_app$aa'('fun_app$ac'('uyr$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$i'('fun_app$ad'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:Nat_n_a_n_vec_fun_fun$ ?v1:N$ ?v2:Nat$ (fun_app$ae(fun_app$af(vbs$(?v0), ?v1), ?v2) = fun_app$a(fun_app$ag(?v0, ?v2), ?v1))
tff(axiom57,axiom,
    ! [A__questionmark_v0: 'Nat_n_a_n_vec_fun_fun$',A__questionmark_v1: 'N$',A__questionmark_v2: 'Nat$'] : 'fun_app$ae'('fun_app$af'('vbs$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$a'('fun_app$ag'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:Nat_n_a_fun_fun$ ?v1:N$ ?v2:Nat$ (fun_app$aa(fun_app$ah(uyf$(?v0), ?v1), ?v2) = fun_app$d(fun_app$ai(?v0, ?v2), ?v1))
tff(axiom58,axiom,
    ! [A__questionmark_v0: 'Nat_n_a_fun_fun$',A__questionmark_v1: 'N$',A__questionmark_v2: 'Nat$'] : 'fun_app$aa'('fun_app$ah'('uyf$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$d'('fun_app$ai'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_fun_nat_a_fun_fun$ ?v1:Nat$ ?v2:N_n_fun$ (fun_app$i(fun_app$ad(uyx$(?v0), ?v1), ?v2) = fun_app$aa(fun_app$ac(?v0, ?v2), ?v1))
tff(axiom59,axiom,
    ! [A__questionmark_v0: 'N_n_fun_nat_a_fun_fun$',A__questionmark_v1: 'Nat$',A__questionmark_v2: 'N_n_fun$'] : 'fun_app$i'('fun_app$ad'('uyx$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$aa'('fun_app$ac'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_fun_n_a_fun_fun$ ?v1:N$ ?v2:N_n_fun$ (fun_app$i(fun_app$aj(uyu$(?v0), ?v1), ?v2) = fun_app$d(fun_app$ak(?v0, ?v2), ?v1))
tff(axiom60,axiom,
    ! [A__questionmark_v0: 'N_n_fun_n_a_fun_fun$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N_n_fun$'] : 'fun_app$i'('fun_app$aj'('uyu$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$d'('fun_app$ak'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_a_n_vec_a_n_vec_fun_fun$ ?v1:A_n_vec$ ?v2:N$ (fun_app$a(vbd$(?v0, ?v1), ?v2) = fun_app$b(fun_app$al(?v0, ?v2), ?v1))
tff(axiom61,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_a_n_vec_fun_fun$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vbd$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('fun_app$al'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_nat_a_n_vec_fun_fun$ ?v1:Nat$ ?v2:N$ (fun_app$a(fun_app$ag(vbz$(?v0), ?v1), ?v2) = fun_app$ae(fun_app$af(?v0, ?v2), ?v1))
tff(axiom62,axiom,
    ! [A__questionmark_v0: 'N_nat_a_n_vec_fun_fun$',A__questionmark_v1: 'Nat$',A__questionmark_v2: 'N$'] : 'fun_app$a'('fun_app$ag'('vbz$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$ae'('fun_app$af'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_nat_a_fun_fun$ ?v1:Nat$ ?v2:N$ (fun_app$d(fun_app$ai(uyc$(?v0), ?v1), ?v2) = fun_app$aa(fun_app$ah(?v0, ?v2), ?v1))
tff(axiom63,axiom,
    ! [A__questionmark_v0: 'N_nat_a_fun_fun$',A__questionmark_v1: 'Nat$',A__questionmark_v2: 'N$'] : 'fun_app$d'('fun_app$ai'('uyc$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$aa'('fun_app$ah'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_n_fun_a_fun_fun$ ?v1:N_n_fun$ ?v2:N$ (fun_app$d(fun_app$ak(uyo$(?v0), ?v1), ?v2) = fun_app$i(fun_app$aj(?v0, ?v2), ?v1))
tff(axiom64,axiom,
    ! [A__questionmark_v0: 'N_n_n_fun_a_fun_fun$',A__questionmark_v1: 'N_n_fun$',A__questionmark_v2: 'N$'] : 'fun_app$d'('fun_app$ak'('uyo$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$i'('fun_app$aj'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_a_n_vec_fun_fun$ ?v1:N$ ?v2:N$ (fun_app$a(fun_app$z(uxz$(?v0), ?v1), ?v2) = fun_app$a(fun_app$z(?v0, ?v2), ?v1))
tff(axiom65,axiom,
    ! [A__questionmark_v0: 'N_n_a_n_vec_fun_fun$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'fun_app$a'('fun_app$z'('uxz$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$a'('fun_app$z'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_a_set_fun_fun$ ?v1:N$ ?v2:N$ (fun_app$am(fun_app$an(uyl$(?v0), ?v1), ?v2) = fun_app$am(fun_app$an(?v0, ?v2), ?v1))
tff(axiom66,axiom,
    ! [A__questionmark_v0: 'N_n_a_set_fun_fun$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'fun_app$am'('fun_app$an'('uyl$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$am'('fun_app$an'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_a_fun_fun$ ?v1:N$ ?v2:N$ (fun_app$d(fun_app$e(uxw$(?v0), ?v1), ?v2) = fun_app$d(fun_app$e(?v0, ?v2), ?v1))
tff(axiom67,axiom,
    ! [A__questionmark_v0: 'N_n_a_fun_fun$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'fun_app$d'('fun_app$e'('uxw$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$d'('fun_app$e'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ (fun_app$a(vaw$(?v0, ?v1), ?v2) = sum$(fun_app$z(vav$(?v0, ?v1), ?v2), top$))
tff(axiom68,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vaw$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$'('fun_app$z'('vav$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),'top$') ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec$ ?v2:N$ (fun_app$f(vau$(?v0, ?v1), ?v2) = sum$b(vat$(?v0, ?v1, ?v2), top$))
tff(axiom69,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$f'('vau$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$b'('vat$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),'top$') ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec$ ?v2:N$ (fun_app$d(uzs$(?v0, ?v1), ?v2) = sum$a(fun_app$e(uzl$(?v0, ?v1), ?v2), top$))
tff(axiom70,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$d'('uzs$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$a'('fun_app$e'('uzl$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),'top$') ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ (fun_app$d(uzu$(?v0, ?v1), ?v2) = sum$a(fun_app$e(uze$(?v0, ?v1), ?v2), top$))
tff(axiom71,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$d'('uzu$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$a'('fun_app$e'('uze$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),'top$') ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec$ ?v2:N$ (fun_app$a(uzt$(?v0, ?v1), ?v2) = sum$(fun_app$z(uzd$(?v0, ?v1), ?v2), top$))
tff(axiom72,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$a'('uzt$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$'('fun_app$z'('uzd$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),'top$') ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_a_fun$ ?v2:N$ (fun_app$a(uyz$(?v0, ?v1), ?v2) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$d(comp$(?v1, vec_nth$(?v0)), ?v2)), fun_app$a(vec_nth$(?v0), ?v2)))
tff(axiom73,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_a_fun$',A__questionmark_v2: 'N$'] : 'fun_app$a'('uyz$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$d'('comp$'(A__questionmark_v1,'vec_nth$'(A__questionmark_v0)),A__questionmark_v2)),'fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v2)) ).

%% ∀ ?v0:N_set$ ?v1:N_a_n_vec_a_n_vec_fun_fun$ ?v2:A_n_vec$ (fun_app$b(vbe$(?v0, ?v1), ?v2) = sum$(vbd$(?v1, ?v2), ?v0))
tff(axiom74,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_a_n_vec_a_n_vec_fun_fun$',A__questionmark_v2: 'A_n_vec$'] : 'fun_app$b'('vbe$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$'('vbd$'(A__questionmark_v1,A__questionmark_v2),A__questionmark_v0) ).

%% ∀ ?v0:N_n_fun_nat_a_fun_fun$ ?v1:N_n_fun_set$ ?v2:Nat$ (fun_app$aa(uyy$(?v0, ?v1), ?v2) = sum$c(fun_app$ad(uyx$(?v0), ?v2), ?v1))
tff(axiom75,axiom,
    ! [A__questionmark_v0: 'N_n_fun_nat_a_fun_fun$',A__questionmark_v1: 'N_n_fun_set$',A__questionmark_v2: 'Nat$'] : 'fun_app$aa'('uyy$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$c'('fun_app$ad'('uyx$'(A__questionmark_v0),A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_fun_n_a_fun_fun$ ?v1:N_n_fun_set$ ?v2:N$ (fun_app$d(uyv$(?v0, ?v1), ?v2) = sum$c(fun_app$aj(uyu$(?v0), ?v2), ?v1))
tff(axiom76,axiom,
    ! [A__questionmark_v0: 'N_n_fun_n_a_fun_fun$',A__questionmark_v1: 'N_n_fun_set$',A__questionmark_v2: 'N$'] : 'fun_app$d'('uyv$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$c'('fun_app$aj'('uyu$'(A__questionmark_v0),A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:Nat_n_n_fun_a_fun_fun$ ?v1:Nat_set$ ?v2:N_n_fun$ (fun_app$i(uys$(?v0, ?v1), ?v2) = sum$d(fun_app$ac(uyr$(?v0), ?v2), ?v1))
tff(axiom77,axiom,
    ! [A__questionmark_v0: 'Nat_n_n_fun_a_fun_fun$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'N_n_fun$'] : 'fun_app$i'('uys$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$d'('fun_app$ac'('uyr$'(A__questionmark_v0),A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_n_fun_a_fun_fun$ ?v1:N_set$ ?v2:N_n_fun$ (fun_app$i(uyp$(?v0, ?v1), ?v2) = sum$a(fun_app$ak(uyo$(?v0), ?v2), ?v1))
tff(axiom78,axiom,
    ! [A__questionmark_v0: 'N_n_n_fun_a_fun_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_n_fun$'] : 'fun_app$i'('uyp$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$a'('fun_app$ak'('uyo$'(A__questionmark_v0),A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_a_set_fun_fun$ ?v1:N_set$ ?v2:N$ (fun_app$am(uym$(?v0, ?v1), ?v2) = sum$e(fun_app$an(uyl$(?v0), ?v2), ?v1))
tff(axiom79,axiom,
    ! [A__questionmark_v0: 'N_n_a_set_fun_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N$'] : 'fun_app$am'('uym$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$e'('fun_app$an'('uyl$'(A__questionmark_v0),A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:Nat_nat_a_fun_fun$ ?v1:Nat_set$ ?v2:Nat$ (fun_app$aa(uyj$(?v0, ?v1), ?v2) = sum$d(fun_app$ab(uyi$(?v0), ?v2), ?v1))
tff(axiom80,axiom,
    ! [A__questionmark_v0: 'Nat_nat_a_fun_fun$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'Nat$'] : 'fun_app$aa'('uyj$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$d'('fun_app$ab'('uyi$'(A__questionmark_v0),A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:Nat_n_a_fun_fun$ ?v1:Nat_set$ ?v2:N$ (fun_app$d(uyg$(?v0, ?v1), ?v2) = sum$d(fun_app$ah(uyf$(?v0), ?v2), ?v1))
tff(axiom81,axiom,
    ! [A__questionmark_v0: 'Nat_n_a_fun_fun$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'N$'] : 'fun_app$d'('uyg$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$d'('fun_app$ah'('uyf$'(A__questionmark_v0),A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_nat_a_fun_fun$ ?v1:N_set$ ?v2:Nat$ (fun_app$aa(uyd$(?v0, ?v1), ?v2) = sum$a(fun_app$ai(uyc$(?v0), ?v2), ?v1))
tff(axiom82,axiom,
    ! [A__questionmark_v0: 'N_nat_a_fun_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'Nat$'] : 'fun_app$aa'('uyd$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$a'('fun_app$ai'('uyc$'(A__questionmark_v0),A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_a_n_vec_fun_fun$ ?v1:N_set$ ?v2:N$ (fun_app$a(uya$(?v0, ?v1), ?v2) = sum$(fun_app$z(uxz$(?v0), ?v2), ?v1))
tff(axiom83,axiom,
    ! [A__questionmark_v0: 'N_n_a_n_vec_fun_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N$'] : 'fun_app$a'('uya$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$'('fun_app$z'('uxz$'(A__questionmark_v0),A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_a_fun_fun$ ?v1:N_set$ ?v2:N$ (fun_app$d(uxx$(?v0, ?v1), ?v2) = sum$a(fun_app$e(uxw$(?v0), ?v2), ?v1))
tff(axiom84,axiom,
    ! [A__questionmark_v0: 'N_n_a_fun_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N$'] : 'fun_app$d'('uxx$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$a'('fun_app$e'('uxw$'(A__questionmark_v0),A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_a_n_vec_fun$ ?v1:N_set$ ?v2:N$ (fun_app$d(uzy$(?v0, ?v1), ?v2) = sum$a(fun_app$e(uuk$(?v0), ?v2), ?v1))
tff(axiom85,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N$'] : 'fun_app$d'('uzy$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$a'('fun_app$e'('uuk$'(A__questionmark_v0),A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_a_n_vec_n_vec_fun$ ?v1:N_set$ ?v2:N$ (fun_app$a(uzx$(?v0, ?v1), ?v2) = sum$(fun_app$z(uuj$(?v0), ?v2), ?v1))
tff(axiom86,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_n_vec_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N$'] : 'fun_app$a'('uzx$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$'('fun_app$z'('uuj$'(A__questionmark_v0),A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:Nat_a_fun$ ?v1:Nat_a_fun$ ?v2:Nat$ (fun_app$aa(vei$(?v0, ?v1), ?v2) = fun_app$k(divide$(fun_app$k(fun_app$l(times$, fun_app$aa(?v0, ?v2)), fun_app$aa(power$(zero$a), ?v2))), fun_app$aa(?v1, ?v2)))
tff(axiom87,axiom,
    ! [A__questionmark_v0: 'Nat_a_fun$',A__questionmark_v1: 'Nat_a_fun$',A__questionmark_v2: 'Nat$'] : 'fun_app$aa'('vei$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$k'('divide$'('fun_app$k'('fun_app$l'('times$','fun_app$aa'(A__questionmark_v0,A__questionmark_v2)),'fun_app$aa'('power$'('zero$a'),A__questionmark_v2))),'fun_app$aa'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec$ ?v2:N$ (fun_app$a(vad$(?v0, ?v1), ?v2) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$d(vec_nth$a(?v1), ?v2)), fun_app$a(vec_nth$(transpose$(?v0)), ?v2)))
tff(axiom88,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vad$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$d'('vec_nth$a'(A__questionmark_v1),A__questionmark_v2)),'fun_app$a'('vec_nth$'('transpose$'(A__questionmark_v0)),A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ (fun_app$a(vbi$(?v0, ?v1), ?v2) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$d(vec_nth$a(?v0), ?v2)), row$(?v2, ?v1)))
tff(axiom89,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vbi$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$d'('vec_nth$a'(A__questionmark_v0),A__questionmark_v2)),'row$'(A__questionmark_v2,A__questionmark_v1)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec$ ?v2:N$ (fun_app$a(vac$(?v0, ?v1), ?v2) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$d(vec_nth$a(?v1), ?v2)), column$(?v2, ?v0)))
tff(axiom90,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vac$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$d'('vec_nth$a'(A__questionmark_v1),A__questionmark_v2)),'column$'(A__questionmark_v2,A__questionmark_v0)) ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec$ ?v2:N$ (fun_app$f(uwi$(?v0, ?v1), ?v2) = times$a(fun_app$f(vec_nth$b(?v0), ?v2), fun_app$f(vec_nth$b(?v1), ?v2)))
tff(axiom91,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$f'('uwi$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'times$a'('fun_app$f'('vec_nth$b'(A__questionmark_v0),A__questionmark_v2),'fun_app$f'('vec_nth$b'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ (fun_app$a(uwj$(?v0, ?v1), ?v2) = fun_app$b(times$b(fun_app$a(vec_nth$(?v0), ?v2)), fun_app$a(vec_nth$(?v1), ?v2)))
tff(axiom92,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$a'('uwj$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('times$b'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v2)),'fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:Nat_n_vec$ ?v1:Nat_n_vec$ ?v2:N$ (fun_app$h(uwg$(?v0, ?v1), ?v2) = fun_app$v(fun_app$ao(times$c, fun_app$h(vec_nth$d(?v0), ?v2)), fun_app$h(vec_nth$d(?v1), ?v2)))
tff(axiom93,axiom,
    ! [A__questionmark_v0: 'Nat_n_vec$',A__questionmark_v1: 'Nat_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$h'('uwg$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$v'('fun_app$ao'('times$c','fun_app$h'('vec_nth$d'(A__questionmark_v0),A__questionmark_v2)),'fun_app$h'('vec_nth$d'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:Int_n_vec$ ?v1:Int_n_vec$ ?v2:N$ (fun_app$ap(uwf$(?v0, ?v1), ?v2) = fun_app$aq(times$d(vec_nth$k(?v0, ?v2)), vec_nth$k(?v1, ?v2)))
tff(axiom94,axiom,
    ! [A__questionmark_v0: 'Int_n_vec$',A__questionmark_v1: 'Int_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$ap'('uwf$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$aq'('times$d'('vec_nth$k'(A__questionmark_v0,A__questionmark_v2)),'vec_nth$k'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_n_n_fun_vec$ ?v1:A_n_n_fun_vec$ ?v2:N_n_fun$ (fun_app$i(uwh$(?v0, ?v1), ?v2) = fun_app$k(fun_app$l(times$, fun_app$i(vec_nth$f(?v0), ?v2)), fun_app$i(vec_nth$f(?v1), ?v2)))
tff(axiom95,axiom,
    ! [A__questionmark_v0: 'A_n_n_fun_vec$',A__questionmark_v1: 'A_n_n_fun_vec$',A__questionmark_v2: 'N_n_fun$'] : 'fun_app$i'('uwh$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$k'('fun_app$l'('times$','fun_app$i'('vec_nth$f'(A__questionmark_v0),A__questionmark_v2)),'fun_app$i'('vec_nth$f'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec$ ?v2:N$ (fun_app$d(uwk$(?v0, ?v1), ?v2) = fun_app$k(fun_app$l(times$, fun_app$d(vec_nth$a(?v0), ?v2)), fun_app$d(vec_nth$a(?v1), ?v2)))
tff(axiom96,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$d'('uwk$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$k'('fun_app$l'('times$','fun_app$d'('vec_nth$a'(A__questionmark_v0),A__questionmark_v2)),'fun_app$d'('vec_nth$a'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ (fun_app$a(vdn$(?v0, ?v1), ?v2) = fun_app$b(plus$(fun_app$a(vec_nth$(?v0), ?v2)), fun_app$a(vec_nth$(?v1), ?v2)))
tff(axiom97,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vdn$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('plus$'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v2)),'fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec$ ?v2:N$ (fun_app$d(vdo$(?v0, ?v1), ?v2) = fun_app$k(plus$a(fun_app$d(vec_nth$a(?v0), ?v2)), fun_app$d(vec_nth$a(?v1), ?v2)))
tff(axiom98,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$d'('vdo$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$k'('plus$a'('fun_app$d'('vec_nth$a'(A__questionmark_v0),A__questionmark_v2)),'fun_app$d'('vec_nth$a'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:N_set$ ?v1:N_bool_fun$ ?v2:N$ (fun_app$t(vds$(?v0, ?v1), ?v2) = (member$f(?v2, ?v0) ∧ fun_app$t(?v1, ?v2)))
tff(axiom99,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_bool_fun$',A__questionmark_v2: 'N$'] :
      ( 'fun_app$t'('vds$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)
    <=> ( 'member$f'(A__questionmark_v2,A__questionmark_v0)
        & 'fun_app$t'(A__questionmark_v1,A__questionmark_v2) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ (fun_app$d(fun_app$e(uzr$(?v0), ?v1), ?v2) = fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v2)), ?v1))
tff(axiom100,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'fun_app$d'('fun_app$e'('uzr$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:N$ ?v1:A_n_vec_n_vec$ ?v2:N$ (fun_app$d(vah$(?v0, ?v1), ?v2) = fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v1), ?v2)), ?v0))
tff(axiom101,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$d'('vah$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v2)),A__questionmark_v0) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_a_fun$ ?v2:N$ (fun_app$a(uvv$(?v0, ?v1), ?v2) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$j(?v1, fun_app$a(vec_nth$(?v0), ?v2))), fun_app$a(vec_nth$(?v0), ?v2)))
tff(axiom102,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_a_fun$',A__questionmark_v2: 'N$'] : 'fun_app$a'('uvv$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$j'(A__questionmark_v1,'fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v2))),'fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v2)) ).

%% ∀ ?v0:N_a_fun$ ?v1:N$ ?v2:N$ (fun_app$d(fun_app$e(uux$(?v0), ?v1), ?v2) = fun_app$k(fun_app$l(times$, fun_app$d(?v0, ?v2)), fun_app$d(vec_nth$a(fun_app$a(vec_nth$(y$), ?v2)), ?v1)))
tff(axiom103,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'fun_app$d'('fun_app$e'('uux$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$k'('fun_app$l'('times$','fun_app$d'(A__questionmark_v0,A__questionmark_v2)),'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'('y$'),A__questionmark_v2)),A__questionmark_v1)) ).

%% ∀ ?v0:N_a_fun$ ?v1:N$ ?v2:N$ (fun_app$d(fun_app$e(uuz$(?v0), ?v1), ?v2) = fun_app$k(fun_app$l(times$, fun_app$d(?v0, ?v2)), fun_app$d(vec_nth$a(fun_app$a(vec_nth$(x$), ?v2)), ?v1)))
tff(axiom104,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'fun_app$d'('fun_app$e'('uuz$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$k'('fun_app$l'('times$','fun_app$d'(A__questionmark_v0,A__questionmark_v2)),'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'('x$'),A__questionmark_v2)),A__questionmark_v1)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N_a_fun$ ?v2:N$ (fun_app$a(uvw$(?v0, ?v1), ?v2) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$d(?v1, ?v2)), fun_app$a(vec_nth$(?v0), ?v2)))
tff(axiom105,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N$'] : 'fun_app$a'('uvw$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$d'(A__questionmark_v1,A__questionmark_v2)),'fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v2)) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_a_n_vec_fun$ ?v2:N$ (fun_app$a(vdf$(?v0, ?v1), ?v2) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$d(?v0, ?v2)), fun_app$a(?v1, ?v2)))
tff(axiom106,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vdf$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$d'(A__questionmark_v0,A__questionmark_v2)),'fun_app$a'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_a_n_vec_fun$ ?v1:A_n_vec_a_n_vec_fun$ ?v2:A_n_vec$ (fun_app$b(vdr$(?v0, ?v1), ?v2) = fun_app$b(plus$(fun_app$b(?v0, ?v2)), fun_app$b(?v1, ?v2)))
tff(axiom107,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_n_vec_fun$',A__questionmark_v1: 'A_n_vec_a_n_vec_fun$',A__questionmark_v2: 'A_n_vec$'] : 'fun_app$b'('vdr$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('plus$'('fun_app$b'(A__questionmark_v0,A__questionmark_v2)),'fun_app$b'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:N_a_n_vec_fun$ ?v1:N_a_n_vec_fun$ ?v2:N$ (fun_app$a(vdp$(?v0, ?v1), ?v2) = fun_app$b(plus$(fun_app$a(?v0, ?v2)), fun_app$a(?v1, ?v2)))
tff(axiom108,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vdp$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('plus$'('fun_app$a'(A__questionmark_v0,A__questionmark_v2)),'fun_app$a'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_a_fun$ ?v2:N$ (fun_app$d(vdq$(?v0, ?v1), ?v2) = fun_app$k(plus$a(fun_app$d(?v0, ?v2)), fun_app$d(?v1, ?v2)))
tff(axiom109,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N$'] : 'fun_app$d'('vdq$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$k'('plus$a'('fun_app$d'(A__questionmark_v0,A__questionmark_v2)),'fun_app$d'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:Nat_bool_fun$ ?v1:Nat_bool_fun$ ?v2:Nat$ (fun_app$m(vcs$(?v0, ?v1), ?v2) = (fun_app$m(?v0, ?v2) ∨ fun_app$m(?v1, ?v2)))
tff(axiom110,axiom,
    ! [A__questionmark_v0: 'Nat_bool_fun$',A__questionmark_v1: 'Nat_bool_fun$',A__questionmark_v2: 'Nat$'] :
      ( 'fun_app$m'('vcs$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)
    <=> ( 'fun_app$m'(A__questionmark_v0,A__questionmark_v2)
        | 'fun_app$m'(A__questionmark_v1,A__questionmark_v2) ) ) ).

%% ∀ ?v0:Nat_bool_fun$ ?v1:Nat_bool_fun$ ?v2:Nat$ (fun_app$m(vcr$(?v0, ?v1), ?v2) = (fun_app$m(?v0, ?v2) ∧ fun_app$m(?v1, ?v2)))
tff(axiom111,axiom,
    ! [A__questionmark_v0: 'Nat_bool_fun$',A__questionmark_v1: 'Nat_bool_fun$',A__questionmark_v2: 'Nat$'] :
      ( 'fun_app$m'('vcr$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)
    <=> ( 'fun_app$m'(A__questionmark_v0,A__questionmark_v2)
        & 'fun_app$m'(A__questionmark_v1,A__questionmark_v2) ) ) ).

%% ∀ ?v0:A_n_vec_a_fun$ ?v1:A_n_vec$ ?v2:A_n_vec$ (fun_app$b(vay$(?v0, ?v1), ?v2) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$j(?v0, ?v2)), ?v1))
tff(axiom112,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_fun$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'A_n_vec$'] : 'fun_app$b'('vay$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$j'(A__questionmark_v0,A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:Nat_a_fun$ ?v1:A_n_vec$ ?v2:Nat$ (fun_app$ae(uun$(?v0, ?v1), ?v2) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$aa(?v0, ?v2)), ?v1))
tff(axiom113,axiom,
    ! [A__questionmark_v0: 'Nat_a_fun$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'Nat$'] : 'fun_app$ae'('uun$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$aa'(A__questionmark_v0,A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:N_n_fun_a_fun$ ?v1:A_n_vec$ ?v2:N_n_fun$ (fun_app$ar(uuo$(?v0, ?v1), ?v2) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$i(?v0, ?v2)), ?v1))
tff(axiom114,axiom,
    ! [A__questionmark_v0: 'N_n_fun_a_fun$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'N_n_fun$'] : 'fun_app$ar'('uuo$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$i'(A__questionmark_v0,A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:N_a_fun$ ?v1:A_n_vec$ ?v2:N$ (fun_app$a(uup$(?v0, ?v1), ?v2) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$d(?v0, ?v2)), ?v1))
tff(axiom115,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$a'('uup$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$d'(A__questionmark_v0,A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:Nat_nat_a_fun_fun$ ?v1:Nat_set$ ?v2:Nat$ (fun_app$aa(uyh$(?v0, ?v1), ?v2) = sum$d(fun_app$ab(?v0, ?v2), ?v1))
tff(axiom116,axiom,
    ! [A__questionmark_v0: 'Nat_nat_a_fun_fun$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'Nat$'] : 'fun_app$aa'('uyh$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$d'('fun_app$ab'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:Nat_n_n_fun_a_fun_fun$ ?v1:N_n_fun_set$ ?v2:Nat$ (fun_app$aa(uyq$(?v0, ?v1), ?v2) = sum$c(fun_app$ad(?v0, ?v2), ?v1))
tff(axiom117,axiom,
    ! [A__questionmark_v0: 'Nat_n_n_fun_a_fun_fun$',A__questionmark_v1: 'N_n_fun_set$',A__questionmark_v2: 'Nat$'] : 'fun_app$aa'('uyq$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$c'('fun_app$ad'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:Nat_n_a_fun_fun$ ?v1:N_set$ ?v2:Nat$ (fun_app$aa(uye$(?v0, ?v1), ?v2) = sum$a(fun_app$ai(?v0, ?v2), ?v1))
tff(axiom118,axiom,
    ! [A__questionmark_v0: 'Nat_n_a_fun_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'Nat$'] : 'fun_app$aa'('uye$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$a'('fun_app$ai'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_fun_nat_a_fun_fun$ ?v1:Nat_set$ ?v2:N_n_fun$ (fun_app$i(uyw$(?v0, ?v1), ?v2) = sum$d(fun_app$ac(?v0, ?v2), ?v1))
tff(axiom119,axiom,
    ! [A__questionmark_v0: 'N_n_fun_nat_a_fun_fun$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'N_n_fun$'] : 'fun_app$i'('uyw$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$d'('fun_app$ac'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_fun_n_a_fun_fun$ ?v1:N_set$ ?v2:N_n_fun$ (fun_app$i(uyt$(?v0, ?v1), ?v2) = sum$a(fun_app$ak(?v0, ?v2), ?v1))
tff(axiom120,axiom,
    ! [A__questionmark_v0: 'N_n_fun_n_a_fun_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_n_fun$'] : 'fun_app$i'('uyt$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$a'('fun_app$ak'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_nat_a_fun_fun$ ?v1:Nat_set$ ?v2:N$ (fun_app$d(uyb$(?v0, ?v1), ?v2) = sum$d(fun_app$ah(?v0, ?v2), ?v1))
tff(axiom121,axiom,
    ! [A__questionmark_v0: 'N_nat_a_fun_fun$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'N$'] : 'fun_app$d'('uyb$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$d'('fun_app$ah'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_n_fun_a_fun_fun$ ?v1:N_n_fun_set$ ?v2:N$ (fun_app$d(uyn$(?v0, ?v1), ?v2) = sum$c(fun_app$aj(?v0, ?v2), ?v1))
tff(axiom122,axiom,
    ! [A__questionmark_v0: 'N_n_n_fun_a_fun_fun$',A__questionmark_v1: 'N_n_fun_set$',A__questionmark_v2: 'N$'] : 'fun_app$d'('uyn$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$c'('fun_app$aj'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_a_n_vec_fun_fun$ ?v1:N_set$ ?v2:N$ (fun_app$a(uxy$(?v0, ?v1), ?v2) = sum$(fun_app$z(?v0, ?v2), ?v1))
tff(axiom123,axiom,
    ! [A__questionmark_v0: 'N_n_a_n_vec_fun_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N$'] : 'fun_app$a'('uxy$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$'('fun_app$z'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_a_set_fun_fun$ ?v1:N_set$ ?v2:N$ (fun_app$am(uyk$(?v0, ?v1), ?v2) = sum$e(fun_app$an(?v0, ?v2), ?v1))
tff(axiom124,axiom,
    ! [A__questionmark_v0: 'N_n_a_set_fun_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N$'] : 'fun_app$am'('uyk$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$e'('fun_app$an'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_a_fun_fun$ ?v1:N_set$ ?v2:N$ (fun_app$d(uxv$(?v0, ?v1), ?v2) = sum$a(fun_app$e(?v0, ?v2), ?v1))
tff(axiom125,axiom,
    ! [A__questionmark_v0: 'N_n_a_fun_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N$'] : 'fun_app$d'('uxv$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$a'('fun_app$e'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_set$ ?v1:N_n_a_n_vec_fun_fun$ ?v2:N$ (fun_app$a(vbm$(?v0, ?v1), ?v2) = sum$(fun_app$z(?v1, ?v2), ?v0))
tff(axiom126,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_n_a_n_vec_fun_fun$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vbm$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$'('fun_app$z'(A__questionmark_v1,A__questionmark_v2),A__questionmark_v0) ).

%% ∀ ?v0:Nat_a_n_vec_fun$ ?v1:N$ ?v2:Nat$ (fun_app$aa(fun_app$ah(uug$(?v0), ?v1), ?v2) = fun_app$d(vec_nth$a(fun_app$ae(?v0, ?v2)), ?v1))
tff(axiom127,axiom,
    ! [A__questionmark_v0: 'Nat_a_n_vec_fun$',A__questionmark_v1: 'N$',A__questionmark_v2: 'Nat$'] : 'fun_app$aa'('fun_app$ah'('uug$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$d'('vec_nth$a'('fun_app$ae'(A__questionmark_v0,A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:N_n_fun_a_n_vec_fun$ ?v1:N$ ?v2:N_n_fun$ (fun_app$i(fun_app$aj(uuh$(?v0), ?v1), ?v2) = fun_app$d(vec_nth$a(fun_app$ar(?v0, ?v2)), ?v1))
tff(axiom128,axiom,
    ! [A__questionmark_v0: 'N_n_fun_a_n_vec_fun$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N_n_fun$'] : 'fun_app$i'('fun_app$aj'('uuh$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$d'('vec_nth$a'('fun_app$ar'(A__questionmark_v0,A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:N_a_n_vec_n_vec_n_vec_fun$ ?v1:N$ ?v2:N$ (fun_app$f(uui$(?v0, ?v1), ?v2) = fun_app$f(vec_nth$b(fun_app$g(?v0, ?v2)), ?v1))
tff(axiom129,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_n_vec_n_vec_fun$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'fun_app$f'('uui$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$f'('vec_nth$b'('fun_app$g'(A__questionmark_v0,A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:N_a_n_vec_n_vec_fun$ ?v1:N$ ?v2:N$ (fun_app$a(fun_app$z(uuj$(?v0), ?v1), ?v2) = fun_app$a(vec_nth$(fun_app$f(?v0, ?v2)), ?v1))
tff(axiom130,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_n_vec_fun$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'fun_app$a'('fun_app$z'('uuj$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$a'('vec_nth$'('fun_app$f'(A__questionmark_v0,A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:N_a_n_vec_fun$ ?v1:N$ ?v2:N$ (fun_app$d(fun_app$e(uuk$(?v0), ?v1), ?v2) = fun_app$d(vec_nth$a(fun_app$a(?v0, ?v2)), ?v1))
tff(axiom131,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'fun_app$d'('fun_app$e'('uuk$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$d'('vec_nth$a'('fun_app$a'(A__questionmark_v0,A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:N_a_fun$ ?v1:A$ ?v2:N$ (fun_app$d(veh$(?v0, ?v1), ?v2) = fun_app$k(divide$(fun_app$d(?v0, ?v2)), ?v1))
tff(axiom132,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'A$',A__questionmark_v2: 'N$'] : 'fun_app$d'('veh$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$k'('divide$'('fun_app$d'(A__questionmark_v0,A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:Nat_a_fun$ ?v1:A$ ?v2:Nat$ (fun_app$aa(uvo$(?v0, ?v1), ?v2) = fun_app$k(fun_app$l(times$, fun_app$aa(?v0, ?v2)), ?v1))
tff(axiom133,axiom,
    ! [A__questionmark_v0: 'Nat_a_fun$',A__questionmark_v1: 'A$',A__questionmark_v2: 'Nat$'] : 'fun_app$aa'('uvo$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$k'('fun_app$l'('times$','fun_app$aa'(A__questionmark_v0,A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:N_n_fun_a_fun$ ?v1:A$ ?v2:N_n_fun$ (fun_app$i(uvp$(?v0, ?v1), ?v2) = fun_app$k(fun_app$l(times$, fun_app$i(?v0, ?v2)), ?v1))
tff(axiom134,axiom,
    ! [A__questionmark_v0: 'N_n_fun_a_fun$',A__questionmark_v1: 'A$',A__questionmark_v2: 'N_n_fun$'] : 'fun_app$i'('uvp$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$k'('fun_app$l'('times$','fun_app$i'(A__questionmark_v0,A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:N_a_n_vec_n_vec_fun$ ?v1:A_n_vec_n_vec$ ?v2:N$ (fun_app$f(uwr$(?v0, ?v1), ?v2) = times$a(fun_app$f(?v0, ?v2), ?v1))
tff(axiom135,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_n_vec_fun$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$f'('uwr$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'times$a'('fun_app$f'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_a_n_vec_fun$ ?v1:A_n_vec$ ?v2:N$ (fun_app$a(uws$(?v0, ?v1), ?v2) = fun_app$b(times$b(fun_app$a(?v0, ?v2)), ?v1))
tff(axiom136,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$a'('uws$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('times$b'('fun_app$a'(A__questionmark_v0,A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:N_a_fun$ ?v1:A$ ?v2:N$ (fun_app$d(uvq$(?v0, ?v1), ?v2) = fun_app$k(fun_app$l(times$, fun_app$d(?v0, ?v2)), ?v1))
tff(axiom137,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'A$',A__questionmark_v2: 'N$'] : 'fun_app$d'('uvq$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$k'('fun_app$l'('times$','fun_app$d'(A__questionmark_v0,A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec$ ?v2:N$ (fun_app$d(veg$(?v0, ?v1), ?v2) = fun_app$k(divide$(fun_app$w(det$, vec_lambda$a(fun_app$z(vef$(?v0, ?v1), ?v2)))), fun_app$w(det$, ?v0)))
tff(axiom138,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$d'('veg$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$k'('divide$'('fun_app$w'('det$','vec_lambda$a'('fun_app$z'('vef$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)))),'fun_app$w'('det$',A__questionmark_v0)) ).

%% ∀ ?v0:N_set$ ?v1:N_set$ ?v2:N_n_fun$ (fun_app$s(vdb$(?v0, ?v1), ?v2) = (∀ ?v3:N$ (member$f(?v3, ?v1) ⇒ member$f(fun_app$y(?v2, ?v3), ?v0)) ∧ ∀ ?v3:N$ (¬member$f(?v3, ?v1) ⇒ (fun_app$y(?v2, ?v3) = ?v3))))
tff(axiom139,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_n_fun$'] :
      ( 'fun_app$s'('vdb$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)
    <=> ( ! [A__questionmark_v3: 'N$'] :
            ( 'member$f'(A__questionmark_v3,A__questionmark_v1)
           => 'member$f'('fun_app$y'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v0) )
        & ! [A__questionmark_v3: 'N$'] :
            ( ~ 'member$f'(A__questionmark_v3,A__questionmark_v1)
           => ( 'fun_app$y'(A__questionmark_v2,A__questionmark_v3) = A__questionmark_v3 ) ) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec$ ?v2:N_a_fun$ (fun_app$(uzz$(?v0, ?v1), ?v2) = (?v1 = sum$(uvw$(?v0, ?v2), top$)))
tff(axiom140,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'N_a_fun$'] :
      ( 'fun_app$'('uzz$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)
    <=> ( A__questionmark_v1 = 'sum$'('uvw$'(A__questionmark_v0,A__questionmark_v2),'top$') ) ) ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ (fun_app$a(uzv$(?v0, ?v1), ?v2) = fun_app$b(times$b(?v0), fun_app$a(vec_nth$(?v1), ?v2)))
tff(axiom141,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$a'('uzv$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('times$b'(A__questionmark_v0),'fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A$ ?v1:A_n_vec$ ?v2:N$ (fun_app$d(uzw$(?v0, ?v1), ?v2) = fun_app$k(fun_app$l(times$, ?v0), fun_app$d(vec_nth$a(?v1), ?v2)))
tff(axiom142,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$d'('uzw$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),'fun_app$d'('vec_nth$a'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec$ ?v1:N_a_n_vec_n_vec_fun$ ?v2:N$ (fun_app$f(uut$(?v0, ?v1), ?v2) = vector_scalar_mult$a(?v0, fun_app$f(?v1, ?v2)))
tff(axiom143,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'N_a_n_vec_n_vec_fun$',A__questionmark_v2: 'N$'] : 'fun_app$f'('uut$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'vector_scalar_mult$a'(A__questionmark_v0,'fun_app$f'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A$ ?v1:N_a_n_vec_fun$ ?v2:N$ (fun_app$a(uuu$(?v0, ?v1), ?v2) = fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), fun_app$a(?v1, ?v2)))
tff(axiom144,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N$'] : 'fun_app$a'('uuu$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),'fun_app$a'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_a_n_vec_fun$ ?v1:A$ ?v2:A_n_vec$ (fun_app$b(vba$(?v0, ?v1), ?v2) = fun_app$b(fun_app$c(vector_scalar_mult$, ?v1), fun_app$b(?v0, ?v2)))
tff(axiom145,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_n_vec_fun$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A_n_vec$'] : 'fun_app$b'('vba$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v1),'fun_app$b'(A__questionmark_v0,A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N_a_n_vec_fun$ ?v2:N$ (fun_app$a(uzq$(?v0, ?v1), ?v2) = fun_app$b(matrix_vector_mult$(?v0), fun_app$a(?v1, ?v2)))
tff(axiom146,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N$'] : 'fun_app$a'('uzq$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('matrix_vector_mult$'(A__questionmark_v0),'fun_app$a'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N_a_n_vec_n_vec_fun$ ?v2:N$ (fun_app$f(uwp$(?v0, ?v1), ?v2) = times$a(?v0, fun_app$f(?v1, ?v2)))
tff(axiom147,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N_a_n_vec_n_vec_fun$',A__questionmark_v2: 'N$'] : 'fun_app$f'('uwp$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'times$a'(A__questionmark_v0,'fun_app$f'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec$ ?v1:N_a_n_vec_fun$ ?v2:N$ (fun_app$a(uwq$(?v0, ?v1), ?v2) = fun_app$b(times$b(?v0), fun_app$a(?v1, ?v2)))
tff(axiom148,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N$'] : 'fun_app$a'('uwq$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('times$b'(A__questionmark_v0),'fun_app$a'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A$ ?v1:Nat_a_fun$ ?v2:Nat$ (fun_app$aa(uvr$(?v0, ?v1), ?v2) = fun_app$k(fun_app$l(times$, ?v0), fun_app$aa(?v1, ?v2)))
tff(axiom149,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'Nat_a_fun$',A__questionmark_v2: 'Nat$'] : 'fun_app$aa'('uvr$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),'fun_app$aa'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A$ ?v1:N_n_fun_a_fun$ ?v2:N_n_fun$ (fun_app$i(uvs$(?v0, ?v1), ?v2) = fun_app$k(fun_app$l(times$, ?v0), fun_app$i(?v1, ?v2)))
tff(axiom150,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'N_n_fun_a_fun$',A__questionmark_v2: 'N_n_fun$'] : 'fun_app$i'('uvs$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),'fun_app$i'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A$ ?v1:N_a_fun$ ?v2:N$ (fun_app$d(uvt$(?v0, ?v1), ?v2) = fun_app$k(fun_app$l(times$, ?v0), fun_app$d(?v1, ?v2)))
tff(axiom151,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N$'] : 'fun_app$d'('uvt$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),'fun_app$d'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:Nat_nat_fun$ ?v1:Nat_bool_fun$ ?v2:Nat$ (fun_app$m(ved$(?v0, ?v1), ?v2) = (0 < (if fun_app$m(?v1, ?v2) of_nat$(fun_app$v(?v0, ?v2)) else 0)))
tff(axiom152,axiom,
    ! [A__questionmark_v0: 'Nat_nat_fun$',A__questionmark_v1: 'Nat_bool_fun$',A__questionmark_v2: 'Nat$'] :
      ( 'fun_app$m'('ved$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)
    <=> ( ( 'fun_app$m'(A__questionmark_v1,A__questionmark_v2)
         => $less(0,'of_nat$'('fun_app$v'(A__questionmark_v0,A__questionmark_v2))) )
        & ( ~ 'fun_app$m'(A__questionmark_v1,A__questionmark_v2)
         => $less(0,0) ) ) ) ).

%% ∀ ?v0:A_n_vec_a_n_vec_fun$ ?v1:N_a_n_vec_fun$ ?v2:N$ (fun_app$a(vbf$(?v0, ?v1), ?v2) = fun_app$b(?v0, fun_app$a(?v1, ?v2)))
tff(axiom153,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_n_vec_fun$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vbf$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'(A__questionmark_v0,'fun_app$a'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A$ ?v1:A_n_vec_n_vec$ ?v2:N$ (fun_app$a(vbl$(?v0, ?v1), ?v2) = vec_lambda$(fun_app$e(vbk$(?v0, ?v1), ?v2)))
tff(axiom154,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vbl$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'vec_lambda$'('fun_app$e'('vbk$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ (fun_app$a(vaj$(?v0, ?v1), ?v2) = vec_lambda$(fun_app$e(vai$(?v0, ?v1), ?v2)))
tff(axiom155,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vaj$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'vec_lambda$'('fun_app$e'('vai$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ (fun_app$a(vap$(?v0, ?v1), ?v2) = vec_lambda$(fun_app$e(uzg$(?v0, ?v1), ?v2)))
tff(axiom156,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vap$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'vec_lambda$'('fun_app$e'('uzg$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:A_n_vec$ (fun_app$p(fun_app$as(vej$(?v0), ?v1), ?v2) = ∃ ?v3:N$ ((?v2 = row$(?v3, ?v0)) ∧ ¬(?v3 = ?v1)))
tff(axiom157,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'A_n_vec$'] :
      ( 'fun_app$p'('fun_app$as'('vej$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2)
    <=> ? [A__questionmark_v3: 'N$'] :
          ( ( A__questionmark_v2 = 'row$'(A__questionmark_v3,A__questionmark_v0) )
          & ( A__questionmark_v3 != A__questionmark_v1 ) ) ) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_nat_set_fun$ ?v2:Nat$ (fun_app$m(vdc$(?v0, ?v1), ?v2) = ∃ ?v3:Nat_nat_fun$ ((?v2 = sum$f(?v3, ?v0)) ∧ ∀ ?v4:Nat$ (member$a(?v4, ?v0) ⇒ member$a(fun_app$v(?v3, ?v4), fun_app$at(?v1, ?v4)))))
tff(axiom158,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_nat_set_fun$',A__questionmark_v2: 'Nat$'] :
      ( 'fun_app$m'('vdc$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)
    <=> ? [A__questionmark_v3: 'Nat_nat_fun$'] :
          ( ( A__questionmark_v2 = 'sum$f'(A__questionmark_v3,A__questionmark_v0) )
          & ! [A__questionmark_v4: 'Nat$'] :
              ( 'member$a'(A__questionmark_v4,A__questionmark_v0)
             => 'member$a'('fun_app$v'(A__questionmark_v3,A__questionmark_v4),'fun_app$at'(A__questionmark_v1,A__questionmark_v4)) ) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_a_n_vec_set_fun$ ?v2:A_n_vec$ (fun_app$p(vdd$(?v0, ?v1), ?v2) = ∃ ?v3:N_a_n_vec_fun$ ((?v2 = sum$(?v3, ?v0)) ∧ ∀ ?v4:N$ (member$f(?v4, ?v0) ⇒ member$(fun_app$a(?v3, ?v4), fun_app$au(?v1, ?v4)))))
tff(axiom159,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_a_n_vec_set_fun$',A__questionmark_v2: 'A_n_vec$'] :
      ( 'fun_app$p'('vdd$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)
    <=> ? [A__questionmark_v3: 'N_a_n_vec_fun$'] :
          ( ( A__questionmark_v2 = 'sum$'(A__questionmark_v3,A__questionmark_v0) )
          & ! [A__questionmark_v4: 'N$'] :
              ( 'member$f'(A__questionmark_v4,A__questionmark_v0)
             => 'member$'('fun_app$a'(A__questionmark_v3,A__questionmark_v4),'fun_app$au'(A__questionmark_v1,A__questionmark_v4)) ) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_a_set_fun$ ?v2:A$ (fun_app$u(vde$(?v0, ?v1), ?v2) = ∃ ?v3:N_a_fun$ ((?v2 = sum$a(?v3, ?v0)) ∧ ∀ ?v4:N$ (member$f(?v4, ?v0) ⇒ member$g(fun_app$d(?v3, ?v4), fun_app$am(?v1, ?v4)))))
tff(axiom160,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_a_set_fun$',A__questionmark_v2: 'A$'] :
      ( 'fun_app$u'('vde$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)
    <=> ? [A__questionmark_v3: 'N_a_fun$'] :
          ( ( A__questionmark_v2 = 'sum$a'(A__questionmark_v3,A__questionmark_v0) )
          & ! [A__questionmark_v4: 'N$'] :
              ( 'member$f'(A__questionmark_v4,A__questionmark_v0)
             => 'member$g'('fun_app$d'(A__questionmark_v3,A__questionmark_v4),'fun_app$am'(A__questionmark_v1,A__questionmark_v4)) ) ) ) ).

%% ∀ ?v0:Nat_bool_fun$ ?v1:Nat_nat_fun$ ?v2:Nat$ (fun_app$m(vcu$(?v0, ?v1), ?v2) = ∃ ?v3:Nat$ ((?v2 = fun_app$v(?v1, ?v3)) ∧ fun_app$m(?v0, ?v3)))
tff(axiom161,axiom,
    ! [A__questionmark_v0: 'Nat_bool_fun$',A__questionmark_v1: 'Nat_nat_fun$',A__questionmark_v2: 'Nat$'] :
      ( 'fun_app$m'('vcu$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)
    <=> ? [A__questionmark_v3: 'Nat$'] :
          ( ( A__questionmark_v2 = 'fun_app$v'(A__questionmark_v1,A__questionmark_v3) )
          & 'fun_app$m'(A__questionmark_v0,A__questionmark_v3) ) ) ).

%% ∀ ?v0:Nat_bool_fun$ ?v1:Nat_nat_bool_fun_fun$ ?v2:Nat$ (fun_app$m(vcn$(?v0, ?v1), ?v2) = ∃ ?v3:Nat$ (fun_app$m(?v0, ?v3) ∧ fun_app$m(fun_app$n(?v1, ?v2), ?v3)))
tff(axiom162,axiom,
    ! [A__questionmark_v0: 'Nat_bool_fun$',A__questionmark_v1: 'Nat_nat_bool_fun_fun$',A__questionmark_v2: 'Nat$'] :
      ( 'fun_app$m'('vcn$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)
    <=> ? [A__questionmark_v3: 'Nat$'] :
          ( 'fun_app$m'(A__questionmark_v0,A__questionmark_v3)
          & 'fun_app$m'('fun_app$n'(A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) ) ) ).

%% ∀ ?v0:N$ ?v1:A_n_vec$ ?v2:A_n_vec_n_vec$ ?v3:N$ (fun_app$a(vbj$(?v0, ?v1, ?v2), ?v3) = (if (?v3 = ?v0) sum$(vbi$(?v1, ?v2), top$) else row$(?v3, ?v2)))
tff(axiom163,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'A_n_vec_n_vec$',A__questionmark_v3: 'N$'] :
      ( ( ( A__questionmark_v3 = A__questionmark_v0 )
       => ( 'fun_app$a'('vbj$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$'('vbi$'(A__questionmark_v1,A__questionmark_v2),'top$') ) )
      & ( ( A__questionmark_v3 != A__questionmark_v0 )
       => ( 'fun_app$a'('vbj$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'row$'(A__questionmark_v3,A__questionmark_v2) ) ) ) ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$a(fun_app$z(vek$(?v0, ?v1), ?v2), ?v3) = (if (?v3 = ?v2) fun_app$b(plus$(row$(?v2, ?v1)), ?v0) else row$(?v3, ?v1)))
tff(axiom164,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] :
      ( ( ( A__questionmark_v3 = A__questionmark_v2 )
       => ( 'fun_app$a'('fun_app$z'('vek$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'fun_app$b'('plus$'('row$'(A__questionmark_v2,A__questionmark_v1)),A__questionmark_v0) ) )
      & ( ( A__questionmark_v3 != A__questionmark_v2 )
       => ( 'fun_app$a'('fun_app$z'('vek$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'row$'(A__questionmark_v3,A__questionmark_v1) ) ) ) ).

%% ∀ ?v0:N$ ?v1:N_a_n_vec_fun$ ?v2:N_a_n_vec_fun$ ?v3:N$ (fun_app$a(vbh$(?v0, ?v1, ?v2), ?v3) = (if (?v3 = ?v0) fun_app$a(?v1, ?v3) else fun_app$a(?v2, ?v3)))
tff(axiom165,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N_a_n_vec_fun$',A__questionmark_v3: 'N$'] :
      ( ( ( A__questionmark_v3 = A__questionmark_v0 )
       => ( 'fun_app$a'('vbh$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'fun_app$a'(A__questionmark_v1,A__questionmark_v3) ) )
      & ( ( A__questionmark_v3 != A__questionmark_v0 )
       => ( 'fun_app$a'('vbh$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'fun_app$a'(A__questionmark_v2,A__questionmark_v3) ) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$d(fun_app$e(uzg$(?v0, ?v1), ?v2), ?v3) = sum$a(fun_app$e(uwo$(?v0, ?v1, ?v2), ?v3), top$))
tff(axiom166,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$d'('fun_app$e'('uzg$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'sum$a'('fun_app$e'('uwo$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),'top$') ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$a(fun_app$z(uzf$(?v0, ?v1), ?v2), ?v3) = sum$(fun_app$z(uwn$(?v0, ?v1, ?v2), ?v3), top$))
tff(axiom167,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$a'('fun_app$z'('uzf$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'sum$'('fun_app$z'('uwn$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),'top$') ).

%% ∀ ?v0:N_n_fun_a_fun$ ?v1:N_n_fun_a_fun$ ?v2:N_n_fun_set$ ?v3:N_n_fun$ (fun_app$i(uxm$(?v0, ?v1, ?v2), ?v3) = sum$c(uxl$(?v0, ?v1, ?v3), ?v2))
tff(axiom168,axiom,
    ! [A__questionmark_v0: 'N_n_fun_a_fun$',A__questionmark_v1: 'N_n_fun_a_fun$',A__questionmark_v2: 'N_n_fun_set$',A__questionmark_v3: 'N_n_fun$'] : 'fun_app$i'('uxm$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$c'('uxl$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v3),A__questionmark_v2) ).

%% ∀ ?v0:N_n_fun_a_fun$ ?v1:Nat_a_fun$ ?v2:Nat_set$ ?v3:N_n_fun$ (fun_app$i(uxk$(?v0, ?v1, ?v2), ?v3) = sum$d(fun_app$ac(uxj$(?v0, ?v1), ?v3), ?v2))
tff(axiom169,axiom,
    ! [A__questionmark_v0: 'N_n_fun_a_fun$',A__questionmark_v1: 'Nat_a_fun$',A__questionmark_v2: 'Nat_set$',A__questionmark_v3: 'N_n_fun$'] : 'fun_app$i'('uxk$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$d'('fun_app$ac'('uxj$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v3),A__questionmark_v2) ).

%% ∀ ?v0:N_n_fun_a_fun$ ?v1:N_a_fun$ ?v2:N_set$ ?v3:N_n_fun$ (fun_app$i(uxi$(?v0, ?v1, ?v2), ?v3) = sum$a(fun_app$ak(uxh$(?v0, ?v1), ?v3), ?v2))
tff(axiom170,axiom,
    ! [A__questionmark_v0: 'N_n_fun_a_fun$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N_set$',A__questionmark_v3: 'N_n_fun$'] : 'fun_app$i'('uxi$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$a'('fun_app$ak'('uxh$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v3),A__questionmark_v2) ).

%% ∀ ?v0:Nat_a_fun$ ?v1:N_n_fun_a_fun$ ?v2:N_n_fun_set$ ?v3:Nat$ (fun_app$aa(uxg$(?v0, ?v1, ?v2), ?v3) = sum$c(fun_app$ad(uxf$(?v0, ?v1), ?v3), ?v2))
tff(axiom171,axiom,
    ! [A__questionmark_v0: 'Nat_a_fun$',A__questionmark_v1: 'N_n_fun_a_fun$',A__questionmark_v2: 'N_n_fun_set$',A__questionmark_v3: 'Nat$'] : 'fun_app$aa'('uxg$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$c'('fun_app$ad'('uxf$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v3),A__questionmark_v2) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_n_fun_a_fun$ ?v2:N_n_fun_set$ ?v3:N$ (fun_app$d(uxe$(?v0, ?v1, ?v2), ?v3) = sum$c(fun_app$aj(uxd$(?v0, ?v1), ?v3), ?v2))
tff(axiom172,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_n_fun_a_fun$',A__questionmark_v2: 'N_n_fun_set$',A__questionmark_v3: 'N$'] : 'fun_app$d'('uxe$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$c'('fun_app$aj'('uxd$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v3),A__questionmark_v2) ).

%% ∀ ?v0:Nat_a_fun$ ?v1:Nat_a_fun$ ?v2:Nat_set$ ?v3:Nat$ (fun_app$aa(uxc$(?v0, ?v1, ?v2), ?v3) = sum$d(fun_app$ab(uxb$(?v0, ?v1), ?v3), ?v2))
tff(axiom173,axiom,
    ! [A__questionmark_v0: 'Nat_a_fun$',A__questionmark_v1: 'Nat_a_fun$',A__questionmark_v2: 'Nat_set$',A__questionmark_v3: 'Nat$'] : 'fun_app$aa'('uxc$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$d'('fun_app$ab'('uxb$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v3),A__questionmark_v2) ).

%% ∀ ?v0:Nat_a_fun$ ?v1:N_a_fun$ ?v2:N_set$ ?v3:Nat$ (fun_app$aa(uxa$(?v0, ?v1, ?v2), ?v3) = sum$a(fun_app$ai(uwz$(?v0, ?v1), ?v3), ?v2))
tff(axiom174,axiom,
    ! [A__questionmark_v0: 'Nat_a_fun$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N_set$',A__questionmark_v3: 'Nat$'] : 'fun_app$aa'('uxa$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$a'('fun_app$ai'('uwz$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v3),A__questionmark_v2) ).

%% ∀ ?v0:N_a_fun$ ?v1:Nat_a_fun$ ?v2:Nat_set$ ?v3:N$ (fun_app$d(uwy$(?v0, ?v1, ?v2), ?v3) = sum$d(fun_app$ah(uwx$(?v0, ?v1), ?v3), ?v2))
tff(axiom175,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'Nat_a_fun$',A__questionmark_v2: 'Nat_set$',A__questionmark_v3: 'N$'] : 'fun_app$d'('uwy$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$d'('fun_app$ah'('uwx$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v3),A__questionmark_v2) ).

%% ∀ ?v0:N_a_n_vec_fun$ ?v1:N_a_n_vec_fun$ ?v2:N_set$ ?v3:N$ (fun_app$a(uww$(?v0, ?v1, ?v2), ?v3) = sum$(fun_app$z(uwv$(?v0, ?v1), ?v3), ?v2))
tff(axiom176,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N_set$',A__questionmark_v3: 'N$'] : 'fun_app$a'('uww$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$'('fun_app$z'('uwv$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v3),A__questionmark_v2) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_a_fun$ ?v2:N_set$ ?v3:N$ (fun_app$d(uwu$(?v0, ?v1, ?v2), ?v3) = sum$a(fun_app$e(uwt$(?v0, ?v1), ?v3), ?v2))
tff(axiom177,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N_set$',A__questionmark_v3: 'N$'] : 'fun_app$d'('uwu$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$a'('fun_app$e'('uwt$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v3),A__questionmark_v2) ).

%% ∀ ?v0:N_set$ ?v1:N_nat_a_n_vec_fun_fun$ ?v2:N_nat_bool_fun_fun$ ?v3:Nat$ (fun_app$ae(vcb$(?v0, ?v1, ?v2), ?v3) = sum$(fun_app$ag(vbz$(?v1), ?v3), collect$(fun_app$av(vca$(?v0, ?v2), ?v3))))
tff(axiom178,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_nat_a_n_vec_fun_fun$',A__questionmark_v2: 'N_nat_bool_fun_fun$',A__questionmark_v3: 'Nat$'] : 'fun_app$ae'('vcb$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$'('fun_app$ag'('vbz$'(A__questionmark_v1),A__questionmark_v3),'collect$'('fun_app$av'('vca$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v3))) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_n_a_n_vec_fun_fun$ ?v2:Nat_n_bool_fun_fun$ ?v3:N$ (fun_app$a(vbu$(?v0, ?v1, ?v2), ?v3) = sum$g(fun_app$af(vbs$(?v1), ?v3), collect$a(fun_app$aw(vbt$(?v0, ?v2), ?v3))))
tff(axiom179,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_n_a_n_vec_fun_fun$',A__questionmark_v2: 'Nat_n_bool_fun_fun$',A__questionmark_v3: 'N$'] : 'fun_app$a'('vbu$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$g'('fun_app$af'('vbs$'(A__questionmark_v1),A__questionmark_v3),'collect$a'('fun_app$aw'('vbt$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v3))) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_n_a_fun_fun$ ?v2:Nat_n_bool_fun_fun$ ?v3:N$ (fun_app$d(vbw$(?v0, ?v1, ?v2), ?v3) = sum$d(fun_app$ah(uyf$(?v1), ?v3), collect$a(fun_app$aw(vbt$(?v0, ?v2), ?v3))))
tff(axiom180,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_n_a_fun_fun$',A__questionmark_v2: 'Nat_n_bool_fun_fun$',A__questionmark_v3: 'N$'] : 'fun_app$d'('vbw$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$d'('fun_app$ah'('uyf$'(A__questionmark_v1),A__questionmark_v3),'collect$a'('fun_app$aw'('vbt$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v3))) ).

%% ∀ ?v0:N_set$ ?v1:N_nat_a_fun_fun$ ?v2:N_nat_bool_fun_fun$ ?v3:Nat$ (fun_app$aa(vch$(?v0, ?v1, ?v2), ?v3) = sum$a(fun_app$ai(uyc$(?v1), ?v3), collect$(fun_app$av(vca$(?v0, ?v2), ?v3))))
tff(axiom181,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_nat_a_fun_fun$',A__questionmark_v2: 'N_nat_bool_fun_fun$',A__questionmark_v3: 'Nat$'] : 'fun_app$aa'('vch$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$a'('fun_app$ai'('uyc$'(A__questionmark_v1),A__questionmark_v3),'collect$'('fun_app$av'('vca$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v3))) ).

%% ∀ ?v0:N_set$ ?v1:N_n_a_n_vec_fun_fun$ ?v2:N_n_bool_fun_fun$ ?v3:N$ (fun_app$a(vcf$(?v0, ?v1, ?v2), ?v3) = sum$(fun_app$z(uxz$(?v1), ?v3), collect$(fun_app$ax(vce$(?v0, ?v2), ?v3))))
tff(axiom182,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_n_a_n_vec_fun_fun$',A__questionmark_v2: 'N_n_bool_fun_fun$',A__questionmark_v3: 'N$'] : 'fun_app$a'('vcf$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$'('fun_app$z'('uxz$'(A__questionmark_v1),A__questionmark_v3),'collect$'('fun_app$ax'('vce$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v3))) ).

%% ∀ ?v0:N_set$ ?v1:N_n_a_fun_fun$ ?v2:N_n_bool_fun_fun$ ?v3:N$ (fun_app$d(vcj$(?v0, ?v1, ?v2), ?v3) = sum$a(fun_app$e(uxw$(?v1), ?v3), collect$(fun_app$ax(vce$(?v0, ?v2), ?v3))))
tff(axiom183,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_n_a_fun_fun$',A__questionmark_v2: 'N_n_bool_fun_fun$',A__questionmark_v3: 'N$'] : 'fun_app$d'('vcj$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$a'('fun_app$e'('uxw$'(A__questionmark_v1),A__questionmark_v3),'collect$'('fun_app$ax'('vce$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v3))) ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$f(vat$(?v0, ?v1, ?v2), ?v3) = vector_scalar_mult$a(fun_app$a(vec_nth$(fun_app$f(vec_nth$b(?v0), ?v2)), ?v3), fun_app$f(vec_nth$b(?v1), ?v3)))
tff(axiom184,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$f'('vat$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'vector_scalar_mult$a'('fun_app$a'('vec_nth$'('fun_app$f'('vec_nth$b'(A__questionmark_v0),A__questionmark_v2)),A__questionmark_v3),'fun_app$f'('vec_nth$b'(A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$a(fun_app$z(vav$(?v0, ?v1), ?v2), ?v3) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v2)), ?v3)), fun_app$a(vec_nth$(?v1), ?v3)))
tff(axiom185,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$a'('fun_app$z'('vav$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v2)),A__questionmark_v3)),'fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$a(fun_app$z(uwm$(?v0, ?v1), ?v2), ?v3) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v1), ?v3)), ?v2)), fun_app$a(vec_nth$(?v0), ?v3)))
tff(axiom186,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$a'('fun_app$z'('uwm$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v3)),A__questionmark_v2)),'fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$f(uzj$(?v0, ?v1, ?v2), ?v3) = times$a(fun_app$f(vec_nth$b(fun_app$g(vec_nth$c(?v0), ?v2)), ?v3), fun_app$f(vec_nth$b(?v1), ?v3)))
tff(axiom187,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$f'('uzj$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'times$a'('fun_app$f'('vec_nth$b'('fun_app$g'('vec_nth$c'(A__questionmark_v0),A__questionmark_v2)),A__questionmark_v3),'fun_app$f'('vec_nth$b'(A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$a(fun_app$z(uzk$(?v0, ?v1), ?v2), ?v3) = fun_app$b(times$b(fun_app$a(vec_nth$(fun_app$f(vec_nth$b(?v0), ?v2)), ?v3)), fun_app$a(vec_nth$(?v1), ?v3)))
tff(axiom188,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$a'('fun_app$z'('uzk$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'fun_app$b'('times$b'('fun_app$a'('vec_nth$'('fun_app$f'('vec_nth$b'(A__questionmark_v0),A__questionmark_v2)),A__questionmark_v3)),'fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:Nat_n_vec_n_vec$ ?v1:Nat_n_vec$ ?v2:N$ ?v3:N$ (fun_app$h(uzh$(?v0, ?v1, ?v2), ?v3) = fun_app$v(fun_app$ao(times$c, fun_app$h(vec_nth$d(vec_nth$e(?v0, ?v2)), ?v3)), fun_app$h(vec_nth$d(?v1), ?v3)))
tff(axiom189,axiom,
    ! [A__questionmark_v0: 'Nat_n_vec_n_vec$',A__questionmark_v1: 'Nat_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$h'('uzh$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'fun_app$v'('fun_app$ao'('times$c','fun_app$h'('vec_nth$d'('vec_nth$e'(A__questionmark_v0,A__questionmark_v2)),A__questionmark_v3)),'fun_app$h'('vec_nth$d'(A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_n_fun_vec_n_vec$ ?v1:A_n_n_fun_vec$ ?v2:N$ ?v3:N_n_fun$ (fun_app$i(fun_app$aj(uzi$(?v0, ?v1), ?v2), ?v3) = fun_app$k(fun_app$l(times$, fun_app$i(vec_nth$f(vec_nth$l(?v0, ?v2)), ?v3)), fun_app$i(vec_nth$f(?v1), ?v3)))
tff(axiom190,axiom,
    ! [A__questionmark_v0: 'A_n_n_fun_vec_n_vec$',A__questionmark_v1: 'A_n_n_fun_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N_n_fun$'] : 'fun_app$i'('fun_app$aj'('uzi$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'fun_app$k'('fun_app$l'('times$','fun_app$i'('vec_nth$f'('vec_nth$l'(A__questionmark_v0,A__questionmark_v2)),A__questionmark_v3)),'fun_app$i'('vec_nth$f'(A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec$ ?v2:N$ ?v3:N$ (fun_app$d(fun_app$e(uzl$(?v0, ?v1), ?v2), ?v3) = fun_app$k(fun_app$l(times$, fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v2)), ?v3)), fun_app$d(vec_nth$a(?v1), ?v3)))
tff(axiom191,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$d'('fun_app$e'('uzl$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'fun_app$k'('fun_app$l'('times$','fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v2)),A__questionmark_v3)),'fun_app$d'('vec_nth$a'(A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$f(uzc$(?v0, ?v1, ?v2), ?v3) = times$a(fun_app$f(vec_nth$b(fun_app$g(vec_nth$c(?v1), ?v3)), ?v2), fun_app$f(vec_nth$b(?v0), ?v3)))
tff(axiom192,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$f'('uzc$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'times$a'('fun_app$f'('vec_nth$b'('fun_app$g'('vec_nth$c'(A__questionmark_v1),A__questionmark_v3)),A__questionmark_v2),'fun_app$f'('vec_nth$b'(A__questionmark_v0),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$a(fun_app$z(uzd$(?v0, ?v1), ?v2), ?v3) = fun_app$b(times$b(fun_app$a(vec_nth$(fun_app$f(vec_nth$b(?v1), ?v3)), ?v2)), fun_app$a(vec_nth$(?v0), ?v3)))
tff(axiom193,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$a'('fun_app$z'('uzd$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'fun_app$b'('times$b'('fun_app$a'('vec_nth$'('fun_app$f'('vec_nth$b'(A__questionmark_v1),A__questionmark_v3)),A__questionmark_v2)),'fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v3)) ).

%% ∀ ?v0:Nat_n_vec$ ?v1:Nat_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$h(uza$(?v0, ?v1, ?v2), ?v3) = fun_app$v(fun_app$ao(times$c, fun_app$h(vec_nth$d(vec_nth$e(?v1, ?v3)), ?v2)), fun_app$h(vec_nth$d(?v0), ?v3)))
tff(axiom194,axiom,
    ! [A__questionmark_v0: 'Nat_n_vec$',A__questionmark_v1: 'Nat_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$h'('uza$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'fun_app$v'('fun_app$ao'('times$c','fun_app$h'('vec_nth$d'('vec_nth$e'(A__questionmark_v1,A__questionmark_v3)),A__questionmark_v2)),'fun_app$h'('vec_nth$d'(A__questionmark_v0),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_n_fun_vec$ ?v1:A_n_vec_n_n_fun_vec$ ?v2:N$ ?v3:N_n_fun$ (fun_app$i(fun_app$aj(uzb$(?v0, ?v1), ?v2), ?v3) = fun_app$k(fun_app$l(times$, fun_app$d(vec_nth$a(fun_app$ar(vec_nth$m(?v1), ?v3)), ?v2)), fun_app$i(vec_nth$f(?v0), ?v3)))
tff(axiom195,axiom,
    ! [A__questionmark_v0: 'A_n_n_fun_vec$',A__questionmark_v1: 'A_n_vec_n_n_fun_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N_n_fun$'] : 'fun_app$i'('fun_app$aj'('uzb$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'fun_app$k'('fun_app$l'('times$','fun_app$d'('vec_nth$a'('fun_app$ar'('vec_nth$m'(A__questionmark_v1),A__questionmark_v3)),A__questionmark_v2)),'fun_app$i'('vec_nth$f'(A__questionmark_v0),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$d(fun_app$e(uze$(?v0, ?v1), ?v2), ?v3) = fun_app$k(fun_app$l(times$, fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v1), ?v3)), ?v2)), fun_app$d(vec_nth$a(?v0), ?v3)))
tff(axiom196,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$d'('fun_app$e'('uze$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'fun_app$k'('fun_app$l'('times$','fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v3)),A__questionmark_v2)),'fun_app$d'('vec_nth$a'(A__questionmark_v0),A__questionmark_v3)) ).

%% ∀ ?v0:Bool ?v1:N_a_fun$ ?v2:N_a_fun$ ?v3:N_a_fun$ (fun_app$(uus$(?v0, ?v1, ?v2), ?v3) = (((?v0 = true) ⇒ (?v3 = ?v1)) ∧ ((?v0 = false) ⇒ (?v3 = ?v2))))
tff(axiom197,axiom,
    ! [A__questionmark_v0: tlbool,A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N_a_fun$',A__questionmark_v3: 'N_a_fun$'] :
      ( 'fun_app$'('uus$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3)
    <=> ( ( ( ( A__questionmark_v0 = tltrue )
          <=> $true )
         => ( A__questionmark_v3 = A__questionmark_v1 ) )
        & ( ( ( A__questionmark_v0 = tltrue )
          <=> $false )
         => ( A__questionmark_v3 = A__questionmark_v2 ) ) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$d(fun_app$e(vai$(?v0, ?v1), ?v2), ?v3) = fun_app$d(vec_nth$a(fun_app$b(coord$(?v1), fun_app$a(vec_nth$(?v0), ?v3))), ?v2))
tff(axiom198,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$d'('fun_app$e'('vai$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'fun_app$d'('vec_nth$a'('fun_app$b'('coord$'(A__questionmark_v1),'fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v3))),A__questionmark_v2) ).

%% ∀ ?v0:Nat_set$ ?v1:N_nat_bool_fun_fun$ ?v2:N$ ?v3:Nat$ (fun_app$m(fun_app$aw(vbx$(?v0, ?v1), ?v2), ?v3) = (member$a(?v3, ?v0) ∧ fun_app$m(fun_app$aw(?v1, ?v2), ?v3)))
tff(axiom199,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'N_nat_bool_fun_fun$',A__questionmark_v2: 'N$',A__questionmark_v3: 'Nat$'] :
      ( 'fun_app$m'('fun_app$aw'('vbx$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3)
    <=> ( 'member$a'(A__questionmark_v3,A__questionmark_v0)
        & 'fun_app$m'('fun_app$aw'(A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) ) ) ).

%% ∀ ?v0:N_set$ ?v1:Nat_n_bool_fun_fun$ ?v2:Nat$ ?v3:N$ (fun_app$t(fun_app$av(vbq$(?v0, ?v1), ?v2), ?v3) = (member$f(?v3, ?v0) ∧ fun_app$t(fun_app$av(?v1, ?v2), ?v3)))
tff(axiom200,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'Nat_n_bool_fun_fun$',A__questionmark_v2: 'Nat$',A__questionmark_v3: 'N$'] :
      ( 'fun_app$t'('fun_app$av'('vbq$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3)
    <=> ( 'member$f'(A__questionmark_v3,A__questionmark_v0)
        & 'fun_app$t'('fun_app$av'(A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_n_bool_fun_fun$ ?v2:N$ ?v3:N$ (fun_app$t(fun_app$ax(vcc$(?v0, ?v1), ?v2), ?v3) = (member$f(?v3, ?v0) ∧ fun_app$t(fun_app$ax(?v1, ?v2), ?v3)))
tff(axiom201,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_n_bool_fun_fun$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] :
      ( 'fun_app$t'('fun_app$ax'('vcc$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3)
    <=> ( 'member$f'(A__questionmark_v3,A__questionmark_v0)
        & 'fun_app$t'('fun_app$ax'(A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) ) ) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_nat_bool_fun_fun$ ?v2:Nat$ ?v3:Nat$ (fun_app$m(fun_app$n(vct$(?v0, ?v1), ?v2), ?v3) = (member$a(?v3, ?v0) ∧ fun_app$m(fun_app$n(?v1, ?v3), ?v2)))
tff(axiom202,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_nat_bool_fun_fun$',A__questionmark_v2: 'Nat$',A__questionmark_v3: 'Nat$'] :
      ( 'fun_app$m'('fun_app$n'('vct$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3)
    <=> ( 'member$a'(A__questionmark_v3,A__questionmark_v0)
        & 'fun_app$m'('fun_app$n'(A__questionmark_v1,A__questionmark_v3),A__questionmark_v2) ) ) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_n_bool_fun_fun$ ?v2:N$ ?v3:Nat$ (fun_app$m(fun_app$aw(vbt$(?v0, ?v1), ?v2), ?v3) = (member$a(?v3, ?v0) ∧ fun_app$t(fun_app$av(?v1, ?v3), ?v2)))
tff(axiom203,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_n_bool_fun_fun$',A__questionmark_v2: 'N$',A__questionmark_v3: 'Nat$'] :
      ( 'fun_app$m'('fun_app$aw'('vbt$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3)
    <=> ( 'member$a'(A__questionmark_v3,A__questionmark_v0)
        & 'fun_app$t'('fun_app$av'(A__questionmark_v1,A__questionmark_v3),A__questionmark_v2) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_nat_bool_fun_fun$ ?v2:Nat$ ?v3:N$ (fun_app$t(fun_app$av(vca$(?v0, ?v1), ?v2), ?v3) = (member$f(?v3, ?v0) ∧ fun_app$m(fun_app$aw(?v1, ?v3), ?v2)))
tff(axiom204,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_nat_bool_fun_fun$',A__questionmark_v2: 'Nat$',A__questionmark_v3: 'N$'] :
      ( 'fun_app$t'('fun_app$av'('vca$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3)
    <=> ( 'member$f'(A__questionmark_v3,A__questionmark_v0)
        & 'fun_app$m'('fun_app$aw'(A__questionmark_v1,A__questionmark_v3),A__questionmark_v2) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_n_bool_fun_fun$ ?v2:N$ ?v3:N$ (fun_app$t(fun_app$ax(vce$(?v0, ?v1), ?v2), ?v3) = (member$f(?v3, ?v0) ∧ fun_app$t(fun_app$ax(?v1, ?v3), ?v2)))
tff(axiom205,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_n_bool_fun_fun$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] :
      ( 'fun_app$t'('fun_app$ax'('vce$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3)
    <=> ( 'member$f'(A__questionmark_v3,A__questionmark_v0)
        & 'fun_app$t'('fun_app$ax'(A__questionmark_v1,A__questionmark_v3),A__questionmark_v2) ) ) ).

%% ∀ ?v0:Nat_a_fun$ ?v1:Nat_a_fun$ ?v2:Nat$ ?v3:Nat$ (fun_app$aa(fun_app$ab(uxb$(?v0, ?v1), ?v2), ?v3) = fun_app$k(fun_app$l(times$, fun_app$aa(?v0, ?v2)), fun_app$aa(?v1, ?v3)))
tff(axiom206,axiom,
    ! [A__questionmark_v0: 'Nat_a_fun$',A__questionmark_v1: 'Nat_a_fun$',A__questionmark_v2: 'Nat$',A__questionmark_v3: 'Nat$'] : 'fun_app$aa'('fun_app$ab'('uxb$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'fun_app$k'('fun_app$l'('times$','fun_app$aa'(A__questionmark_v0,A__questionmark_v2)),'fun_app$aa'(A__questionmark_v1,A__questionmark_v3)) ).

%% ∀ ?v0:Nat_a_fun$ ?v1:N_n_fun_a_fun$ ?v2:Nat$ ?v3:N_n_fun$ (fun_app$i(fun_app$ad(uxf$(?v0, ?v1), ?v2), ?v3) = fun_app$k(fun_app$l(times$, fun_app$aa(?v0, ?v2)), fun_app$i(?v1, ?v3)))
tff(axiom207,axiom,
    ! [A__questionmark_v0: 'Nat_a_fun$',A__questionmark_v1: 'N_n_fun_a_fun$',A__questionmark_v2: 'Nat$',A__questionmark_v3: 'N_n_fun$'] : 'fun_app$i'('fun_app$ad'('uxf$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'fun_app$k'('fun_app$l'('times$','fun_app$aa'(A__questionmark_v0,A__questionmark_v2)),'fun_app$i'(A__questionmark_v1,A__questionmark_v3)) ).

%% ∀ ?v0:Nat_a_fun$ ?v1:N_a_fun$ ?v2:Nat$ ?v3:N$ (fun_app$d(fun_app$ai(uwz$(?v0, ?v1), ?v2), ?v3) = fun_app$k(fun_app$l(times$, fun_app$aa(?v0, ?v2)), fun_app$d(?v1, ?v3)))
tff(axiom208,axiom,
    ! [A__questionmark_v0: 'Nat_a_fun$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'Nat$',A__questionmark_v3: 'N$'] : 'fun_app$d'('fun_app$ai'('uwz$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'fun_app$k'('fun_app$l'('times$','fun_app$aa'(A__questionmark_v0,A__questionmark_v2)),'fun_app$d'(A__questionmark_v1,A__questionmark_v3)) ).

%% ∀ ?v0:N_n_fun_a_fun$ ?v1:Nat_a_fun$ ?v2:N_n_fun$ ?v3:Nat$ (fun_app$aa(fun_app$ac(uxj$(?v0, ?v1), ?v2), ?v3) = fun_app$k(fun_app$l(times$, fun_app$i(?v0, ?v2)), fun_app$aa(?v1, ?v3)))
tff(axiom209,axiom,
    ! [A__questionmark_v0: 'N_n_fun_a_fun$',A__questionmark_v1: 'Nat_a_fun$',A__questionmark_v2: 'N_n_fun$',A__questionmark_v3: 'Nat$'] : 'fun_app$aa'('fun_app$ac'('uxj$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'fun_app$k'('fun_app$l'('times$','fun_app$i'(A__questionmark_v0,A__questionmark_v2)),'fun_app$aa'(A__questionmark_v1,A__questionmark_v3)) ).

%% ∀ ?v0:N_n_fun_a_fun$ ?v1:N_n_fun_a_fun$ ?v2:N_n_fun$ ?v3:N_n_fun$ (fun_app$i(uxl$(?v0, ?v1, ?v2), ?v3) = fun_app$k(fun_app$l(times$, fun_app$i(?v0, ?v2)), fun_app$i(?v1, ?v3)))
tff(axiom210,axiom,
    ! [A__questionmark_v0: 'N_n_fun_a_fun$',A__questionmark_v1: 'N_n_fun_a_fun$',A__questionmark_v2: 'N_n_fun$',A__questionmark_v3: 'N_n_fun$'] : 'fun_app$i'('uxl$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'fun_app$k'('fun_app$l'('times$','fun_app$i'(A__questionmark_v0,A__questionmark_v2)),'fun_app$i'(A__questionmark_v1,A__questionmark_v3)) ).

%% ∀ ?v0:N_n_fun_a_fun$ ?v1:N_a_fun$ ?v2:N_n_fun$ ?v3:N$ (fun_app$d(fun_app$ak(uxh$(?v0, ?v1), ?v2), ?v3) = fun_app$k(fun_app$l(times$, fun_app$i(?v0, ?v2)), fun_app$d(?v1, ?v3)))
tff(axiom211,axiom,
    ! [A__questionmark_v0: 'N_n_fun_a_fun$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N_n_fun$',A__questionmark_v3: 'N$'] : 'fun_app$d'('fun_app$ak'('uxh$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'fun_app$k'('fun_app$l'('times$','fun_app$i'(A__questionmark_v0,A__questionmark_v2)),'fun_app$d'(A__questionmark_v1,A__questionmark_v3)) ).

%% ∀ ?v0:N_a_n_vec_fun$ ?v1:N_a_n_vec_fun$ ?v2:N$ ?v3:N$ (fun_app$a(fun_app$z(uwv$(?v0, ?v1), ?v2), ?v3) = fun_app$b(times$b(fun_app$a(?v0, ?v2)), fun_app$a(?v1, ?v3)))
tff(axiom212,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$a'('fun_app$z'('uwv$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'fun_app$b'('times$b'('fun_app$a'(A__questionmark_v0,A__questionmark_v2)),'fun_app$a'(A__questionmark_v1,A__questionmark_v3)) ).

%% ∀ ?v0:N_a_fun$ ?v1:Nat_a_fun$ ?v2:N$ ?v3:Nat$ (fun_app$aa(fun_app$ah(uwx$(?v0, ?v1), ?v2), ?v3) = fun_app$k(fun_app$l(times$, fun_app$d(?v0, ?v2)), fun_app$aa(?v1, ?v3)))
tff(axiom213,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'Nat_a_fun$',A__questionmark_v2: 'N$',A__questionmark_v3: 'Nat$'] : 'fun_app$aa'('fun_app$ah'('uwx$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'fun_app$k'('fun_app$l'('times$','fun_app$d'(A__questionmark_v0,A__questionmark_v2)),'fun_app$aa'(A__questionmark_v1,A__questionmark_v3)) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_n_fun_a_fun$ ?v2:N$ ?v3:N_n_fun$ (fun_app$i(fun_app$aj(uxd$(?v0, ?v1), ?v2), ?v3) = fun_app$k(fun_app$l(times$, fun_app$d(?v0, ?v2)), fun_app$i(?v1, ?v3)))
tff(axiom214,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_n_fun_a_fun$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N_n_fun$'] : 'fun_app$i'('fun_app$aj'('uxd$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'fun_app$k'('fun_app$l'('times$','fun_app$d'(A__questionmark_v0,A__questionmark_v2)),'fun_app$i'(A__questionmark_v1,A__questionmark_v3)) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_a_fun$ ?v2:N$ ?v3:N$ (fun_app$d(fun_app$e(uwt$(?v0, ?v1), ?v2), ?v3) = fun_app$k(fun_app$l(times$, fun_app$d(?v0, ?v2)), fun_app$d(?v1, ?v3)))
tff(axiom215,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$d'('fun_app$e'('uwt$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'fun_app$k'('fun_app$l'('times$','fun_app$d'(A__questionmark_v0,A__questionmark_v2)),'fun_app$d'(A__questionmark_v1,A__questionmark_v3)) ).

%% ∀ ?v0:N_set$ ?v1:N_n_a_n_vec_fun_fun$ ?v2:N_n_bool_fun_fun$ ?v3:N$ (fun_app$a(vcd$(?v0, ?v1, ?v2), ?v3) = sum$(fun_app$z(?v1, ?v3), collect$(fun_app$ax(vcc$(?v0, ?v2), ?v3))))
tff(axiom216,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_n_a_n_vec_fun_fun$',A__questionmark_v2: 'N_n_bool_fun_fun$',A__questionmark_v3: 'N$'] : 'fun_app$a'('vcd$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$'('fun_app$z'(A__questionmark_v1,A__questionmark_v3),'collect$'('fun_app$ax'('vcc$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v3))) ).

%% ∀ ?v0:N_set$ ?v1:N_n_a_fun_fun$ ?v2:N_n_bool_fun_fun$ ?v3:N$ (fun_app$d(vci$(?v0, ?v1, ?v2), ?v3) = sum$a(fun_app$e(?v1, ?v3), collect$(fun_app$ax(vcc$(?v0, ?v2), ?v3))))
tff(axiom217,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_n_a_fun_fun$',A__questionmark_v2: 'N_n_bool_fun_fun$',A__questionmark_v3: 'N$'] : 'fun_app$d'('vci$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$a'('fun_app$e'(A__questionmark_v1,A__questionmark_v3),'collect$'('fun_app$ax'('vcc$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v3))) ).

%% ∀ ?v0:Nat_set$ ?v1:N_nat_a_n_vec_fun_fun$ ?v2:N_nat_bool_fun_fun$ ?v3:N$ (fun_app$a(vby$(?v0, ?v1, ?v2), ?v3) = sum$g(fun_app$af(?v1, ?v3), collect$a(fun_app$aw(vbx$(?v0, ?v2), ?v3))))
tff(axiom218,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'N_nat_a_n_vec_fun_fun$',A__questionmark_v2: 'N_nat_bool_fun_fun$',A__questionmark_v3: 'N$'] : 'fun_app$a'('vby$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$g'('fun_app$af'(A__questionmark_v1,A__questionmark_v3),'collect$a'('fun_app$aw'('vbx$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v3))) ).

%% ∀ ?v0:Nat_set$ ?v1:N_nat_a_fun_fun$ ?v2:N_nat_bool_fun_fun$ ?v3:N$ (fun_app$d(vcg$(?v0, ?v1, ?v2), ?v3) = sum$d(fun_app$ah(?v1, ?v3), collect$a(fun_app$aw(vbx$(?v0, ?v2), ?v3))))
tff(axiom219,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'N_nat_a_fun_fun$',A__questionmark_v2: 'N_nat_bool_fun_fun$',A__questionmark_v3: 'N$'] : 'fun_app$d'('vcg$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$d'('fun_app$ah'(A__questionmark_v1,A__questionmark_v3),'collect$a'('fun_app$aw'('vbx$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v3))) ).

%% ∀ ?v0:N_set$ ?v1:Nat_n_a_n_vec_fun_fun$ ?v2:Nat_n_bool_fun_fun$ ?v3:Nat$ (fun_app$ae(vbr$(?v0, ?v1, ?v2), ?v3) = sum$(fun_app$ag(?v1, ?v3), collect$(fun_app$av(vbq$(?v0, ?v2), ?v3))))
tff(axiom220,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'Nat_n_a_n_vec_fun_fun$',A__questionmark_v2: 'Nat_n_bool_fun_fun$',A__questionmark_v3: 'Nat$'] : 'fun_app$ae'('vbr$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$'('fun_app$ag'(A__questionmark_v1,A__questionmark_v3),'collect$'('fun_app$av'('vbq$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v3))) ).

%% ∀ ?v0:N_set$ ?v1:Nat_n_a_fun_fun$ ?v2:Nat_n_bool_fun_fun$ ?v3:Nat$ (fun_app$aa(vbv$(?v0, ?v1, ?v2), ?v3) = sum$a(fun_app$ai(?v1, ?v3), collect$(fun_app$av(vbq$(?v0, ?v2), ?v3))))
tff(axiom221,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'Nat_n_a_fun_fun$',A__questionmark_v2: 'Nat_n_bool_fun_fun$',A__questionmark_v3: 'Nat$'] : 'fun_app$aa'('vbv$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'sum$a'('fun_app$ai'(A__questionmark_v1,A__questionmark_v3),'collect$'('fun_app$av'('vbq$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v3))) ).

%% ∀ ?v0:A$ ?v1:A_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$d(fun_app$e(vbk$(?v0, ?v1), ?v2), ?v3) = fun_app$k(fun_app$l(times$, ?v0), fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v1), ?v2)), ?v3)))
tff(axiom222,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$d'('fun_app$e'('vbk$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v2)),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec$ ?v2:N$ ?v3:N$ (fun_app$a(fun_app$z(vef$(?v0, ?v1), ?v2), ?v3) = vec_lambda$(fun_app$e(vee$(?v0, ?v1, ?v2), ?v3)))
tff(axiom223,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$a'('fun_app$z'('vef$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'vec_lambda$'('fun_app$e'('vee$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3)) ).

%% ∀ ?v0:N$ ?v1:A_n_vec_n_vec$ ?v2:A_n_vec$ ?v3:N$ (fun_app$a(var$(?v0, ?v1, ?v2), ?v3) = vec_lambda$(fun_app$e(vaq$(?v0, ?v1, ?v2), ?v3)))
tff(axiom224,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'A_n_vec$',A__questionmark_v3: 'N$'] : 'fun_app$a'('var$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'vec_lambda$'('fun_app$e'('vaq$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ ?v3:N$ (fun_app$a(fun_app$z(vas$(?v0, ?v1), ?v2), ?v3) = vec_lambda$(fun_app$e(vam$(?v0, ?v1, ?v2), ?v3)))
tff(axiom225,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$a'('fun_app$z'('vas$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'vec_lambda$'('fun_app$e'('vam$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ ?v3:N$ (fun_app$a(fun_app$z(vao$(?v0, ?v1), ?v2), ?v3) = vec_lambda$(fun_app$e(val$(?v0, ?v1, ?v2), ?v3)))
tff(axiom226,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$a'('fun_app$z'('vao$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'vec_lambda$'('fun_app$e'('val$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:A$ ?v3:N$ (fun_app$a(vak$(?v0, ?v1, ?v2), ?v3) = vec_lambda$(fun_app$e(vaf$(?v0, ?v1, ?v2), ?v3)))
tff(axiom227,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'A$',A__questionmark_v3: 'N$'] : 'fun_app$a'('vak$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'vec_lambda$'('fun_app$e'('vaf$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:A$ ?v3:N$ (fun_app$a(van$(?v0, ?v1, ?v2), ?v3) = vec_lambda$(fun_app$e(vae$(?v0, ?v1, ?v2), ?v3)))
tff(axiom228,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'A$',A__questionmark_v3: 'N$'] : 'fun_app$a'('van$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'vec_lambda$'('fun_app$e'('vae$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:A_n_vec_a_n_vec_fun$ ?v3:N$ (fun_app$a(vab$(?v0, ?v1, ?v2), ?v3) = vec_lambda$(fun_app$e(vaa$(?v0, ?v1, ?v2), ?v3)))
tff(axiom229,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'A_n_vec_a_n_vec_fun$',A__questionmark_v3: 'N$'] : 'fun_app$a'('vab$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'vec_lambda$'('fun_app$e'('vaa$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3)) ).

%% ∀ ?v0:N_set$ ?v1:N_n_a_n_vec_fun_fun$ ?v2:N_a_n_vec_fun$ ?v3:N_n_fun$ (fun_app$i(vda$(?v0, ?v1, ?v2), ?v3) = fun_app$w(det$, vec_lambda$a(vcz$(?v0, ?v1, ?v2, ?v3))))
tff(axiom230,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_n_a_n_vec_fun_fun$',A__questionmark_v2: 'N_a_n_vec_fun$',A__questionmark_v3: 'N_n_fun$'] : 'fun_app$i'('vda$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'fun_app$w'('det$','vec_lambda$a'('vcz$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3))) ).

%% ∀ ?v0:N$ ?v1:N_n_a_n_vec_fun_fun$ ?v2:N_a_n_vec_fun$ ?v3:N$ (fun_app$d(vcm$(?v0, ?v1, ?v2), ?v3) = fun_app$w(det$, vec_lambda$a(fun_app$z(vcl$(?v0, ?v1, ?v2), ?v3))))
tff(axiom231,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'N_n_a_n_vec_fun_fun$',A__questionmark_v2: 'N_a_n_vec_fun$',A__questionmark_v3: 'N$'] : 'fun_app$d'('vcm$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'fun_app$w'('det$','vec_lambda$a'('fun_app$z'('vcl$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3))) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_set$ ?v2:Nat$ ?v3:Nat_nat_fun$ (fun_app$q(vcw$(?v0, ?v1, ?v2), ?v3) = ∀ ?v4:Nat$ ((member$a(?v4, ?v0) ⇒ member$a(fun_app$v(?v3, ?v4), ?v1)) ∧ (¬member$a(?v4, ?v0) ⇒ (fun_app$v(?v3, ?v4) = ?v2))))
tff(axiom232,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'Nat$',A__questionmark_v3: 'Nat_nat_fun$'] :
      ( 'fun_app$q'('vcw$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3)
    <=> ! [A__questionmark_v4: 'Nat$'] :
          ( ( 'member$a'(A__questionmark_v4,A__questionmark_v0)
           => 'member$a'('fun_app$v'(A__questionmark_v3,A__questionmark_v4),A__questionmark_v1) )
          & ( ~ 'member$a'(A__questionmark_v4,A__questionmark_v0)
           => ( 'fun_app$v'(A__questionmark_v3,A__questionmark_v4) = A__questionmark_v2 ) ) ) ) ).

%% ∀ ?v0:Nat_bool_fun$ ?v1:Nat_bool_fun$ ?v2:Nat_nat_nat_fun_fun$ ?v3:Nat$ (fun_app$m(vcv$(?v0, ?v1, ?v2), ?v3) = ∃ ?v4:Nat$ ?v5:Nat$ ((?v3 = fun_app$v(fun_app$ao(?v2, ?v4), ?v5)) ∧ (fun_app$m(?v0, ?v4) ∧ fun_app$m(?v1, ?v5))))
tff(axiom233,axiom,
    ! [A__questionmark_v0: 'Nat_bool_fun$',A__questionmark_v1: 'Nat_bool_fun$',A__questionmark_v2: 'Nat_nat_nat_fun_fun$',A__questionmark_v3: 'Nat$'] :
      ( 'fun_app$m'('vcv$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3)
    <=> ? [A__questionmark_v4: 'Nat$',A__questionmark_v5: 'Nat$'] :
          ( ( A__questionmark_v3 = 'fun_app$v'('fun_app$ao'(A__questionmark_v2,A__questionmark_v4),A__questionmark_v5) )
          & 'fun_app$m'(A__questionmark_v0,A__questionmark_v4)
          & 'fun_app$m'(A__questionmark_v1,A__questionmark_v5) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_n_a_n_vec_fun_fun$ ?v2:N_a_n_vec_fun$ ?v3:N_n_fun$ ?v4:N$ (fun_app$a(vcz$(?v0, ?v1, ?v2, ?v3), ?v4) = (if member$f(?v4, ?v0) fun_app$a(fun_app$z(?v1, ?v4), fun_app$y(?v3, ?v4)) else fun_app$a(?v2, ?v4)))
tff(axiom234,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_n_a_n_vec_fun_fun$',A__questionmark_v2: 'N_a_n_vec_fun$',A__questionmark_v3: 'N_n_fun$',A__questionmark_v4: 'N$'] :
      ( ( 'member$f'(A__questionmark_v4,A__questionmark_v0)
       => ( 'fun_app$a'('vcz$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4) = 'fun_app$a'('fun_app$z'(A__questionmark_v1,A__questionmark_v4),'fun_app$y'(A__questionmark_v3,A__questionmark_v4)) ) )
      & ( ~ 'member$f'(A__questionmark_v4,A__questionmark_v0)
       => ( 'fun_app$a'('vcz$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4) = 'fun_app$a'(A__questionmark_v2,A__questionmark_v4) ) ) ) ).

%% ∀ ?v0:N$ ?v1:N_n_a_n_vec_fun_fun$ ?v2:N_a_n_vec_fun$ ?v3:N$ ?v4:N$ (fun_app$a(fun_app$z(vcl$(?v0, ?v1, ?v2), ?v3), ?v4) = (if (?v4 = ?v0) fun_app$a(fun_app$z(?v1, ?v4), ?v3) else fun_app$a(?v2, ?v4)))
tff(axiom235,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'N_n_a_n_vec_fun_fun$',A__questionmark_v2: 'N_a_n_vec_fun$',A__questionmark_v3: 'N$',A__questionmark_v4: 'N$'] :
      ( ( ( A__questionmark_v4 = A__questionmark_v0 )
       => ( 'fun_app$a'('fun_app$z'('vcl$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),A__questionmark_v4) = 'fun_app$a'('fun_app$z'(A__questionmark_v1,A__questionmark_v4),A__questionmark_v3) ) )
      & ( ( A__questionmark_v4 != A__questionmark_v0 )
       => ( 'fun_app$a'('fun_app$z'('vcl$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),A__questionmark_v4) = 'fun_app$a'(A__questionmark_v2,A__questionmark_v4) ) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:A$ ?v3:N$ ?v4:N$ (fun_app$d(fun_app$e(vaf$(?v0, ?v1, ?v2), ?v3), ?v4) = (if (?v4 = ?v1) fun_app$k(fun_app$l(times$, fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v3)), ?v4)), ?v2) else fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v3)), ?v4)))
tff(axiom236,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'A$',A__questionmark_v3: 'N$',A__questionmark_v4: 'N$'] :
      ( ( ( A__questionmark_v4 = A__questionmark_v1 )
       => ( 'fun_app$d'('fun_app$e'('vaf$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),A__questionmark_v4) = 'fun_app$k'('fun_app$l'('times$','fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v3)),A__questionmark_v4)),A__questionmark_v2) ) )
      & ( ( A__questionmark_v4 != A__questionmark_v1 )
       => ( 'fun_app$d'('fun_app$e'('vaf$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),A__questionmark_v4) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v3)),A__questionmark_v4) ) ) ) ).

%% ∀ ?v0:N$ ?v1:N$ ?v2:A_n_vec_n_vec$ ?v3:A$ ?v4:N$ (fun_app$a(vdg$(?v0, ?v1, ?v2, ?v3), ?v4) = (if (?v4 = ?v0) fun_app$b(plus$(row$(?v0, ?v2)), fun_app$b(fun_app$c(vector_scalar_mult$, ?v3), row$(?v1, ?v2))) else row$(?v4, ?v2)))
tff(axiom237,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'N$',A__questionmark_v2: 'A_n_vec_n_vec$',A__questionmark_v3: 'A$',A__questionmark_v4: 'N$'] :
      ( ( ( A__questionmark_v4 = A__questionmark_v0 )
       => ( 'fun_app$a'('vdg$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4) = 'fun_app$b'('plus$'('row$'(A__questionmark_v0,A__questionmark_v2)),'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v3),'row$'(A__questionmark_v1,A__questionmark_v2))) ) )
      & ( ( A__questionmark_v4 != A__questionmark_v0 )
       => ( 'fun_app$a'('vdg$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4) = 'row$'(A__questionmark_v4,A__questionmark_v2) ) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ ?v3:N$ ?v4:N$ (fun_app$d(fun_app$e(vam$(?v0, ?v1, ?v2), ?v3), ?v4) = (if (?v3 = ?v1) fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v2)), ?v4) else (if (?v3 = ?v2) fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v1)), ?v4) else fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v3)), ?v4))))
tff(axiom238,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$',A__questionmark_v4: 'N$'] :
      ( ( ( A__questionmark_v3 = A__questionmark_v1 )
       => ( 'fun_app$d'('fun_app$e'('vam$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),A__questionmark_v4) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v2)),A__questionmark_v4) ) )
      & ( ( A__questionmark_v3 != A__questionmark_v1 )
       => ( ( ( A__questionmark_v3 = A__questionmark_v2 )
           => ( 'fun_app$d'('fun_app$e'('vam$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),A__questionmark_v4) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v4) ) )
          & ( ( A__questionmark_v3 != A__questionmark_v2 )
           => ( 'fun_app$d'('fun_app$e'('vam$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),A__questionmark_v4) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v3)),A__questionmark_v4) ) ) ) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ ?v3:N$ ?v4:N$ (fun_app$d(fun_app$e(val$(?v0, ?v1, ?v2), ?v3), ?v4) = (if (?v4 = ?v1) fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v3)), ?v2) else (if (?v4 = ?v2) fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v3)), ?v1) else fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v3)), ?v4))))
tff(axiom239,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$',A__questionmark_v4: 'N$'] :
      ( ( ( A__questionmark_v4 = A__questionmark_v1 )
       => ( 'fun_app$d'('fun_app$e'('val$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),A__questionmark_v4) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v3)),A__questionmark_v2) ) )
      & ( ( A__questionmark_v4 != A__questionmark_v1 )
       => ( ( ( A__questionmark_v4 = A__questionmark_v2 )
           => ( 'fun_app$d'('fun_app$e'('val$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),A__questionmark_v4) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v3)),A__questionmark_v1) ) )
          & ( ( A__questionmark_v4 != A__questionmark_v2 )
           => ( 'fun_app$d'('fun_app$e'('val$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),A__questionmark_v4) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v3)),A__questionmark_v4) ) ) ) ) ) ).

%% ∀ ?v0:N$ ?v1:A_n_vec_n_vec$ ?v2:A_n_vec$ ?v3:N$ ?v4:N$ (fun_app$d(fun_app$e(vaq$(?v0, ?v1, ?v2), ?v3), ?v4) = (if (?v4 = ?v0) fun_app$d(vec_nth$a(fun_app$b(matrix_vector_mult$(?v1), ?v2)), ?v3) else fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v1), ?v3)), ?v4)))
tff(axiom240,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'A_n_vec$',A__questionmark_v3: 'N$',A__questionmark_v4: 'N$'] :
      ( ( ( A__questionmark_v4 = A__questionmark_v0 )
       => ( 'fun_app$d'('fun_app$e'('vaq$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),A__questionmark_v4) = 'fun_app$d'('vec_nth$a'('fun_app$b'('matrix_vector_mult$'(A__questionmark_v1),A__questionmark_v2)),A__questionmark_v3) ) )
      & ( ( A__questionmark_v4 != A__questionmark_v0 )
       => ( 'fun_app$d'('fun_app$e'('vaq$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),A__questionmark_v4) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v3)),A__questionmark_v4) ) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_set$ ?v2:N_n_a_n_vec_fun_fun$ ?v3:N_a_n_vec_fun$ ?v4:N$ (fun_app$a(vcy$(?v0, ?v1, ?v2, ?v3), ?v4) = (if member$f(?v4, ?v1) sum$(fun_app$z(?v2, ?v4), ?v0) else fun_app$a(?v3, ?v4)))
tff(axiom241,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_n_a_n_vec_fun_fun$',A__questionmark_v3: 'N_a_n_vec_fun$',A__questionmark_v4: 'N$'] :
      ( ( 'member$f'(A__questionmark_v4,A__questionmark_v1)
       => ( 'fun_app$a'('vcy$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4) = 'sum$'('fun_app$z'(A__questionmark_v2,A__questionmark_v4),A__questionmark_v0) ) )
      & ( ~ 'member$f'(A__questionmark_v4,A__questionmark_v1)
       => ( 'fun_app$a'('vcy$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4) = 'fun_app$a'(A__questionmark_v3,A__questionmark_v4) ) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N$ ?v2:N_n_a_n_vec_fun_fun$ ?v3:N_a_n_vec_fun$ ?v4:N$ (fun_app$a(vck$(?v0, ?v1, ?v2, ?v3), ?v4) = (if (?v4 = ?v1) sum$(fun_app$z(?v2, ?v4), ?v0) else fun_app$a(?v3, ?v4)))
tff(axiom242,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N_n_a_n_vec_fun_fun$',A__questionmark_v3: 'N_a_n_vec_fun$',A__questionmark_v4: 'N$'] :
      ( ( ( A__questionmark_v4 = A__questionmark_v1 )
       => ( 'fun_app$a'('vck$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4) = 'sum$'('fun_app$z'(A__questionmark_v2,A__questionmark_v4),A__questionmark_v0) ) )
      & ( ( A__questionmark_v4 != A__questionmark_v1 )
       => ( 'fun_app$a'('vck$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4) = 'fun_app$a'(A__questionmark_v3,A__questionmark_v4) ) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:A$ ?v3:N$ ?v4:N$ (fun_app$d(fun_app$e(vae$(?v0, ?v1, ?v2), ?v3), ?v4) = (if (?v3 = ?v1) fun_app$k(fun_app$l(times$, ?v2), fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v1)), ?v4)) else fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v3)), ?v4)))
tff(axiom243,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'A$',A__questionmark_v3: 'N$',A__questionmark_v4: 'N$'] :
      ( ( ( A__questionmark_v3 = A__questionmark_v1 )
       => ( 'fun_app$d'('fun_app$e'('vae$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),A__questionmark_v4) = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v2),'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v4)) ) )
      & ( ( A__questionmark_v3 != A__questionmark_v1 )
       => ( 'fun_app$d'('fun_app$e'('vae$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),A__questionmark_v4) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v3)),A__questionmark_v4) ) ) ) ).

%% ∀ ?v0:N$ ?v1:A$ ?v2:N_a_n_vec_fun$ ?v3:N_a_n_vec_fun$ ?v4:N$ (fun_app$a(vbg$(?v0, ?v1, ?v2, ?v3), ?v4) = (if (?v4 = ?v0) fun_app$b(fun_app$c(vector_scalar_mult$, ?v1), fun_app$a(?v2, ?v4)) else fun_app$a(?v3, ?v4)))
tff(axiom244,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'A$',A__questionmark_v2: 'N_a_n_vec_fun$',A__questionmark_v3: 'N_a_n_vec_fun$',A__questionmark_v4: 'N$'] :
      ( ( ( A__questionmark_v4 = A__questionmark_v0 )
       => ( 'fun_app$a'('vbg$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v1),'fun_app$a'(A__questionmark_v2,A__questionmark_v4)) ) )
      & ( ( A__questionmark_v4 != A__questionmark_v0 )
       => ( 'fun_app$a'('vbg$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4) = 'fun_app$a'(A__questionmark_v3,A__questionmark_v4) ) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec$ ?v2:N$ ?v3:N$ ?v4:N$ (fun_app$d(fun_app$e(vee$(?v0, ?v1, ?v2), ?v3), ?v4) = (if (?v4 = ?v2) fun_app$d(vec_nth$a(?v1), ?v3) else fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v3)), ?v4)))
tff(axiom245,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$',A__questionmark_v4: 'N$'] :
      ( ( ( A__questionmark_v4 = A__questionmark_v2 )
       => ( 'fun_app$d'('fun_app$e'('vee$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),A__questionmark_v4) = 'fun_app$d'('vec_nth$a'(A__questionmark_v1),A__questionmark_v3) ) )
      & ( ( A__questionmark_v4 != A__questionmark_v2 )
       => ( 'fun_app$d'('fun_app$e'('vee$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),A__questionmark_v4) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v3)),A__questionmark_v4) ) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:A_n_vec_a_n_vec_fun$ ?v3:N$ ?v4:N$ (fun_app$a(fun_app$z(uwl$(?v0, ?v1, ?v2), ?v3), ?v4) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$d(vec_nth$a(fun_app$a(vec_nth$(matrix$(?v0, ?v1, ?v2)), ?v4)), ?v3)), fun_app$a(vec_nth$(?v1), ?v4)))
tff(axiom246,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'A_n_vec_a_n_vec_fun$',A__questionmark_v3: 'N$',A__questionmark_v4: 'N$'] : 'fun_app$a'('fun_app$z'('uwl$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),A__questionmark_v4) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'('matrix$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2)),A__questionmark_v4)),A__questionmark_v3)),'fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v4)) ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec$ ?v2:N$ ?v3:N$ ?v4:N$ (fun_app$a(fun_app$z(uwn$(?v0, ?v1, ?v2), ?v3), ?v4) = fun_app$b(times$b(fun_app$a(vec_nth$(fun_app$f(vec_nth$b(?v0), ?v2)), ?v4)), fun_app$a(vec_nth$(fun_app$f(vec_nth$b(?v1), ?v4)), ?v3)))
tff(axiom247,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$',A__questionmark_v4: 'N$'] : 'fun_app$a'('fun_app$z'('uwn$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),A__questionmark_v4) = 'fun_app$b'('times$b'('fun_app$a'('vec_nth$'('fun_app$f'('vec_nth$b'(A__questionmark_v0),A__questionmark_v2)),A__questionmark_v4)),'fun_app$a'('vec_nth$'('fun_app$f'('vec_nth$b'(A__questionmark_v1),A__questionmark_v4)),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ ?v3:N$ ?v4:N$ (fun_app$d(fun_app$e(uwo$(?v0, ?v1, ?v2), ?v3), ?v4) = fun_app$k(fun_app$l(times$, fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v2)), ?v4)), fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v1), ?v4)), ?v3)))
tff(axiom248,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$',A__questionmark_v4: 'N$'] : 'fun_app$d'('fun_app$e'('uwo$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),A__questionmark_v4) = 'fun_app$k'('fun_app$l'('times$','fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v2)),A__questionmark_v4)),'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v4)),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:A_n_vec_a_n_vec_fun$ ?v3:N$ ?v4:N$ (fun_app$d(fun_app$e(vaa$(?v0, ?v1, ?v2), ?v3), ?v4) = fun_app$d(vec_nth$a(fun_app$b(coord$(?v1), fun_app$b(?v2, fun_app$a(vec_nth$(?v0), ?v4)))), ?v3))
tff(axiom249,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'A_n_vec_a_n_vec_fun$',A__questionmark_v3: 'N$',A__questionmark_v4: 'N$'] : 'fun_app$d'('fun_app$e'('vaa$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),A__questionmark_v4) = 'fun_app$d'('vec_nth$a'('fun_app$b'('coord$'(A__questionmark_v1),'fun_app$b'(A__questionmark_v2,'fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v4)))),A__questionmark_v3) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ ?v3:A$ ?v4:N$ (fun_app$a(vea$(?v0, ?v1, ?v2, ?v3), ?v4) = vec_lambda$(fun_app$e(vdx$(?v0, ?v1, ?v2, ?v3), ?v4)))
tff(axiom250,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$',A__questionmark_v3: 'A$',A__questionmark_v4: 'N$'] : 'fun_app$a'('vea$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4) = 'vec_lambda$'('fun_app$e'('vdx$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ ?v3:A$ ?v4:N$ (fun_app$a(vdz$(?v0, ?v1, ?v2, ?v3), ?v4) = vec_lambda$(fun_app$e(vdw$(?v0, ?v1, ?v2, ?v3), ?v4)))
tff(axiom251,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$',A__questionmark_v3: 'A$',A__questionmark_v4: 'N$'] : 'fun_app$a'('vdz$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4) = 'vec_lambda$'('fun_app$e'('vdw$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ ?v3:A$ ?v4:N$ ?v5:N$ (fun_app$d(fun_app$e(vdw$(?v0, ?v1, ?v2, ?v3), ?v4), ?v5) = (if (?v5 = ?v1) fun_app$k(plus$a(fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v4)), ?v1)), fun_app$k(fun_app$l(times$, fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v4)), ?v2)), ?v3)) else fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v4)), ?v5)))
tff(axiom252,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$',A__questionmark_v3: 'A$',A__questionmark_v4: 'N$',A__questionmark_v5: 'N$'] :
      ( ( ( A__questionmark_v5 = A__questionmark_v1 )
       => ( 'fun_app$d'('fun_app$e'('vdw$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4),A__questionmark_v5) = 'fun_app$k'('plus$a'('fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v4)),A__questionmark_v1)),'fun_app$k'('fun_app$l'('times$','fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v4)),A__questionmark_v2)),A__questionmark_v3)) ) )
      & ( ( A__questionmark_v5 != A__questionmark_v1 )
       => ( 'fun_app$d'('fun_app$e'('vdw$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4),A__questionmark_v5) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v4)),A__questionmark_v5) ) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ ?v3:A$ ?v4:N$ ?v5:N$ (fun_app$d(fun_app$e(vdx$(?v0, ?v1, ?v2, ?v3), ?v4), ?v5) = (if (?v4 = ?v1) fun_app$k(plus$a(fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v1)), ?v5)), fun_app$k(fun_app$l(times$, ?v3), fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v2)), ?v5))) else fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v4)), ?v5)))
tff(axiom253,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$',A__questionmark_v3: 'A$',A__questionmark_v4: 'N$',A__questionmark_v5: 'N$'] :
      ( ( ( A__questionmark_v4 = A__questionmark_v1 )
       => ( 'fun_app$d'('fun_app$e'('vdx$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4),A__questionmark_v5) = 'fun_app$k'('plus$a'('fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v5)),'fun_app$k'('fun_app$l'('times$',A__questionmark_v3),'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v2)),A__questionmark_v5))) ) )
      & ( ( A__questionmark_v4 != A__questionmark_v1 )
       => ( 'fun_app$d'('fun_app$e'('vdx$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4),A__questionmark_v5) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v4)),A__questionmark_v5) ) ) ) ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec$ (fun_app$b(uzn$(?v0), ?v1) = ?v0)
tff(axiom254,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec$'] : 'fun_app$b'('uzn$'(A__questionmark_v0),A__questionmark_v1) = A__questionmark_v0 ).

%% ∀ ?v0:A_n_vec$ ?v1:A$ (fun_app$o(uzo$(?v0), ?v1) = ?v0)
tff(axiom255,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A$'] : 'fun_app$o'('uzo$'(A__questionmark_v0),A__questionmark_v1) = A__questionmark_v0 ).

%% ∀ ?v0:A$ ?v1:A_n_vec$ (fun_app$j(uzm$(?v0), ?v1) = ?v0)
tff(axiom256,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A_n_vec$'] : 'fun_app$j'('uzm$'(A__questionmark_v0),A__questionmark_v1) = A__questionmark_v0 ).

%% ∀ ?v0:A$ ?v1:A$ (fun_app$k(uzp$(?v0), ?v1) = ?v0)
tff(axiom257,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$'] : 'fun_app$k'('uzp$'(A__questionmark_v0),A__questionmark_v1) = A__questionmark_v0 ).

%% ∀ ?v0:A_n_vec$ (fun_app$b(vbb$, ?v0) = ?v0)
tff(axiom258,axiom,
    ! [A__questionmark_v0: 'A_n_vec$'] : 'fun_app$b'('vbb$',A__questionmark_v0) = A__questionmark_v0 ).

%% ∀ ?v0:A$ (fun_app$k(vaz$, ?v0) = ?v0)
tff(axiom259,axiom,
    ! [A__questionmark_v0: 'A$'] : 'fun_app$k'('vaz$',A__questionmark_v0) = A__questionmark_v0 ).

%% ∀ ?v0:A_n_vec$ (fun_app$b(vdv$, ?v0) = zero$)
tff(axiom260,axiom,
    ! [A__questionmark_v0: 'A_n_vec$'] : 'fun_app$b'('vdv$',A__questionmark_v0) = 'zero$' ).

%% ∀ ?v0:N$ (fun_app$a(vdh$, ?v0) = zero$)
tff(axiom261,axiom,
    ! [A__questionmark_v0: 'N$'] : 'fun_app$a'('vdh$',A__questionmark_v0) = 'zero$' ).

%% ∀ ?v0:N$ (fun_app$d(vdi$, ?v0) = zero$a)
tff(axiom262,axiom,
    ! [A__questionmark_v0: 'N$'] : 'fun_app$d'('vdi$',A__questionmark_v0) = 'zero$a' ).

%% ∀ ?v0:A$ (fun_app$k(vdy$, ?v0) = zero$a)
tff(axiom263,axiom,
    ! [A__questionmark_v0: 'A$'] : 'fun_app$k'('vdy$',A__questionmark_v0) = 'zero$a' ).

%% ∀ ?v0:A_n_vec$ (fun_app$p(uvx$, ?v0) = true)
tff(axiom264,axiom,
    ! [A__questionmark_v0: 'A_n_vec$'] :
      ( 'fun_app$p'('uvx$',A__questionmark_v0)
    <=> $true ) ).

%% ∀ ?v0:Nat$ (fun_app$m(uwd$, ?v0) = true)
tff(axiom265,axiom,
    ! [A__questionmark_v0: 'Nat$'] :
      ( 'fun_app$m'('uwd$',A__questionmark_v0)
    <=> $true ) ).

%% ∀ ?v0:Nat_nat_fun$ (fun_app$q(uvz$, ?v0) = true)
tff(axiom266,axiom,
    ! [A__questionmark_v0: 'Nat_nat_fun$'] :
      ( 'fun_app$q'('uvz$',A__questionmark_v0)
    <=> $true ) ).

%% ∀ ?v0:N_a_n_vec_fun$ (fun_app$r(uwa$, ?v0) = true)
tff(axiom267,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$'] :
      ( 'fun_app$r'('uwa$',A__questionmark_v0)
    <=> $true ) ).

%% ∀ ?v0:N_n_fun$ (fun_app$s(uvy$, ?v0) = true)
tff(axiom268,axiom,
    ! [A__questionmark_v0: 'N_n_fun$'] :
      ( 'fun_app$s'('uvy$',A__questionmark_v0)
    <=> $true ) ).

%% ∀ ?v0:N_a_fun$ (fun_app$(uwb$, ?v0) = true)
tff(axiom269,axiom,
    ! [A__questionmark_v0: 'N_a_fun$'] :
      ( 'fun_app$'('uwb$',A__questionmark_v0)
    <=> $true ) ).

%% ∀ ?v0:N$ (fun_app$t(uwe$, ?v0) = true)
tff(axiom270,axiom,
    ! [A__questionmark_v0: 'N$'] :
      ( 'fun_app$t'('uwe$',A__questionmark_v0)
    <=> $true ) ).

%% ∀ ?v0:A$ (fun_app$u(uwc$, ?v0) = true)
tff(axiom271,axiom,
    ! [A__questionmark_v0: 'A$'] :
      ( 'fun_app$u'('uwc$',A__questionmark_v0)
    <=> $true ) ).

%% ¬(the$(uua$) = h$)
tff(conjecture272,conjecture,
    'the$'('uua$') = 'h$' ).

%% (sum$(uub$, top$) = fun_app$a(vec_nth$(x$), x$a))
tff(axiom273,axiom,
    'sum$'('uub$','top$') = 'fun_app$a'('vec_nth$'('x$'),'x$a') ).

%% ∀ ?v0:N$ (fun_app$e(t$, ?v0) = the$(uuc$(?v0)))
tff(axiom274,axiom,
    ! [A__questionmark_v0: 'N$'] : 'fun_app$e'('t$',A__questionmark_v0) = 'the$'('uuc$'(A__questionmark_v0)) ).

%% (∀ ?v0:N_a_fun$ ((sum$(uu$(?v0), top$) = fun_app$a(vec_nth$(x$), x$a)) ⇒ false) ⇒ false)
tff(axiom275,axiom,
    ( ! [A__questionmark_v0: 'N_a_fun$'] :
        ( ( 'sum$'('uu$'(A__questionmark_v0),'top$') = 'fun_app$a'('vec_nth$'('x$'),'x$a') )
       => $false )
   => $false ) ).

%% ∀ ?v0:N$ (fun_app$e(t$, ?v0) = the$(uuc$(?v0)))
tff(axiom276,axiom,
    ! [A__questionmark_v0: 'N$'] : 'fun_app$e'('t$',A__questionmark_v0) = 'the$'('uuc$'(A__questionmark_v0)) ).

%% (sum$(uud$, top$) = v$)
tff(axiom277,axiom,
    'sum$'('uud$','top$') = 'v$' ).

%% (∀ ?v0:N_a_fun$ ((sum$(uue$(?v0), top$) = v$) ⇒ false) ⇒ false)
tff(axiom278,axiom,
    ( ! [A__questionmark_v0: 'N_a_fun$'] :
        ( ( 'sum$'('uue$'(A__questionmark_v0),'top$') = 'v$' )
       => $false )
   => $false ) ).

%% (∀ ?v0:N_a_fun$ ((sum$(uu$(?v0), top$) = v$) ⇒ false) ⇒ false)
tff(axiom279,axiom,
    ( ! [A__questionmark_v0: 'N_a_fun$'] :
        ( ( 'sum$'('uu$'(A__questionmark_v0),'top$') = 'v$' )
       => $false )
   => $false ) ).

%% (sum$(uuf$, top$) = v$)
tff(axiom280,axiom,
    'sum$'('uuf$','top$') = 'v$' ).

%% ∀ ?v0:Nat_a_n_vec_fun$ ?v1:Nat_set$ ?v2:N$ (fun_app$d(vec_nth$a(sum$g(?v0, ?v1)), ?v2) = sum$d(fun_app$ah(uug$(?v0), ?v2), ?v1))
tff(axiom281,axiom,
    ! [A__questionmark_v0: 'Nat_a_n_vec_fun$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'N$'] : 'fun_app$d'('vec_nth$a'('sum$g'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$d'('fun_app$ah'('uug$'(A__questionmark_v0),A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_fun_a_n_vec_fun$ ?v1:N_n_fun_set$ ?v2:N$ (fun_app$d(vec_nth$a(sum$h(?v0, ?v1)), ?v2) = sum$c(fun_app$aj(uuh$(?v0), ?v2), ?v1))
tff(axiom282,axiom,
    ! [A__questionmark_v0: 'N_n_fun_a_n_vec_fun$',A__questionmark_v1: 'N_n_fun_set$',A__questionmark_v2: 'N$'] : 'fun_app$d'('vec_nth$a'('sum$h'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$c'('fun_app$aj'('uuh$'(A__questionmark_v0),A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_a_n_vec_n_vec_n_vec_fun$ ?v1:N_set$ ?v2:N$ (fun_app$f(vec_nth$b(sum$i(?v0, ?v1)), ?v2) = sum$b(uui$(?v0, ?v2), ?v1))
tff(axiom283,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_n_vec_n_vec_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N$'] : 'fun_app$f'('vec_nth$b'('sum$i'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$b'('uui$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_a_n_vec_n_vec_fun$ ?v1:N_set$ ?v2:N$ (fun_app$a(vec_nth$(sum$b(?v0, ?v1)), ?v2) = sum$(fun_app$z(uuj$(?v0), ?v2), ?v1))
tff(axiom284,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_n_vec_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vec_nth$'('sum$b'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$'('fun_app$z'('uuj$'(A__questionmark_v0),A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_a_n_vec_fun$ ?v1:N_set$ ?v2:N$ (fun_app$d(vec_nth$a(sum$(?v0, ?v1)), ?v2) = sum$a(fun_app$e(uuk$(?v0), ?v2), ?v1))
tff(axiom285,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N$'] : 'fun_app$d'('vec_nth$a'('sum$'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$a'('fun_app$e'('uuk$'(A__questionmark_v0),A__questionmark_v2),A__questionmark_v1) ).

%% (sum$(uud$, top$) = sum$(uuf$, top$))
tff(axiom286,axiom,
    'sum$'('uud$','top$') = 'sum$'('uuf$','top$') ).

%% ∀ ?v0:N_a_fun_bool_fun$ ?v1:N_a_fun$ ((fun_app$(?v0, ?v1) ∧ ∀ ?v2:N_a_fun$ (fun_app$(?v0, ?v2) ⇒ (?v2 = ?v1))) ⇒ (the$(?v0) = ?v1))
tff(axiom287,axiom,
    ! [A__questionmark_v0: 'N_a_fun_bool_fun$',A__questionmark_v1: 'N_a_fun$'] :
      ( ( 'fun_app$'(A__questionmark_v0,A__questionmark_v1)
        & ! [A__questionmark_v2: 'N_a_fun$'] :
            ( 'fun_app$'(A__questionmark_v0,A__questionmark_v2)
           => ( A__questionmark_v2 = A__questionmark_v1 ) ) )
     => ( 'the$'(A__questionmark_v0) = A__questionmark_v1 ) ) ).

%% ∀ ?v0:N_a_fun$ (the$(uul$(?v0)) = ?v0)
tff(axiom288,axiom,
    ! [A__questionmark_v0: 'N_a_fun$'] : 'the$'('uul$'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:N_a_fun$ (the$(uum$(?v0)) = ?v0)
tff(axiom289,axiom,
    ! [A__questionmark_v0: 'N_a_fun$'] : 'the$'('uum$'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:Nat_a_fun$ ?v1:Nat_set$ ?v2:A_n_vec$ (fun_app$b(fun_app$c(vector_scalar_mult$, sum$d(?v0, ?v1)), ?v2) = sum$g(uun$(?v0, ?v2), ?v1))
tff(axiom290,axiom,
    ! [A__questionmark_v0: 'Nat_a_fun$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'A_n_vec$'] : 'fun_app$b'('fun_app$c'('vector_scalar_mult$','sum$d'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$g'('uun$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_fun_a_fun$ ?v1:N_n_fun_set$ ?v2:A_n_vec$ (fun_app$b(fun_app$c(vector_scalar_mult$, sum$c(?v0, ?v1)), ?v2) = sum$h(uuo$(?v0, ?v2), ?v1))
tff(axiom291,axiom,
    ! [A__questionmark_v0: 'N_n_fun_a_fun$',A__questionmark_v1: 'N_n_fun_set$',A__questionmark_v2: 'A_n_vec$'] : 'fun_app$b'('fun_app$c'('vector_scalar_mult$','sum$c'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$h'('uuo$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_set$ ?v2:A_n_vec$ (fun_app$b(fun_app$c(vector_scalar_mult$, sum$a(?v0, ?v1)), ?v2) = sum$(uup$(?v0, ?v2), ?v1))
tff(axiom292,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'A_n_vec$'] : 'fun_app$b'('fun_app$c'('vector_scalar_mult$','sum$a'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$'('uup$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:A_n_vec$ (sum$(uuq$(?v0), top$) = ?v0)
tff(axiom293,axiom,
    ! [A__questionmark_v0: 'A_n_vec$'] : 'sum$'('uuq$'(A__questionmark_v0),'top$') = A__questionmark_v0 ).

%% ∀ ?v0:A_n_vec_a_fun$ ?v1:A_n_vec$ ((sum$(uur$(?v0), top$) = ?v1) = ∀ ?v2:N$ (fun_app$j(?v0, fun_app$a(vec_nth$(cart_basis$), ?v2)) = fun_app$d(vec_nth$a(?v1), ?v2)))
tff(axiom294,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_fun$',A__questionmark_v1: 'A_n_vec$'] :
      ( ( 'sum$'('uur$'(A__questionmark_v0),'top$') = A__questionmark_v1 )
    <=> ! [A__questionmark_v2: 'N$'] : 'fun_app$j'(A__questionmark_v0,'fun_app$a'('vec_nth$'('cart_basis$'),A__questionmark_v2)) = 'fun_app$d'('vec_nth$a'(A__questionmark_v1),A__questionmark_v2) ) ).

%% ∀ ?v0:N_a_n_vec_n_vec_fun$ ?v1:N_a_n_vec_n_vec_fun_bool_fun$ ((member$h(?v0, top$a) ∧ ∀ ?v2:A_n_vec_n_vec_n_vec$ fun_app$ay(?v1, vec_nth$b(?v2))) ⇒ fun_app$ay(?v1, ?v0))
tff(axiom295,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_n_vec_fun$',A__questionmark_v1: 'N_a_n_vec_n_vec_fun_bool_fun$'] :
      ( ( 'member$h'(A__questionmark_v0,'top$a')
        & ! [A__questionmark_v2: 'A_n_vec_n_vec_n_vec$'] : 'fun_app$ay'(A__questionmark_v1,'vec_nth$b'(A__questionmark_v2)) )
     => 'fun_app$ay'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:N_nat_fun$ ?v1:N_nat_fun_bool_fun$ ((member$i(?v0, top$b) ∧ ∀ ?v2:Nat_n_vec$ fun_app$az(?v1, vec_nth$d(?v2))) ⇒ fun_app$az(?v1, ?v0))
tff(axiom296,axiom,
    ! [A__questionmark_v0: 'N_nat_fun$',A__questionmark_v1: 'N_nat_fun_bool_fun$'] :
      ( ( 'member$i'(A__questionmark_v0,'top$b')
        & ! [A__questionmark_v2: 'Nat_n_vec$'] : 'fun_app$az'(A__questionmark_v1,'vec_nth$d'(A__questionmark_v2)) )
     => 'fun_app$az'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:N_a_n_vec_fun$ ?v1:N_a_n_vec_fun_bool_fun$ ((member$c(?v0, top$c) ∧ ∀ ?v2:A_n_vec_n_vec$ fun_app$r(?v1, vec_nth$(?v2))) ⇒ fun_app$r(?v1, ?v0))
tff(axiom297,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$',A__questionmark_v1: 'N_a_n_vec_fun_bool_fun$'] :
      ( ( 'member$c'(A__questionmark_v0,'top$c')
        & ! [A__questionmark_v2: 'A_n_vec_n_vec$'] : 'fun_app$r'(A__questionmark_v1,'vec_nth$'(A__questionmark_v2)) )
     => 'fun_app$r'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_a_fun_bool_fun$ ((member$e(?v0, top$d) ∧ ∀ ?v2:A_n_vec$ fun_app$(?v1, vec_nth$a(?v2))) ⇒ fun_app$(?v1, ?v0))
tff(axiom298,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_a_fun_bool_fun$'] :
      ( ( 'member$e'(A__questionmark_v0,'top$d')
        & ! [A__questionmark_v2: 'A_n_vec$'] : 'fun_app$'(A__questionmark_v1,'vec_nth$a'(A__questionmark_v2)) )
     => 'fun_app$'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:N_a_n_vec_n_vec_fun$ ((member$h(?v0, top$a) ∧ ∀ ?v1:A_n_vec_n_vec_n_vec$ ((?v0 = vec_nth$b(?v1)) ⇒ false)) ⇒ false)
tff(axiom299,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_n_vec_fun$'] :
      ( ( 'member$h'(A__questionmark_v0,'top$a')
        & ! [A__questionmark_v1: 'A_n_vec_n_vec_n_vec$'] :
            ( ( A__questionmark_v0 = 'vec_nth$b'(A__questionmark_v1) )
           => $false ) )
     => $false ) ).

%% ∀ ?v0:N_nat_fun$ ((member$i(?v0, top$b) ∧ ∀ ?v1:Nat_n_vec$ ((?v0 = vec_nth$d(?v1)) ⇒ false)) ⇒ false)
tff(axiom300,axiom,
    ! [A__questionmark_v0: 'N_nat_fun$'] :
      ( ( 'member$i'(A__questionmark_v0,'top$b')
        & ! [A__questionmark_v1: 'Nat_n_vec$'] :
            ( ( A__questionmark_v0 = 'vec_nth$d'(A__questionmark_v1) )
           => $false ) )
     => $false ) ).

%% ∀ ?v0:N_a_n_vec_fun$ ((member$c(?v0, top$c) ∧ ∀ ?v1:A_n_vec_n_vec$ ((?v0 = vec_nth$(?v1)) ⇒ false)) ⇒ false)
tff(axiom301,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$'] :
      ( ( 'member$c'(A__questionmark_v0,'top$c')
        & ! [A__questionmark_v1: 'A_n_vec_n_vec$'] :
            ( ( A__questionmark_v0 = 'vec_nth$'(A__questionmark_v1) )
           => $false ) )
     => $false ) ).

%% ∀ ?v0:N_a_fun$ ((member$e(?v0, top$d) ∧ ∀ ?v1:A_n_vec$ ((?v0 = vec_nth$a(?v1)) ⇒ false)) ⇒ false)
tff(axiom302,axiom,
    ! [A__questionmark_v0: 'N_a_fun$'] :
      ( ( 'member$e'(A__questionmark_v0,'top$d')
        & ! [A__questionmark_v1: 'A_n_vec$'] :
            ( ( A__questionmark_v0 = 'vec_nth$a'(A__questionmark_v1) )
           => $false ) )
     => $false ) ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ member$h(vec_nth$b(?v0), top$a)
tff(axiom303,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$'] : 'member$h'('vec_nth$b'(A__questionmark_v0),'top$a') ).

%% ∀ ?v0:Nat_n_vec$ member$i(vec_nth$d(?v0), top$b)
tff(axiom304,axiom,
    ! [A__questionmark_v0: 'Nat_n_vec$'] : 'member$i'('vec_nth$d'(A__questionmark_v0),'top$b') ).

%% ∀ ?v0:A_n_vec_n_vec$ member$c(vec_nth$(?v0), top$c)
tff(axiom305,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$'] : 'member$c'('vec_nth$'(A__questionmark_v0),'top$c') ).

%% ∀ ?v0:A_n_vec$ member$e(vec_nth$a(?v0), top$d)
tff(axiom306,axiom,
    ! [A__questionmark_v0: 'A_n_vec$'] : 'member$e'('vec_nth$a'(A__questionmark_v0),'top$d') ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_a_fun$ ?v2:Nat_a_fun$ (∀ ?v3:Nat$ (member$a(?v3, ?v0) ⇒ (fun_app$aa(?v1, ?v3) = fun_app$aa(?v2, ?v3))) ⇒ (sum$d(?v1, ?v0) = sum$d(?v2, ?v0)))
tff(axiom307,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_a_fun$',A__questionmark_v2: 'Nat_a_fun$'] :
      ( ! [A__questionmark_v3: 'Nat$'] :
          ( 'member$a'(A__questionmark_v3,A__questionmark_v0)
         => ( 'fun_app$aa'(A__questionmark_v1,A__questionmark_v3) = 'fun_app$aa'(A__questionmark_v2,A__questionmark_v3) ) )
     => ( 'sum$d'(A__questionmark_v1,A__questionmark_v0) = 'sum$d'(A__questionmark_v2,A__questionmark_v0) ) ) ).

%% ∀ ?v0:N_n_fun_set$ ?v1:N_n_fun_a_fun$ ?v2:N_n_fun_a_fun$ (∀ ?v3:N_n_fun$ (member$d(?v3, ?v0) ⇒ (fun_app$i(?v1, ?v3) = fun_app$i(?v2, ?v3))) ⇒ (sum$c(?v1, ?v0) = sum$c(?v2, ?v0)))
tff(axiom308,axiom,
    ! [A__questionmark_v0: 'N_n_fun_set$',A__questionmark_v1: 'N_n_fun_a_fun$',A__questionmark_v2: 'N_n_fun_a_fun$'] :
      ( ! [A__questionmark_v3: 'N_n_fun$'] :
          ( 'member$d'(A__questionmark_v3,A__questionmark_v0)
         => ( 'fun_app$i'(A__questionmark_v1,A__questionmark_v3) = 'fun_app$i'(A__questionmark_v2,A__questionmark_v3) ) )
     => ( 'sum$c'(A__questionmark_v1,A__questionmark_v0) = 'sum$c'(A__questionmark_v2,A__questionmark_v0) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_a_n_vec_n_vec_fun$ ?v2:N_a_n_vec_n_vec_fun$ (∀ ?v3:N$ (member$f(?v3, ?v0) ⇒ (fun_app$f(?v1, ?v3) = fun_app$f(?v2, ?v3))) ⇒ (sum$b(?v1, ?v0) = sum$b(?v2, ?v0)))
tff(axiom309,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_a_n_vec_n_vec_fun$',A__questionmark_v2: 'N_a_n_vec_n_vec_fun$'] :
      ( ! [A__questionmark_v3: 'N$'] :
          ( 'member$f'(A__questionmark_v3,A__questionmark_v0)
         => ( 'fun_app$f'(A__questionmark_v1,A__questionmark_v3) = 'fun_app$f'(A__questionmark_v2,A__questionmark_v3) ) )
     => ( 'sum$b'(A__questionmark_v1,A__questionmark_v0) = 'sum$b'(A__questionmark_v2,A__questionmark_v0) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_a_n_vec_set_fun$ ?v2:N_a_n_vec_set_fun$ (∀ ?v3:N$ (member$f(?v3, ?v0) ⇒ (fun_app$au(?v1, ?v3) = fun_app$au(?v2, ?v3))) ⇒ (sum$j(?v1, ?v0) = sum$j(?v2, ?v0)))
tff(axiom310,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_a_n_vec_set_fun$',A__questionmark_v2: 'N_a_n_vec_set_fun$'] :
      ( ! [A__questionmark_v3: 'N$'] :
          ( 'member$f'(A__questionmark_v3,A__questionmark_v0)
         => ( 'fun_app$au'(A__questionmark_v1,A__questionmark_v3) = 'fun_app$au'(A__questionmark_v2,A__questionmark_v3) ) )
     => ( 'sum$j'(A__questionmark_v1,A__questionmark_v0) = 'sum$j'(A__questionmark_v2,A__questionmark_v0) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_a_set_fun$ ?v2:N_a_set_fun$ (∀ ?v3:N$ (member$f(?v3, ?v0) ⇒ (fun_app$am(?v1, ?v3) = fun_app$am(?v2, ?v3))) ⇒ (sum$e(?v1, ?v0) = sum$e(?v2, ?v0)))
tff(axiom311,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_a_set_fun$',A__questionmark_v2: 'N_a_set_fun$'] :
      ( ! [A__questionmark_v3: 'N$'] :
          ( 'member$f'(A__questionmark_v3,A__questionmark_v0)
         => ( 'fun_app$am'(A__questionmark_v1,A__questionmark_v3) = 'fun_app$am'(A__questionmark_v2,A__questionmark_v3) ) )
     => ( 'sum$e'(A__questionmark_v1,A__questionmark_v0) = 'sum$e'(A__questionmark_v2,A__questionmark_v0) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_a_n_vec_fun$ ?v2:N_a_n_vec_fun$ (∀ ?v3:N$ (member$f(?v3, ?v0) ⇒ (fun_app$a(?v1, ?v3) = fun_app$a(?v2, ?v3))) ⇒ (sum$(?v1, ?v0) = sum$(?v2, ?v0)))
tff(axiom312,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N_a_n_vec_fun$'] :
      ( ! [A__questionmark_v3: 'N$'] :
          ( 'member$f'(A__questionmark_v3,A__questionmark_v0)
         => ( 'fun_app$a'(A__questionmark_v1,A__questionmark_v3) = 'fun_app$a'(A__questionmark_v2,A__questionmark_v3) ) )
     => ( 'sum$'(A__questionmark_v1,A__questionmark_v0) = 'sum$'(A__questionmark_v2,A__questionmark_v0) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_a_fun$ ?v2:N_a_fun$ (∀ ?v3:N$ (member$f(?v3, ?v0) ⇒ (fun_app$d(?v1, ?v3) = fun_app$d(?v2, ?v3))) ⇒ (sum$a(?v1, ?v0) = sum$a(?v2, ?v0)))
tff(axiom313,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N_a_fun$'] :
      ( ! [A__questionmark_v3: 'N$'] :
          ( 'member$f'(A__questionmark_v3,A__questionmark_v0)
         => ( 'fun_app$d'(A__questionmark_v1,A__questionmark_v3) = 'fun_app$d'(A__questionmark_v2,A__questionmark_v3) ) )
     => ( 'sum$a'(A__questionmark_v1,A__questionmark_v0) = 'sum$a'(A__questionmark_v2,A__questionmark_v0) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A_n_vec$ (fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), fun_app$b(fun_app$c(vector_scalar_mult$, ?v1), ?v2)) = fun_app$b(fun_app$c(vector_scalar_mult$, ?v1), fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), ?v2)))
tff(axiom314,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A_n_vec$'] : 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v1),A__questionmark_v2)) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v1),'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),A__questionmark_v2)) ).

%% ∀ ?v0:Bool ?v1:A_n_vec_n_vec_n_vec$ ?v2:A_n_vec_n_vec_n_vec$ ?v3:N$ (fun_app$f(vec_nth$b((if ?v0 ?v1 else ?v2)), ?v3) = (if ?v0 fun_app$f(vec_nth$b(?v1), ?v3) else fun_app$f(vec_nth$b(?v2), ?v3)))
tff(axiom315,axiom,
    ! [A__questionmark_v0: tlbool,A__questionmark_v1: 'A_n_vec_n_vec_n_vec$',A__questionmark_v2: 'A_n_vec_n_vec_n_vec$',A__questionmark_v3: 'N$'] :
      ( ( ( A__questionmark_v0 = tltrue )
       => ( ( ( A__questionmark_v0 = tltrue )
           => ( 'fun_app$f'('vec_nth$b'(A__questionmark_v1),A__questionmark_v3) = 'fun_app$f'('vec_nth$b'(A__questionmark_v1),A__questionmark_v3) ) )
          & ( ( A__questionmark_v0 != tltrue )
           => ( 'fun_app$f'('vec_nth$b'(A__questionmark_v1),A__questionmark_v3) = 'fun_app$f'('vec_nth$b'(A__questionmark_v2),A__questionmark_v3) ) ) ) )
      & ( ( A__questionmark_v0 != tltrue )
       => ( ( ( A__questionmark_v0 = tltrue )
           => ( 'fun_app$f'('vec_nth$b'(A__questionmark_v2),A__questionmark_v3) = 'fun_app$f'('vec_nth$b'(A__questionmark_v1),A__questionmark_v3) ) )
          & ( ( A__questionmark_v0 != tltrue )
           => ( 'fun_app$f'('vec_nth$b'(A__questionmark_v2),A__questionmark_v3) = 'fun_app$f'('vec_nth$b'(A__questionmark_v2),A__questionmark_v3) ) ) ) ) ) ).

%% ∀ ?v0:Bool ?v1:Nat_n_vec$ ?v2:Nat_n_vec$ ?v3:N$ (fun_app$h(vec_nth$d((if ?v0 ?v1 else ?v2)), ?v3) = (if ?v0 fun_app$h(vec_nth$d(?v1), ?v3) else fun_app$h(vec_nth$d(?v2), ?v3)))
tff(axiom316,axiom,
    ! [A__questionmark_v0: tlbool,A__questionmark_v1: 'Nat_n_vec$',A__questionmark_v2: 'Nat_n_vec$',A__questionmark_v3: 'N$'] :
      ( ( ( A__questionmark_v0 = tltrue )
       => ( ( ( A__questionmark_v0 = tltrue )
           => ( 'fun_app$h'('vec_nth$d'(A__questionmark_v1),A__questionmark_v3) = 'fun_app$h'('vec_nth$d'(A__questionmark_v1),A__questionmark_v3) ) )
          & ( ( A__questionmark_v0 != tltrue )
           => ( 'fun_app$h'('vec_nth$d'(A__questionmark_v1),A__questionmark_v3) = 'fun_app$h'('vec_nth$d'(A__questionmark_v2),A__questionmark_v3) ) ) ) )
      & ( ( A__questionmark_v0 != tltrue )
       => ( ( ( A__questionmark_v0 = tltrue )
           => ( 'fun_app$h'('vec_nth$d'(A__questionmark_v2),A__questionmark_v3) = 'fun_app$h'('vec_nth$d'(A__questionmark_v1),A__questionmark_v3) ) )
          & ( ( A__questionmark_v0 != tltrue )
           => ( 'fun_app$h'('vec_nth$d'(A__questionmark_v2),A__questionmark_v3) = 'fun_app$h'('vec_nth$d'(A__questionmark_v2),A__questionmark_v3) ) ) ) ) ) ).

%% ∀ ?v0:Bool ?v1:A_n_vec_n_vec$ ?v2:A_n_vec_n_vec$ ?v3:N$ (fun_app$a(vec_nth$((if ?v0 ?v1 else ?v2)), ?v3) = (if ?v0 fun_app$a(vec_nth$(?v1), ?v3) else fun_app$a(vec_nth$(?v2), ?v3)))
tff(axiom317,axiom,
    ! [A__questionmark_v0: tlbool,A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'A_n_vec_n_vec$',A__questionmark_v3: 'N$'] :
      ( ( ( A__questionmark_v0 = tltrue )
       => ( ( ( A__questionmark_v0 = tltrue )
           => ( 'fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v3) = 'fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v3) ) )
          & ( ( A__questionmark_v0 != tltrue )
           => ( 'fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v3) = 'fun_app$a'('vec_nth$'(A__questionmark_v2),A__questionmark_v3) ) ) ) )
      & ( ( A__questionmark_v0 != tltrue )
       => ( ( ( A__questionmark_v0 = tltrue )
           => ( 'fun_app$a'('vec_nth$'(A__questionmark_v2),A__questionmark_v3) = 'fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v3) ) )
          & ( ( A__questionmark_v0 != tltrue )
           => ( 'fun_app$a'('vec_nth$'(A__questionmark_v2),A__questionmark_v3) = 'fun_app$a'('vec_nth$'(A__questionmark_v2),A__questionmark_v3) ) ) ) ) ) ).

%% ∀ ?v0:Bool ?v1:A_n_vec$ ?v2:A_n_vec$ ?v3:N$ (fun_app$d(vec_nth$a((if ?v0 ?v1 else ?v2)), ?v3) = (if ?v0 fun_app$d(vec_nth$a(?v1), ?v3) else fun_app$d(vec_nth$a(?v2), ?v3)))
tff(axiom318,axiom,
    ! [A__questionmark_v0: tlbool,A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'A_n_vec$',A__questionmark_v3: 'N$'] :
      ( ( ( A__questionmark_v0 = tltrue )
       => ( ( ( A__questionmark_v0 = tltrue )
           => ( 'fun_app$d'('vec_nth$a'(A__questionmark_v1),A__questionmark_v3) = 'fun_app$d'('vec_nth$a'(A__questionmark_v1),A__questionmark_v3) ) )
          & ( ( A__questionmark_v0 != tltrue )
           => ( 'fun_app$d'('vec_nth$a'(A__questionmark_v1),A__questionmark_v3) = 'fun_app$d'('vec_nth$a'(A__questionmark_v2),A__questionmark_v3) ) ) ) )
      & ( ( A__questionmark_v0 != tltrue )
       => ( ( ( A__questionmark_v0 = tltrue )
           => ( 'fun_app$d'('vec_nth$a'(A__questionmark_v2),A__questionmark_v3) = 'fun_app$d'('vec_nth$a'(A__questionmark_v1),A__questionmark_v3) ) )
          & ( ( A__questionmark_v0 != tltrue )
           => ( 'fun_app$d'('vec_nth$a'(A__questionmark_v2),A__questionmark_v3) = 'fun_app$d'('vec_nth$a'(A__questionmark_v2),A__questionmark_v3) ) ) ) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec$ ((?v0 = ?v1) = ∀ ?v2:N$ (fun_app$f(vec_nth$b(?v0), ?v2) = fun_app$f(vec_nth$b(?v1), ?v2)))
tff(axiom319,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$'] :
      ( ( A__questionmark_v0 = A__questionmark_v1 )
    <=> ! [A__questionmark_v2: 'N$'] : 'fun_app$f'('vec_nth$b'(A__questionmark_v0),A__questionmark_v2) = 'fun_app$f'('vec_nth$b'(A__questionmark_v1),A__questionmark_v2) ) ).

%% ∀ ?v0:Nat_n_vec$ ?v1:Nat_n_vec$ ((?v0 = ?v1) = ∀ ?v2:N$ (fun_app$h(vec_nth$d(?v0), ?v2) = fun_app$h(vec_nth$d(?v1), ?v2)))
tff(axiom320,axiom,
    ! [A__questionmark_v0: 'Nat_n_vec$',A__questionmark_v1: 'Nat_n_vec$'] :
      ( ( A__questionmark_v0 = A__questionmark_v1 )
    <=> ! [A__questionmark_v2: 'N$'] : 'fun_app$h'('vec_nth$d'(A__questionmark_v0),A__questionmark_v2) = 'fun_app$h'('vec_nth$d'(A__questionmark_v1),A__questionmark_v2) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ((?v0 = ?v1) = ∀ ?v2:N$ (fun_app$a(vec_nth$(?v0), ?v2) = fun_app$a(vec_nth$(?v1), ?v2)))
tff(axiom321,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$'] :
      ( ( A__questionmark_v0 = A__questionmark_v1 )
    <=> ! [A__questionmark_v2: 'N$'] : 'fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v2) = 'fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v2) ) ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec$ ((?v0 = ?v1) = ∀ ?v2:N$ (fun_app$d(vec_nth$a(?v0), ?v2) = fun_app$d(vec_nth$a(?v1), ?v2)))
tff(axiom322,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec$'] :
      ( ( A__questionmark_v0 = A__questionmark_v1 )
    <=> ! [A__questionmark_v2: 'N$'] : 'fun_app$d'('vec_nth$a'(A__questionmark_v0),A__questionmark_v2) = 'fun_app$d'('vec_nth$a'(A__questionmark_v1),A__questionmark_v2) ) ).

%% ∀ ?v0:N_a_n_vec_n_vec_bool_fun_fun$ (∀ ?v1:N$ ∃ ?v2:A_n_vec_n_vec$ fun_app$x(fun_app$ba(?v0, ?v1), ?v2) = ∃ ?v1:A_n_vec_n_vec_n_vec$ ∀ ?v2:N$ fun_app$x(fun_app$ba(?v0, ?v2), fun_app$f(vec_nth$b(?v1), ?v2)))
tff(axiom323,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_n_vec_bool_fun_fun$'] :
      ( ! [A__questionmark_v1: 'N$'] :
        ? [A__questionmark_v2: 'A_n_vec_n_vec$'] : 'fun_app$x'('fun_app$ba'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)
    <=> ? [A__questionmark_v1: 'A_n_vec_n_vec_n_vec$'] :
        ! [A__questionmark_v2: 'N$'] : 'fun_app$x'('fun_app$ba'(A__questionmark_v0,A__questionmark_v2),'fun_app$f'('vec_nth$b'(A__questionmark_v1),A__questionmark_v2)) ) ).

%% ∀ ?v0:N_nat_bool_fun_fun$ (∀ ?v1:N$ ∃ ?v2:Nat$ fun_app$m(fun_app$aw(?v0, ?v1), ?v2) = ∃ ?v1:Nat_n_vec$ ∀ ?v2:N$ fun_app$m(fun_app$aw(?v0, ?v2), fun_app$h(vec_nth$d(?v1), ?v2)))
tff(axiom324,axiom,
    ! [A__questionmark_v0: 'N_nat_bool_fun_fun$'] :
      ( ! [A__questionmark_v1: 'N$'] :
        ? [A__questionmark_v2: 'Nat$'] : 'fun_app$m'('fun_app$aw'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)
    <=> ? [A__questionmark_v1: 'Nat_n_vec$'] :
        ! [A__questionmark_v2: 'N$'] : 'fun_app$m'('fun_app$aw'(A__questionmark_v0,A__questionmark_v2),'fun_app$h'('vec_nth$d'(A__questionmark_v1),A__questionmark_v2)) ) ).

%% ∀ ?v0:N_a_n_vec_bool_fun_fun$ (∀ ?v1:N$ ∃ ?v2:A_n_vec$ fun_app$p(fun_app$as(?v0, ?v1), ?v2) = ∃ ?v1:A_n_vec_n_vec$ ∀ ?v2:N$ fun_app$p(fun_app$as(?v0, ?v2), fun_app$a(vec_nth$(?v1), ?v2)))
tff(axiom325,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_bool_fun_fun$'] :
      ( ! [A__questionmark_v1: 'N$'] :
        ? [A__questionmark_v2: 'A_n_vec$'] : 'fun_app$p'('fun_app$as'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)
    <=> ? [A__questionmark_v1: 'A_n_vec_n_vec$'] :
        ! [A__questionmark_v2: 'N$'] : 'fun_app$p'('fun_app$as'(A__questionmark_v0,A__questionmark_v2),'fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v2)) ) ).

%% ∀ ?v0:N_a_bool_fun_fun$ (∀ ?v1:N$ ∃ ?v2:A$ fun_app$u(fun_app$bb(?v0, ?v1), ?v2) = ∃ ?v1:A_n_vec$ ∀ ?v2:N$ fun_app$u(fun_app$bb(?v0, ?v2), fun_app$d(vec_nth$a(?v1), ?v2)))
tff(axiom326,axiom,
    ! [A__questionmark_v0: 'N_a_bool_fun_fun$'] :
      ( ! [A__questionmark_v1: 'N$'] :
        ? [A__questionmark_v2: 'A$'] : 'fun_app$u'('fun_app$bb'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)
    <=> ? [A__questionmark_v1: 'A_n_vec$'] :
        ! [A__questionmark_v2: 'N$'] : 'fun_app$u'('fun_app$bb'(A__questionmark_v0,A__questionmark_v2),'fun_app$d'('vec_nth$a'(A__questionmark_v1),A__questionmark_v2)) ) ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec$ ((vec_nth$b(?v0) = vec_nth$b(?v1)) = (?v0 = ?v1))
tff(axiom327,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$'] :
      ( ( 'vec_nth$b'(A__questionmark_v0) = 'vec_nth$b'(A__questionmark_v1) )
    <=> ( A__questionmark_v0 = A__questionmark_v1 ) ) ).

%% ∀ ?v0:Nat_n_vec$ ?v1:Nat_n_vec$ ((vec_nth$d(?v0) = vec_nth$d(?v1)) = (?v0 = ?v1))
tff(axiom328,axiom,
    ! [A__questionmark_v0: 'Nat_n_vec$',A__questionmark_v1: 'Nat_n_vec$'] :
      ( ( 'vec_nth$d'(A__questionmark_v0) = 'vec_nth$d'(A__questionmark_v1) )
    <=> ( A__questionmark_v0 = A__questionmark_v1 ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ((vec_nth$(?v0) = vec_nth$(?v1)) = (?v0 = ?v1))
tff(axiom329,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$'] :
      ( ( 'vec_nth$'(A__questionmark_v0) = 'vec_nth$'(A__questionmark_v1) )
    <=> ( A__questionmark_v0 = A__questionmark_v1 ) ) ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec$ ((vec_nth$a(?v0) = vec_nth$a(?v1)) = (?v0 = ?v1))
tff(axiom330,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec$'] :
      ( ( 'vec_nth$a'(A__questionmark_v0) = 'vec_nth$a'(A__questionmark_v1) )
    <=> ( A__questionmark_v0 = A__questionmark_v1 ) ) ).

%% ∀ ?v0:N_a_fun_bool_fun$ ?v1:N_a_fun$ ((∃ ?v2:N_a_fun$ (fun_app$(?v0, ?v2) ∧ ∀ ?v3:N_a_fun$ (fun_app$(?v0, ?v3) ⇒ (?v3 = ?v2))) ∧ fun_app$(?v0, ?v1)) ⇒ (the$(?v0) = ?v1))
tff(axiom331,axiom,
    ! [A__questionmark_v0: 'N_a_fun_bool_fun$',A__questionmark_v1: 'N_a_fun$'] :
      ( ( ? [A__questionmark_v2: 'N_a_fun$'] :
            ( 'fun_app$'(A__questionmark_v0,A__questionmark_v2)
            & ! [A__questionmark_v3: 'N_a_fun$'] :
                ( 'fun_app$'(A__questionmark_v0,A__questionmark_v3)
               => ( A__questionmark_v3 = A__questionmark_v2 ) ) )
        & 'fun_app$'(A__questionmark_v0,A__questionmark_v1) )
     => ( 'the$'(A__questionmark_v0) = A__questionmark_v1 ) ) ).

%% ∀ ?v0:N_a_fun_bool_fun$ ?v1:N_a_fun_bool_fun$ ((∃ ?v2:N_a_fun$ (fun_app$(?v0, ?v2) ∧ ∀ ?v3:N_a_fun$ (fun_app$(?v0, ?v3) ⇒ (?v3 = ?v2))) ∧ ∀ ?v2:N_a_fun$ (fun_app$(?v0, ?v2) ⇒ fun_app$(?v1, ?v2))) ⇒ fun_app$(?v1, the$(?v0)))
tff(axiom332,axiom,
    ! [A__questionmark_v0: 'N_a_fun_bool_fun$',A__questionmark_v1: 'N_a_fun_bool_fun$'] :
      ( ( ? [A__questionmark_v2: 'N_a_fun$'] :
            ( 'fun_app$'(A__questionmark_v0,A__questionmark_v2)
            & ! [A__questionmark_v3: 'N_a_fun$'] :
                ( 'fun_app$'(A__questionmark_v0,A__questionmark_v3)
               => ( A__questionmark_v3 = A__questionmark_v2 ) ) )
        & ! [A__questionmark_v2: 'N_a_fun$'] :
            ( 'fun_app$'(A__questionmark_v0,A__questionmark_v2)
           => 'fun_app$'(A__questionmark_v1,A__questionmark_v2) ) )
     => 'fun_app$'(A__questionmark_v1,'the$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:Bool ?v1:N_a_fun$ ?v2:N_a_fun$ ((if ?v0 ?v1 else ?v2) = the$(uus$(?v0, ?v1, ?v2)))
tff(axiom333,axiom,
    ! [A__questionmark_v0: tlbool,A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N_a_fun$'] :
      ( ( ( A__questionmark_v0 = tltrue )
       => ( A__questionmark_v1 = 'the$'('uus$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2)) ) )
      & ( ( A__questionmark_v0 != tltrue )
       => ( A__questionmark_v2 = 'the$'('uus$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2)) ) ) ) ).

%% ∀ ?v0:N_a_fun_bool_fun$ ?v1:N_a_fun$ ?v2:N_a_fun_bool_fun$ ((fun_app$(?v0, ?v1) ∧ (∀ ?v3:N_a_fun$ (fun_app$(?v0, ?v3) ⇒ (?v3 = ?v1)) ∧ ∀ ?v3:N_a_fun$ (fun_app$(?v0, ?v3) ⇒ fun_app$(?v2, ?v3)))) ⇒ fun_app$(?v2, the$(?v0)))
tff(axiom334,axiom,
    ! [A__questionmark_v0: 'N_a_fun_bool_fun$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N_a_fun_bool_fun$'] :
      ( ( 'fun_app$'(A__questionmark_v0,A__questionmark_v1)
        & ! [A__questionmark_v3: 'N_a_fun$'] :
            ( 'fun_app$'(A__questionmark_v0,A__questionmark_v3)
           => ( A__questionmark_v3 = A__questionmark_v1 ) )
        & ! [A__questionmark_v3: 'N_a_fun$'] :
            ( 'fun_app$'(A__questionmark_v0,A__questionmark_v3)
           => 'fun_app$'(A__questionmark_v2,A__questionmark_v3) ) )
     => 'fun_app$'(A__questionmark_v2,'the$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:N_a_fun_bool_fun$ (∃ ?v1:N_a_fun$ (fun_app$(?v0, ?v1) ∧ ∀ ?v2:N_a_fun$ (fun_app$(?v0, ?v2) ⇒ (?v2 = ?v1))) ⇒ fun_app$(?v0, the$(?v0)))
tff(axiom335,axiom,
    ! [A__questionmark_v0: 'N_a_fun_bool_fun$'] :
      ( ? [A__questionmark_v1: 'N_a_fun$'] :
          ( 'fun_app$'(A__questionmark_v0,A__questionmark_v1)
          & ! [A__questionmark_v2: 'N_a_fun$'] :
              ( 'fun_app$'(A__questionmark_v0,A__questionmark_v2)
             => ( A__questionmark_v2 = A__questionmark_v1 ) ) )
     => 'fun_app$'(A__questionmark_v0,'the$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:N_a_fun_bool_fun$ ?v1:N_a_fun$ ((fun_app$(?v0, ?v1) ∧ ∀ ?v2:N_a_fun$ (fun_app$(?v0, ?v2) ⇒ (?v2 = ?v1))) ⇒ fun_app$(?v0, the$(?v0)))
tff(axiom336,axiom,
    ! [A__questionmark_v0: 'N_a_fun_bool_fun$',A__questionmark_v1: 'N_a_fun$'] :
      ( ( 'fun_app$'(A__questionmark_v0,A__questionmark_v1)
        & ! [A__questionmark_v2: 'N_a_fun$'] :
            ( 'fun_app$'(A__questionmark_v0,A__questionmark_v2)
           => ( A__questionmark_v2 = A__questionmark_v1 ) ) )
     => 'fun_app$'(A__questionmark_v0,'the$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:A_n_vec$ ?v1:N_a_n_vec_n_vec_fun$ ?v2:N_set$ (sum$b(uut$(?v0, ?v1), ?v2) = vector_scalar_mult$a(?v0, sum$b(?v1, ?v2)))
tff(axiom337,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'N_a_n_vec_n_vec_fun$',A__questionmark_v2: 'N_set$'] : 'sum$b'('uut$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'vector_scalar_mult$a'(A__questionmark_v0,'sum$b'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A$ ?v1:N_a_n_vec_fun$ ?v2:N_set$ (sum$(uuu$(?v0, ?v1), ?v2) = fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), sum$(?v1, ?v2)))
tff(axiom338,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N_set$'] : 'sum$'('uuu$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),'sum$'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A$ ?v1:N_a_n_vec_fun$ ?v2:N_set$ (fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), sum$(?v1, ?v2)) = sum$(uuu$(?v0, ?v1), ?v2))
tff(axiom339,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N_set$'] : 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),'sum$'(A__questionmark_v1,A__questionmark_v2)) = 'sum$'('uuu$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) ).

%% ∀ ?v0:N_a_fun$ ?v1:A_n_vec$ ((sum$(uuv$(?v0), top$) = ?v1) = ∀ ?v2:N$ (fun_app$d(?v0, ?v2) = fun_app$d(vec_nth$a(?v1), ?v2)))
tff(axiom340,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'A_n_vec$'] :
      ( ( 'sum$'('uuv$'(A__questionmark_v0),'top$') = A__questionmark_v1 )
    <=> ! [A__questionmark_v2: 'N$'] : 'fun_app$d'(A__questionmark_v0,A__questionmark_v2) = 'fun_app$d'('vec_nth$a'(A__questionmark_v1),A__questionmark_v2) ) ).

%% ∀ ?v0:N$ (fun_app$d(w$, ?v0) = sum$a(fun_app$e(uuw$, ?v0), top$))
tff(axiom341,axiom,
    ! [A__questionmark_v0: 'N$'] : 'fun_app$d'('w$',A__questionmark_v0) = 'sum$a'('fun_app$e'('uuw$',A__questionmark_v0),'top$') ).

%% ∀ ?v0:A_a_fun$ ?v1:A_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$d(vec_nth$a(fun_app$a(vec_nth$(map_matrix$(?v0, ?v1)), ?v2)), ?v3) = fun_app$k(?v0, fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v1), ?v2)), ?v3)))
tff(axiom342,axiom,
    ! [A__questionmark_v0: 'A_a_fun$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'('map_matrix$'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2)),A__questionmark_v3) = 'fun_app$k'(A__questionmark_v0,'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v2)),A__questionmark_v3)) ).

%% ∀ ?v0:A_a_n_vec_fun$ ?v1:A_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$a(vec_nth$(fun_app$f(vec_nth$b(map_matrix$a(?v0, ?v1)), ?v2)), ?v3) = fun_app$o(?v0, fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v1), ?v2)), ?v3)))
tff(axiom343,axiom,
    ! [A__questionmark_v0: 'A_a_n_vec_fun$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$a'('vec_nth$'('fun_app$f'('vec_nth$b'('map_matrix$a'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2)),A__questionmark_v3) = 'fun_app$o'(A__questionmark_v0,'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v2)),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_a_fun$ ?v1:A_n_vec_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$d(vec_nth$a(fun_app$a(vec_nth$(map_matrix$b(?v0, ?v1)), ?v2)), ?v3) = fun_app$j(?v0, fun_app$a(vec_nth$(fun_app$f(vec_nth$b(?v1), ?v2)), ?v3)))
tff(axiom344,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_fun$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'('map_matrix$b'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2)),A__questionmark_v3) = 'fun_app$j'(A__questionmark_v0,'fun_app$a'('vec_nth$'('fun_app$f'('vec_nth$b'(A__questionmark_v1),A__questionmark_v2)),A__questionmark_v3)) ).

%% ∀ ?v0:Nat_a_fun$ ?v1:Nat_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$d(vec_nth$a(fun_app$a(vec_nth$(map_matrix$c(?v0, ?v1)), ?v2)), ?v3) = fun_app$aa(?v0, fun_app$h(vec_nth$d(vec_nth$e(?v1, ?v2)), ?v3)))
tff(axiom345,axiom,
    ! [A__questionmark_v0: 'Nat_a_fun$',A__questionmark_v1: 'Nat_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'('map_matrix$c'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2)),A__questionmark_v3) = 'fun_app$aa'(A__questionmark_v0,'fun_app$h'('vec_nth$d'('vec_nth$e'(A__questionmark_v1,A__questionmark_v2)),A__questionmark_v3)) ).

%% ∀ ?v0:A_nat_fun$ ?v1:A_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$h(vec_nth$d(vec_nth$e(map_matrix$d(?v0, ?v1), ?v2)), ?v3) = fun_app$bc(?v0, fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v1), ?v2)), ?v3)))
tff(axiom346,axiom,
    ! [A__questionmark_v0: 'A_nat_fun$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$h'('vec_nth$d'('vec_nth$e'('map_matrix$d'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)),A__questionmark_v3) = 'fun_app$bc'(A__questionmark_v0,'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v2)),A__questionmark_v3)) ).

%% ∀ ?v0:Nat_a_n_vec_fun$ ?v1:Nat_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$a(vec_nth$(fun_app$f(vec_nth$b(map_matrix$e(?v0, ?v1)), ?v2)), ?v3) = fun_app$ae(?v0, fun_app$h(vec_nth$d(vec_nth$e(?v1, ?v2)), ?v3)))
tff(axiom347,axiom,
    ! [A__questionmark_v0: 'Nat_a_n_vec_fun$',A__questionmark_v1: 'Nat_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$a'('vec_nth$'('fun_app$f'('vec_nth$b'('map_matrix$e'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2)),A__questionmark_v3) = 'fun_app$ae'(A__questionmark_v0,'fun_app$h'('vec_nth$d'('vec_nth$e'(A__questionmark_v1,A__questionmark_v2)),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_nat_fun$ ?v1:A_n_vec_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$h(vec_nth$d(vec_nth$e(map_matrix$f(?v0, ?v1), ?v2)), ?v3) = fun_app$bd(?v0, fun_app$a(vec_nth$(fun_app$f(vec_nth$b(?v1), ?v2)), ?v3)))
tff(axiom348,axiom,
    ! [A__questionmark_v0: 'A_n_vec_nat_fun$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$h'('vec_nth$d'('vec_nth$e'('map_matrix$f'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)),A__questionmark_v3) = 'fun_app$bd'(A__questionmark_v0,'fun_app$a'('vec_nth$'('fun_app$f'('vec_nth$b'(A__questionmark_v1),A__questionmark_v2)),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_a_n_vec_fun$ ?v1:A_n_vec_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$a(vec_nth$(fun_app$f(vec_nth$b(map_matrix$g(?v0, ?v1)), ?v2)), ?v3) = fun_app$b(?v0, fun_app$a(vec_nth$(fun_app$f(vec_nth$b(?v1), ?v2)), ?v3)))
tff(axiom349,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_n_vec_fun$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$a'('vec_nth$'('fun_app$f'('vec_nth$b'('map_matrix$g'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2)),A__questionmark_v3) = 'fun_app$b'(A__questionmark_v0,'fun_app$a'('vec_nth$'('fun_app$f'('vec_nth$b'(A__questionmark_v1),A__questionmark_v2)),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_n_vec_a_fun$ ?v1:A_n_vec_n_vec_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$d(vec_nth$a(fun_app$a(vec_nth$(map_matrix$h(?v0, ?v1)), ?v2)), ?v3) = fun_app$w(?v0, fun_app$f(vec_nth$b(fun_app$g(vec_nth$c(?v1), ?v2)), ?v3)))
tff(axiom350,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_a_fun$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'('map_matrix$h'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2)),A__questionmark_v3) = 'fun_app$w'(A__questionmark_v0,'fun_app$f'('vec_nth$b'('fun_app$g'('vec_nth$c'(A__questionmark_v1),A__questionmark_v2)),A__questionmark_v3)) ).

%% ∀ ?v0:A_a_n_vec_n_vec_fun$ ?v1:A_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$f(vec_nth$b(fun_app$g(vec_nth$c(map_matrix$i(?v0, ?v1)), ?v2)), ?v3) = fun_app$be(?v0, fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v1), ?v2)), ?v3)))
tff(axiom351,axiom,
    ! [A__questionmark_v0: 'A_a_n_vec_n_vec_fun$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$f'('vec_nth$b'('fun_app$g'('vec_nth$c'('map_matrix$i'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2)),A__questionmark_v3) = 'fun_app$be'(A__questionmark_v0,'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v2)),A__questionmark_v3)) ).

%% ∀ ?v0:N$ (fun_app$d(w$, ?v0) = sum$a(fun_app$e(uuw$, ?v0), top$))
tff(axiom352,axiom,
    ! [A__questionmark_v0: 'N$'] : 'fun_app$d'('w$',A__questionmark_v0) = 'sum$a'('fun_app$e'('uuw$',A__questionmark_v0),'top$') ).

%% (the$(uuy$) = f$)
tff(axiom353,axiom,
    'the$'('uuy$') = 'f$' ).

%% (the$(uva$) = g$)
tff(axiom354,axiom,
    'the$'('uva$') = 'g$' ).

%% ∀ ?v0:Nat$ (member$a(?v0, top$e) = true)
tff(axiom355,axiom,
    ! [A__questionmark_v0: 'Nat$'] :
      ( 'member$a'(A__questionmark_v0,'top$e')
    <=> $true ) ).

%% ∀ ?v0:N_a_n_vec_fun$ (member$c(?v0, top$c) = true)
tff(axiom356,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$'] :
      ( 'member$c'(A__questionmark_v0,'top$c')
    <=> $true ) ).

%% ∀ ?v0:N_a_fun$ (member$e(?v0, top$d) = true)
tff(axiom357,axiom,
    ! [A__questionmark_v0: 'N_a_fun$'] :
      ( 'member$e'(A__questionmark_v0,'top$d')
    <=> $true ) ).

%% ∀ ?v0:A$ (member$g(?v0, top$f) = true)
tff(axiom358,axiom,
    ! [A__questionmark_v0: 'A$'] :
      ( 'member$g'(A__questionmark_v0,'top$f')
    <=> $true ) ).

%% ∀ ?v0:N$ (member$f(?v0, top$) = true)
tff(axiom359,axiom,
    ! [A__questionmark_v0: 'N$'] :
      ( 'member$f'(A__questionmark_v0,'top$')
    <=> $true ) ).

%% ∀ ?v0:Nat$ member$a(?v0, top$e)
tff(axiom360,axiom,
    ! [A__questionmark_v0: 'Nat$'] : 'member$a'(A__questionmark_v0,'top$e') ).

%% ∀ ?v0:N_a_n_vec_fun$ member$c(?v0, top$c)
tff(axiom361,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$'] : 'member$c'(A__questionmark_v0,'top$c') ).

%% ∀ ?v0:N_a_fun$ member$e(?v0, top$d)
tff(axiom362,axiom,
    ! [A__questionmark_v0: 'N_a_fun$'] : 'member$e'(A__questionmark_v0,'top$d') ).

%% ∀ ?v0:A$ member$g(?v0, top$f)
tff(axiom363,axiom,
    ! [A__questionmark_v0: 'A$'] : 'member$g'(A__questionmark_v0,'top$f') ).

%% ∀ ?v0:N$ member$f(?v0, top$)
tff(axiom364,axiom,
    ! [A__questionmark_v0: 'N$'] : 'member$f'(A__questionmark_v0,'top$') ).

%% ∀ ?v0:Nat$ (fun_app$m(top$g, ?v0) = top$h)
tff(axiom365,axiom,
    ! [A__questionmark_v0: 'Nat$'] :
      ( 'fun_app$m'('top$g',A__questionmark_v0)
    <=> 'top$h' ) ).

%% ∀ ?v0:N$ (fun_app$t(top$i, ?v0) = top$h)
tff(axiom366,axiom,
    ! [A__questionmark_v0: 'N$'] :
      ( 'fun_app$t'('top$i',A__questionmark_v0)
    <=> 'top$h' ) ).

%% ∀ ?v0:Nat_n_vec_n_vec$ (trace$(?v0) = sum$k(uvb$(?v0), top$))
tff(axiom367,axiom,
    ! [A__questionmark_v0: 'Nat_n_vec_n_vec$'] : 'trace$'(A__questionmark_v0) = 'sum$k'('uvb$'(A__questionmark_v0),'top$') ).

%% ∀ ?v0:A_n_n_fun_vec_n_n_fun_vec$ (trace$a(?v0) = sum$c(uvc$(?v0), top$j))
tff(axiom368,axiom,
    ! [A__questionmark_v0: 'A_n_n_fun_vec_n_n_fun_vec$'] : 'trace$a'(A__questionmark_v0) = 'sum$c'('uvc$'(A__questionmark_v0),'top$j') ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec_n_vec$ (trace$b(?v0) = sum$b(uvd$(?v0), top$))
tff(axiom369,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec_n_vec$'] : 'trace$b'(A__questionmark_v0) = 'sum$b'('uvd$'(A__questionmark_v0),'top$') ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ (trace$c(?v0) = sum$(uve$(?v0), top$))
tff(axiom370,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$'] : 'trace$c'(A__questionmark_v0) = 'sum$'('uve$'(A__questionmark_v0),'top$') ).

%% ∀ ?v0:A_n_vec_n_vec$ (fun_app$w(trace$d, ?v0) = sum$a(uvf$(?v0), top$))
tff(axiom371,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$'] : 'fun_app$w'('trace$d',A__questionmark_v0) = 'sum$a'('uvf$'(A__questionmark_v0),'top$') ).

%% is_basis$(set_of_vector$(y$))
tff(axiom372,axiom,
    'is_basis$'('set_of_vector$'('y$')) ).

%% is_basis$(set_of_vector$(x$))
tff(axiom373,axiom,
    'is_basis$'('set_of_vector$'('x$')) ).

%% ∀ ?v0:N_a_n_vec_fun$ ?v1:N_a_n_vec_fun_bool_fun$ (member$c(?v0, collect$b(?v1)) = fun_app$r(?v1, ?v0))
tff(axiom374,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$',A__questionmark_v1: 'N_a_n_vec_fun_bool_fun$'] :
      ( 'member$c'(A__questionmark_v0,'collect$b'(A__questionmark_v1))
    <=> 'fun_app$r'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_a_fun_bool_fun$ (member$e(?v0, collect$c(?v1)) = fun_app$(?v1, ?v0))
tff(axiom375,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_a_fun_bool_fun$'] :
      ( 'member$e'(A__questionmark_v0,'collect$c'(A__questionmark_v1))
    <=> 'fun_app$'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:N$ ?v1:N_bool_fun$ (member$f(?v0, collect$(?v1)) = fun_app$t(?v1, ?v0))
tff(axiom376,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'N_bool_fun$'] :
      ( 'member$f'(A__questionmark_v0,'collect$'(A__questionmark_v1))
    <=> 'fun_app$t'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec_bool_fun$ (member$(?v0, collect$d(?v1)) = fun_app$p(?v1, ?v0))
tff(axiom377,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec_bool_fun$'] :
      ( 'member$'(A__questionmark_v0,'collect$d'(A__questionmark_v1))
    <=> 'fun_app$p'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:A$ ?v1:A_bool_fun$ (member$g(?v0, collect$e(?v1)) = fun_app$u(?v1, ?v0))
tff(axiom378,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A_bool_fun$'] :
      ( 'member$g'(A__questionmark_v0,'collect$e'(A__questionmark_v1))
    <=> 'fun_app$u'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:N_n_fun$ ?v1:N_n_fun_bool_fun$ (member$d(?v0, collect$f(?v1)) = fun_app$s(?v1, ?v0))
tff(axiom379,axiom,
    ! [A__questionmark_v0: 'N_n_fun$',A__questionmark_v1: 'N_n_fun_bool_fun$'] :
      ( 'member$d'(A__questionmark_v0,'collect$f'(A__questionmark_v1))
    <=> 'fun_app$s'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:Nat_nat_fun$ ?v1:Nat_nat_fun_bool_fun$ (member$b(?v0, collect$g(?v1)) = fun_app$q(?v1, ?v0))
tff(axiom380,axiom,
    ! [A__questionmark_v0: 'Nat_nat_fun$',A__questionmark_v1: 'Nat_nat_fun_bool_fun$'] :
      ( 'member$b'(A__questionmark_v0,'collect$g'(A__questionmark_v1))
    <=> 'fun_app$q'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:Nat$ ?v1:Nat_bool_fun$ (member$a(?v0, collect$a(?v1)) = fun_app$m(?v1, ?v0))
tff(axiom381,axiom,
    ! [A__questionmark_v0: 'Nat$',A__questionmark_v1: 'Nat_bool_fun$'] :
      ( 'member$a'(A__questionmark_v0,'collect$a'(A__questionmark_v1))
    <=> 'fun_app$m'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:N_a_n_vec_fun_set$ (collect$b(uvg$(?v0)) = ?v0)
tff(axiom382,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun_set$'] : 'collect$b'('uvg$'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:N_a_fun_set$ (collect$c(uvh$(?v0)) = ?v0)
tff(axiom383,axiom,
    ! [A__questionmark_v0: 'N_a_fun_set$'] : 'collect$c'('uvh$'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:N_set$ (collect$(uvi$(?v0)) = ?v0)
tff(axiom384,axiom,
    ! [A__questionmark_v0: 'N_set$'] : 'collect$'('uvi$'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:A_n_vec_set$ (collect$d(uvj$(?v0)) = ?v0)
tff(axiom385,axiom,
    ! [A__questionmark_v0: 'A_n_vec_set$'] : 'collect$d'('uvj$'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:A_set$ (collect$e(uvk$(?v0)) = ?v0)
tff(axiom386,axiom,
    ! [A__questionmark_v0: 'A_set$'] : 'collect$e'('uvk$'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:N_n_fun_set$ (collect$f(uvl$(?v0)) = ?v0)
tff(axiom387,axiom,
    ! [A__questionmark_v0: 'N_n_fun_set$'] : 'collect$f'('uvl$'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:Nat_nat_fun_set$ (collect$g(uvm$(?v0)) = ?v0)
tff(axiom388,axiom,
    ! [A__questionmark_v0: 'Nat_nat_fun_set$'] : 'collect$g'('uvm$'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:Nat_set$ (collect$a(uvn$(?v0)) = ?v0)
tff(axiom389,axiom,
    ! [A__questionmark_v0: 'Nat_set$'] : 'collect$a'('uvn$'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:N_bool_fun$ ?v1:N_bool_fun$ (∀ ?v2:N$ (fun_app$t(?v0, ?v2) = fun_app$t(?v1, ?v2)) ⇒ (collect$(?v0) = collect$(?v1)))
tff(axiom390,axiom,
    ! [A__questionmark_v0: 'N_bool_fun$',A__questionmark_v1: 'N_bool_fun$'] :
      ( ! [A__questionmark_v2: 'N$'] :
          ( 'fun_app$t'(A__questionmark_v0,A__questionmark_v2)
        <=> 'fun_app$t'(A__questionmark_v1,A__questionmark_v2) )
     => ( 'collect$'(A__questionmark_v0) = 'collect$'(A__questionmark_v1) ) ) ).

%% ∀ ?v0:A_n_vec_bool_fun$ ?v1:A_n_vec_bool_fun$ (∀ ?v2:A_n_vec$ (fun_app$p(?v0, ?v2) = fun_app$p(?v1, ?v2)) ⇒ (collect$d(?v0) = collect$d(?v1)))
tff(axiom391,axiom,
    ! [A__questionmark_v0: 'A_n_vec_bool_fun$',A__questionmark_v1: 'A_n_vec_bool_fun$'] :
      ( ! [A__questionmark_v2: 'A_n_vec$'] :
          ( 'fun_app$p'(A__questionmark_v0,A__questionmark_v2)
        <=> 'fun_app$p'(A__questionmark_v1,A__questionmark_v2) )
     => ( 'collect$d'(A__questionmark_v0) = 'collect$d'(A__questionmark_v1) ) ) ).

%% ∀ ?v0:A_bool_fun$ ?v1:A_bool_fun$ (∀ ?v2:A$ (fun_app$u(?v0, ?v2) = fun_app$u(?v1, ?v2)) ⇒ (collect$e(?v0) = collect$e(?v1)))
tff(axiom392,axiom,
    ! [A__questionmark_v0: 'A_bool_fun$',A__questionmark_v1: 'A_bool_fun$'] :
      ( ! [A__questionmark_v2: 'A$'] :
          ( 'fun_app$u'(A__questionmark_v0,A__questionmark_v2)
        <=> 'fun_app$u'(A__questionmark_v1,A__questionmark_v2) )
     => ( 'collect$e'(A__questionmark_v0) = 'collect$e'(A__questionmark_v1) ) ) ).

%% ∀ ?v0:N_n_fun_bool_fun$ ?v1:N_n_fun_bool_fun$ (∀ ?v2:N_n_fun$ (fun_app$s(?v0, ?v2) = fun_app$s(?v1, ?v2)) ⇒ (collect$f(?v0) = collect$f(?v1)))
tff(axiom393,axiom,
    ! [A__questionmark_v0: 'N_n_fun_bool_fun$',A__questionmark_v1: 'N_n_fun_bool_fun$'] :
      ( ! [A__questionmark_v2: 'N_n_fun$'] :
          ( 'fun_app$s'(A__questionmark_v0,A__questionmark_v2)
        <=> 'fun_app$s'(A__questionmark_v1,A__questionmark_v2) )
     => ( 'collect$f'(A__questionmark_v0) = 'collect$f'(A__questionmark_v1) ) ) ).

%% ∀ ?v0:Nat_nat_fun_bool_fun$ ?v1:Nat_nat_fun_bool_fun$ (∀ ?v2:Nat_nat_fun$ (fun_app$q(?v0, ?v2) = fun_app$q(?v1, ?v2)) ⇒ (collect$g(?v0) = collect$g(?v1)))
tff(axiom394,axiom,
    ! [A__questionmark_v0: 'Nat_nat_fun_bool_fun$',A__questionmark_v1: 'Nat_nat_fun_bool_fun$'] :
      ( ! [A__questionmark_v2: 'Nat_nat_fun$'] :
          ( 'fun_app$q'(A__questionmark_v0,A__questionmark_v2)
        <=> 'fun_app$q'(A__questionmark_v1,A__questionmark_v2) )
     => ( 'collect$g'(A__questionmark_v0) = 'collect$g'(A__questionmark_v1) ) ) ).

%% ∀ ?v0:Nat_bool_fun$ ?v1:Nat_bool_fun$ (∀ ?v2:Nat$ (fun_app$m(?v0, ?v2) = fun_app$m(?v1, ?v2)) ⇒ (collect$a(?v0) = collect$a(?v1)))
tff(axiom395,axiom,
    ! [A__questionmark_v0: 'Nat_bool_fun$',A__questionmark_v1: 'Nat_bool_fun$'] :
      ( ! [A__questionmark_v2: 'Nat$'] :
          ( 'fun_app$m'(A__questionmark_v0,A__questionmark_v2)
        <=> 'fun_app$m'(A__questionmark_v1,A__questionmark_v2) )
     => ( 'collect$a'(A__questionmark_v0) = 'collect$a'(A__questionmark_v1) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A_n_vec$ (fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), fun_app$b(fun_app$c(vector_scalar_mult$, ?v1), ?v2)) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$k(fun_app$l(times$, ?v0), ?v1)), ?v2))
tff(axiom396,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A_n_vec$'] : 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v1),A__questionmark_v2)) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec$ ?v2:A_n_vec_n_vec$ (vector_scalar_mult$a(?v0, vector_scalar_mult$a(?v1, ?v2)) = vector_scalar_mult$a(fun_app$b(times$b(?v0), ?v1), ?v2))
tff(axiom397,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'A_n_vec_n_vec$'] : 'vector_scalar_mult$a'(A__questionmark_v0,'vector_scalar_mult$a'(A__questionmark_v1,A__questionmark_v2)) = 'vector_scalar_mult$a'('fun_app$b'('times$b'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A_n_vec$ (fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), fun_app$b(fun_app$c(vector_scalar_mult$, ?v1), ?v2)) = fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$k(fun_app$l(times$, ?v0), ?v1)), ?v2))
tff(axiom398,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A_n_vec$'] : 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v1),A__questionmark_v2)) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec$ ?v2:N$ (fun_app$f(vec_nth$b(times$e(?v0, ?v1)), ?v2) = times$a(fun_app$f(vec_nth$b(?v0), ?v2), fun_app$f(vec_nth$b(?v1), ?v2)))
tff(axiom399,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$f'('vec_nth$b'('times$e'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'times$a'('fun_app$f'('vec_nth$b'(A__questionmark_v0),A__questionmark_v2),'fun_app$f'('vec_nth$b'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:Nat_n_vec$ ?v1:Nat_n_vec$ ?v2:N$ (fun_app$h(vec_nth$d(times$f(?v0, ?v1)), ?v2) = fun_app$v(fun_app$ao(times$c, fun_app$h(vec_nth$d(?v0), ?v2)), fun_app$h(vec_nth$d(?v1), ?v2)))
tff(axiom400,axiom,
    ! [A__questionmark_v0: 'Nat_n_vec$',A__questionmark_v1: 'Nat_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$h'('vec_nth$d'('times$f'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'fun_app$v'('fun_app$ao'('times$c','fun_app$h'('vec_nth$d'(A__questionmark_v0),A__questionmark_v2)),'fun_app$h'('vec_nth$d'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ (fun_app$a(vec_nth$(times$a(?v0, ?v1)), ?v2) = fun_app$b(times$b(fun_app$a(vec_nth$(?v0), ?v2)), fun_app$a(vec_nth$(?v1), ?v2)))
tff(axiom401,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vec_nth$'('times$a'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'fun_app$b'('times$b'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v2)),'fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec$ ?v2:N$ (fun_app$d(vec_nth$a(fun_app$b(times$b(?v0), ?v1)), ?v2) = fun_app$k(fun_app$l(times$, fun_app$d(vec_nth$a(?v0), ?v2)), fun_app$d(vec_nth$a(?v1), ?v2)))
tff(axiom402,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$d'('vec_nth$a'('fun_app$b'('times$b'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$k'('fun_app$l'('times$','fun_app$d'('vec_nth$a'(A__questionmark_v0),A__questionmark_v2)),'fun_app$d'('vec_nth$a'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec$ ?v2:N$ (fun_app$f(vec_nth$b(vector_scalar_mult$b(?v0, ?v1)), ?v2) = times$a(?v0, fun_app$f(vec_nth$b(?v1), ?v2)))
tff(axiom403,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$f'('vec_nth$b'('vector_scalar_mult$b'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'times$a'(A__questionmark_v0,'fun_app$f'('vec_nth$b'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:Nat$ ?v1:Nat_n_vec$ ?v2:N$ (fun_app$h(vec_nth$d(vector_scalar_mult$c(?v0, ?v1)), ?v2) = fun_app$v(fun_app$ao(times$c, ?v0), fun_app$h(vec_nth$d(?v1), ?v2)))
tff(axiom404,axiom,
    ! [A__questionmark_v0: 'Nat$',A__questionmark_v1: 'Nat_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$h'('vec_nth$d'('vector_scalar_mult$c'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'fun_app$v'('fun_app$ao'('times$c',A__questionmark_v0),'fun_app$h'('vec_nth$d'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ (fun_app$a(vec_nth$(vector_scalar_mult$a(?v0, ?v1)), ?v2) = fun_app$b(times$b(?v0), fun_app$a(vec_nth$(?v1), ?v2)))
tff(axiom405,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vec_nth$'('vector_scalar_mult$a'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'fun_app$b'('times$b'(A__questionmark_v0),'fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A$ ?v1:A_n_vec$ ?v2:N$ (fun_app$d(vec_nth$a(fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), ?v1)), ?v2) = fun_app$k(fun_app$l(times$, ?v0), fun_app$d(vec_nth$a(?v1), ?v2)))
tff(axiom406,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$d'('vec_nth$a'('fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),'fun_app$d'('vec_nth$a'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (fun_app$k(fun_app$l(times$, ?v0), fun_app$k(fun_app$l(times$, ?v1), ?v2)) = fun_app$k(fun_app$l(times$, fun_app$k(fun_app$l(times$, ?v0), ?v1)), ?v2))
tff(axiom407,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] : 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),'fun_app$k'('fun_app$l'('times$',A__questionmark_v1),A__questionmark_v2)) = 'fun_app$k'('fun_app$l'('times$','fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (fun_app$k(fun_app$l(times$, ?v0), fun_app$k(fun_app$l(times$, ?v1), ?v2)) = fun_app$k(fun_app$l(times$, ?v1), fun_app$k(fun_app$l(times$, ?v0), ?v2)))
tff(axiom408,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] : 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),'fun_app$k'('fun_app$l'('times$',A__questionmark_v1),A__questionmark_v2)) = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v1),'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2)) ).

%% (top$k = collect$d(top$l))
tff(axiom409,axiom,
    'top$k' = 'collect$d'('top$l') ).

%% (top$j = collect$f(top$m))
tff(axiom410,axiom,
    'top$j' = 'collect$f'('top$m') ).

%% (top$n = collect$g(top$o))
tff(axiom411,axiom,
    'top$n' = 'collect$g'('top$o') ).

%% (top$c = collect$b(top$p))
tff(axiom412,axiom,
    'top$c' = 'collect$b'('top$p') ).

%% (top$d = collect$c(top$q))
tff(axiom413,axiom,
    'top$d' = 'collect$c'('top$q') ).

%% (top$f = collect$e(top$r))
tff(axiom414,axiom,
    'top$f' = 'collect$e'('top$r') ).

%% (top$e = collect$a(top$g))
tff(axiom415,axiom,
    'top$e' = 'collect$a'('top$g') ).

%% (top$ = collect$(top$i))
tff(axiom416,axiom,
    'top$' = 'collect$'('top$i') ).

%% is_basis$(set_of_vector$(cart_basis$))
tff(axiom417,axiom,
    'is_basis$'('set_of_vector$'('cart_basis$')) ).

%% ∀ ?v0:Nat_a_fun$ ?v1:Nat_set$ ?v2:A$ (fun_app$k(fun_app$l(times$, sum$d(?v0, ?v1)), ?v2) = sum$d(uvo$(?v0, ?v2), ?v1))
tff(axiom418,axiom,
    ! [A__questionmark_v0: 'Nat_a_fun$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'A$'] : 'fun_app$k'('fun_app$l'('times$','sum$d'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$d'('uvo$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_fun_a_fun$ ?v1:N_n_fun_set$ ?v2:A$ (fun_app$k(fun_app$l(times$, sum$c(?v0, ?v1)), ?v2) = sum$c(uvp$(?v0, ?v2), ?v1))
tff(axiom419,axiom,
    ! [A__questionmark_v0: 'N_n_fun_a_fun$',A__questionmark_v1: 'N_n_fun_set$',A__questionmark_v2: 'A$'] : 'fun_app$k'('fun_app$l'('times$','sum$c'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$c'('uvp$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_set$ ?v2:A$ (fun_app$k(fun_app$l(times$, sum$a(?v0, ?v1)), ?v2) = sum$a(uvq$(?v0, ?v2), ?v1))
tff(axiom420,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'A$'] : 'fun_app$k'('fun_app$l'('times$','sum$a'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$a'('uvq$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:A$ ?v1:Nat_a_fun$ ?v2:Nat_set$ (fun_app$k(fun_app$l(times$, ?v0), sum$d(?v1, ?v2)) = sum$d(uvr$(?v0, ?v1), ?v2))
tff(axiom421,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'Nat_a_fun$',A__questionmark_v2: 'Nat_set$'] : 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),'sum$d'(A__questionmark_v1,A__questionmark_v2)) = 'sum$d'('uvr$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) ).

%% ∀ ?v0:A$ ?v1:N_n_fun_a_fun$ ?v2:N_n_fun_set$ (fun_app$k(fun_app$l(times$, ?v0), sum$c(?v1, ?v2)) = sum$c(uvs$(?v0, ?v1), ?v2))
tff(axiom422,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'N_n_fun_a_fun$',A__questionmark_v2: 'N_n_fun_set$'] : 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),'sum$c'(A__questionmark_v1,A__questionmark_v2)) = 'sum$c'('uvs$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) ).

%% ∀ ?v0:A$ ?v1:N_a_fun$ ?v2:N_set$ (fun_app$k(fun_app$l(times$, ?v0), sum$a(?v1, ?v2)) = sum$a(uvt$(?v0, ?v1), ?v2))
tff(axiom423,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N_set$'] : 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),'sum$a'(A__questionmark_v1,A__questionmark_v2)) = 'sum$a'('uvt$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_a_fun$ (is_basis$(set_of_vector$(?v0)) ⇒ (sum$l(uvu$(?v1), set_of_vector$(?v0)) = sum$(uvv$(?v0, ?v1), top$)))
tff(axiom424,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_a_fun$'] :
      ( 'is_basis$'('set_of_vector$'(A__questionmark_v0))
     => ( 'sum$l'('uvu$'(A__questionmark_v1),'set_of_vector$'(A__questionmark_v0)) = 'sum$'('uvv$'(A__questionmark_v0,A__questionmark_v1),'top$') ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N_a_fun$ ?v2:N_a_fun$ ((is_basis$(set_of_vector$(?v0)) ∧ (sum$(uvw$(?v0, ?v1), top$) = sum$(uvw$(?v0, ?v2), top$))) ⇒ (?v2 = ?v1))
tff(axiom425,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N_a_fun$'] :
      ( ( 'is_basis$'('set_of_vector$'(A__questionmark_v0))
        & ( 'sum$'('uvw$'(A__questionmark_v0,A__questionmark_v1),'top$') = 'sum$'('uvw$'(A__questionmark_v0,A__questionmark_v2),'top$') ) )
     => ( A__questionmark_v2 = A__questionmark_v1 ) ) ).

%% ∀ ?v0:Nat_set$ (∀ ?v1:Nat$ member$a(?v1, ?v0) ⇒ (top$e = ?v0))
tff(axiom426,axiom,
    ! [A__questionmark_v0: 'Nat_set$'] :
      ( ! [A__questionmark_v1: 'Nat$'] : 'member$a'(A__questionmark_v1,A__questionmark_v0)
     => ( 'top$e' = A__questionmark_v0 ) ) ).

%% ∀ ?v0:N_a_n_vec_fun_set$ (∀ ?v1:N_a_n_vec_fun$ member$c(?v1, ?v0) ⇒ (top$c = ?v0))
tff(axiom427,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun_set$'] :
      ( ! [A__questionmark_v1: 'N_a_n_vec_fun$'] : 'member$c'(A__questionmark_v1,A__questionmark_v0)
     => ( 'top$c' = A__questionmark_v0 ) ) ).

%% ∀ ?v0:N_a_fun_set$ (∀ ?v1:N_a_fun$ member$e(?v1, ?v0) ⇒ (top$d = ?v0))
tff(axiom428,axiom,
    ! [A__questionmark_v0: 'N_a_fun_set$'] :
      ( ! [A__questionmark_v1: 'N_a_fun$'] : 'member$e'(A__questionmark_v1,A__questionmark_v0)
     => ( 'top$d' = A__questionmark_v0 ) ) ).

%% ∀ ?v0:A_set$ (∀ ?v1:A$ member$g(?v1, ?v0) ⇒ (top$f = ?v0))
tff(axiom429,axiom,
    ! [A__questionmark_v0: 'A_set$'] :
      ( ! [A__questionmark_v1: 'A$'] : 'member$g'(A__questionmark_v1,A__questionmark_v0)
     => ( 'top$f' = A__questionmark_v0 ) ) ).

%% ∀ ?v0:N_set$ (∀ ?v1:N$ member$f(?v1, ?v0) ⇒ (top$ = ?v0))
tff(axiom430,axiom,
    ! [A__questionmark_v0: 'N_set$'] :
      ( ! [A__questionmark_v1: 'N$'] : 'member$f'(A__questionmark_v1,A__questionmark_v0)
     => ( 'top$' = A__questionmark_v0 ) ) ).

%% ∃ ?v0:Nat$ member$a(?v0, top$e)
tff(axiom431,axiom,
    ? [A__questionmark_v0: 'Nat$'] : 'member$a'(A__questionmark_v0,'top$e') ).

%% ∃ ?v0:N_a_n_vec_fun$ member$c(?v0, top$c)
tff(axiom432,axiom,
    ? [A__questionmark_v0: 'N_a_n_vec_fun$'] : 'member$c'(A__questionmark_v0,'top$c') ).

%% ∃ ?v0:N_a_fun$ member$e(?v0, top$d)
tff(axiom433,axiom,
    ? [A__questionmark_v0: 'N_a_fun$'] : 'member$e'(A__questionmark_v0,'top$d') ).

%% ∃ ?v0:A$ member$g(?v0, top$f)
tff(axiom434,axiom,
    ? [A__questionmark_v0: 'A$'] : 'member$g'(A__questionmark_v0,'top$f') ).

%% ∃ ?v0:N$ member$f(?v0, top$)
tff(axiom435,axiom,
    ? [A__questionmark_v0: 'N$'] : 'member$f'(A__questionmark_v0,'top$') ).

%% (top$k = collect$d(uvx$))
tff(axiom436,axiom,
    'top$k' = 'collect$d'('uvx$') ).

%% (top$j = collect$f(uvy$))
tff(axiom437,axiom,
    'top$j' = 'collect$f'('uvy$') ).

%% (top$n = collect$g(uvz$))
tff(axiom438,axiom,
    'top$n' = 'collect$g'('uvz$') ).

%% (top$c = collect$b(uwa$))
tff(axiom439,axiom,
    'top$c' = 'collect$b'('uwa$') ).

%% (top$d = collect$c(uwb$))
tff(axiom440,axiom,
    'top$d' = 'collect$c'('uwb$') ).

%% (top$f = collect$e(uwc$))
tff(axiom441,axiom,
    'top$f' = 'collect$e'('uwc$') ).

%% (top$e = collect$a(uwd$))
tff(axiom442,axiom,
    'top$e' = 'collect$a'('uwd$') ).

%% (top$ = collect$(uwe$))
tff(axiom443,axiom,
    'top$' = 'collect$'('uwe$') ).

%% ∀ ?v0:Int_n_vec$ ?v1:Int_n_vec$ (scalar_product$(?v0, ?v1) = sum$m(uwf$(?v0, ?v1), top$))
tff(axiom444,axiom,
    ! [A__questionmark_v0: 'Int_n_vec$',A__questionmark_v1: 'Int_n_vec$'] : 'scalar_product$'(A__questionmark_v0,A__questionmark_v1) = 'sum$m'('uwf$'(A__questionmark_v0,A__questionmark_v1),'top$') ).

%% ∀ ?v0:Nat_n_vec$ ?v1:Nat_n_vec$ (scalar_product$a(?v0, ?v1) = sum$k(uwg$(?v0, ?v1), top$))
tff(axiom445,axiom,
    ! [A__questionmark_v0: 'Nat_n_vec$',A__questionmark_v1: 'Nat_n_vec$'] : 'scalar_product$a'(A__questionmark_v0,A__questionmark_v1) = 'sum$k'('uwg$'(A__questionmark_v0,A__questionmark_v1),'top$') ).

%% ∀ ?v0:A_n_n_fun_vec$ ?v1:A_n_n_fun_vec$ (scalar_product$b(?v0, ?v1) = sum$c(uwh$(?v0, ?v1), top$j))
tff(axiom446,axiom,
    ! [A__questionmark_v0: 'A_n_n_fun_vec$',A__questionmark_v1: 'A_n_n_fun_vec$'] : 'scalar_product$b'(A__questionmark_v0,A__questionmark_v1) = 'sum$c'('uwh$'(A__questionmark_v0,A__questionmark_v1),'top$j') ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec$ (scalar_product$c(?v0, ?v1) = sum$b(uwi$(?v0, ?v1), top$))
tff(axiom447,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$'] : 'scalar_product$c'(A__questionmark_v0,A__questionmark_v1) = 'sum$b'('uwi$'(A__questionmark_v0,A__questionmark_v1),'top$') ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ (scalar_product$d(?v0, ?v1) = sum$(uwj$(?v0, ?v1), top$))
tff(axiom448,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$'] : 'scalar_product$d'(A__questionmark_v0,A__questionmark_v1) = 'sum$'('uwj$'(A__questionmark_v0,A__questionmark_v1),'top$') ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec$ (fun_app$j(scalar_product$e(?v0), ?v1) = sum$a(uwk$(?v0, ?v1), top$))
tff(axiom449,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec$'] : 'fun_app$j'('scalar_product$e'(A__questionmark_v0),A__questionmark_v1) = 'sum$a'('uwk$'(A__questionmark_v0,A__questionmark_v1),'top$') ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:A_n_vec_a_n_vec_fun$ ?v3:N$ ((is_basis$(set_of_vector$(?v0)) ∧ is_basis$(set_of_vector$(?v1))) ⇒ (fun_app$b(?v2, fun_app$a(vec_nth$(?v0), ?v3)) = sum$(fun_app$z(uwl$(?v0, ?v1, ?v2), ?v3), top$)))
tff(axiom450,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'A_n_vec_a_n_vec_fun$',A__questionmark_v3: 'N$'] :
      ( ( 'is_basis$'('set_of_vector$'(A__questionmark_v0))
        & 'is_basis$'('set_of_vector$'(A__questionmark_v1)) )
     => ( 'fun_app$b'(A__questionmark_v2,'fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v3)) = 'sum$'('fun_app$z'('uwl$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),'top$') ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:A_n_vec_a_n_vec_fun$ ?v3:A_n_vec_n_vec$ ((is_basis$(set_of_vector$(?v0)) ∧ (is_basis$(set_of_vector$(?v1)) ∧ ∀ ?v4:N$ (fun_app$b(?v2, fun_app$a(vec_nth$(?v0), ?v4)) = sum$(fun_app$z(uwm$(?v1, ?v3), ?v4), top$)))) ⇒ (matrix$(?v0, ?v1, ?v2) = ?v3))
tff(axiom451,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'A_n_vec_a_n_vec_fun$',A__questionmark_v3: 'A_n_vec_n_vec$'] :
      ( ( 'is_basis$'('set_of_vector$'(A__questionmark_v0))
        & 'is_basis$'('set_of_vector$'(A__questionmark_v1))
        & ! [A__questionmark_v4: 'N$'] : 'fun_app$b'(A__questionmark_v2,'fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v4)) = 'sum$'('fun_app$z'('uwm$'(A__questionmark_v1,A__questionmark_v3),A__questionmark_v4),'top$') )
     => ( 'matrix$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2) = A__questionmark_v3 ) ) ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$a(vec_nth$(fun_app$f(mat_mult_row$(?v0, ?v1), ?v2)), ?v3) = sum$(fun_app$z(uwn$(?v0, ?v1, ?v2), ?v3), top$))
tff(axiom452,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$a'('vec_nth$'('fun_app$f'('mat_mult_row$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)),A__questionmark_v3) = 'sum$'('fun_app$z'('uwn$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),'top$') ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ ?v3:N$ (fun_app$d(vec_nth$a(fun_app$a(mat_mult_row$a(?v0, ?v1), ?v2)), ?v3) = sum$a(fun_app$e(uwo$(?v0, ?v1, ?v2), ?v3), top$))
tff(axiom453,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$d'('vec_nth$a'('fun_app$a'('mat_mult_row$a'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)),A__questionmark_v3) = 'sum$a'('fun_app$e'('uwo$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3),'top$') ).

%% ∀ ?v0:N_a_n_vec_fun$ ?v1:N_a_n_vec_fun_set$ ?v2:N_a_n_vec_fun$ ?v3:N_a_n_vec_fun_set$ ((member$c(?v0, ?v1) ∧ member$c(?v2, ?v3)) ⇒ member$c(times$g(?v0, ?v2), times$h(?v1, ?v3)))
tff(axiom454,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$',A__questionmark_v1: 'N_a_n_vec_fun_set$',A__questionmark_v2: 'N_a_n_vec_fun$',A__questionmark_v3: 'N_a_n_vec_fun_set$'] :
      ( ( 'member$c'(A__questionmark_v0,A__questionmark_v1)
        & 'member$c'(A__questionmark_v2,A__questionmark_v3) )
     => 'member$c'('times$g'(A__questionmark_v0,A__questionmark_v2),'times$h'(A__questionmark_v1,A__questionmark_v3)) ) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_a_fun_set$ ?v2:N_a_fun$ ?v3:N_a_fun_set$ ((member$e(?v0, ?v1) ∧ member$e(?v2, ?v3)) ⇒ member$e(times$i(?v0, ?v2), times$j(?v1, ?v3)))
tff(axiom455,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_a_fun_set$',A__questionmark_v2: 'N_a_fun$',A__questionmark_v3: 'N_a_fun_set$'] :
      ( ( 'member$e'(A__questionmark_v0,A__questionmark_v1)
        & 'member$e'(A__questionmark_v2,A__questionmark_v3) )
     => 'member$e'('times$i'(A__questionmark_v0,A__questionmark_v2),'times$j'(A__questionmark_v1,A__questionmark_v3)) ) ).

%% ∀ ?v0:Nat$ ?v1:Nat_set$ ?v2:Nat$ ?v3:Nat_set$ ((member$a(?v0, ?v1) ∧ member$a(?v2, ?v3)) ⇒ member$a(fun_app$v(fun_app$ao(times$c, ?v0), ?v2), times$k(?v1, ?v3)))
tff(axiom456,axiom,
    ! [A__questionmark_v0: 'Nat$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'Nat$',A__questionmark_v3: 'Nat_set$'] :
      ( ( 'member$a'(A__questionmark_v0,A__questionmark_v1)
        & 'member$a'(A__questionmark_v2,A__questionmark_v3) )
     => 'member$a'('fun_app$v'('fun_app$ao'('times$c',A__questionmark_v0),A__questionmark_v2),'times$k'(A__questionmark_v1,A__questionmark_v3)) ) ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec_set$ ?v2:A_n_vec$ ?v3:A_n_vec_set$ ((member$(?v0, ?v1) ∧ member$(?v2, ?v3)) ⇒ member$(fun_app$b(times$b(?v0), ?v2), times$l(?v1, ?v3)))
tff(axiom457,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec_set$',A__questionmark_v2: 'A_n_vec$',A__questionmark_v3: 'A_n_vec_set$'] :
      ( ( 'member$'(A__questionmark_v0,A__questionmark_v1)
        & 'member$'(A__questionmark_v2,A__questionmark_v3) )
     => 'member$'('fun_app$b'('times$b'(A__questionmark_v0),A__questionmark_v2),'times$l'(A__questionmark_v1,A__questionmark_v3)) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec_set$ ?v2:A_n_vec_n_vec$ ?v3:A_n_vec_n_vec_set$ ((member$j(?v0, ?v1) ∧ member$j(?v2, ?v3)) ⇒ member$j(times$a(?v0, ?v2), times$m(?v1, ?v3)))
tff(axiom458,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_set$',A__questionmark_v2: 'A_n_vec_n_vec$',A__questionmark_v3: 'A_n_vec_n_vec_set$'] :
      ( ( 'member$j'(A__questionmark_v0,A__questionmark_v1)
        & 'member$j'(A__questionmark_v2,A__questionmark_v3) )
     => 'member$j'('times$a'(A__questionmark_v0,A__questionmark_v2),'times$m'(A__questionmark_v1,A__questionmark_v3)) ) ).

%% ∀ ?v0:A_set$ ?v1:A_set_set$ ?v2:A_set$ ?v3:A_set_set$ ((member$k(?v0, ?v1) ∧ member$k(?v2, ?v3)) ⇒ member$k(times$n(?v0, ?v2), times$o(?v1, ?v3)))
tff(axiom459,axiom,
    ! [A__questionmark_v0: 'A_set$',A__questionmark_v1: 'A_set_set$',A__questionmark_v2: 'A_set$',A__questionmark_v3: 'A_set_set$'] :
      ( ( 'member$k'(A__questionmark_v0,A__questionmark_v1)
        & 'member$k'(A__questionmark_v2,A__questionmark_v3) )
     => 'member$k'('times$n'(A__questionmark_v0,A__questionmark_v2),'times$o'(A__questionmark_v1,A__questionmark_v3)) ) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_set_set$ ?v2:Nat_set$ ?v3:Nat_set_set$ ((member$l(?v0, ?v1) ∧ member$l(?v2, ?v3)) ⇒ member$l(times$k(?v0, ?v2), times$p(?v1, ?v3)))
tff(axiom460,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_set_set$',A__questionmark_v2: 'Nat_set$',A__questionmark_v3: 'Nat_set_set$'] :
      ( ( 'member$l'(A__questionmark_v0,A__questionmark_v1)
        & 'member$l'(A__questionmark_v2,A__questionmark_v3) )
     => 'member$l'('times$k'(A__questionmark_v0,A__questionmark_v2),'times$p'(A__questionmark_v1,A__questionmark_v3)) ) ).

%% ∀ ?v0:Int ?v1:Int_set$ ?v2:Int ?v3:Int_set$ ((member$m(?v0, ?v1) ∧ member$m(?v2, ?v3)) ⇒ member$m(fun_app$aq(times$d(?v0), ?v2), times$q(?v1, ?v3)))
tff(axiom461,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: 'Int_set$',A__questionmark_v2: $int,A__questionmark_v3: 'Int_set$'] :
      ( ( 'member$m'(A__questionmark_v0,A__questionmark_v1)
        & 'member$m'(A__questionmark_v2,A__questionmark_v3) )
     => 'member$m'('fun_app$aq'('times$d'(A__questionmark_v0),A__questionmark_v2),'times$q'(A__questionmark_v1,A__questionmark_v3)) ) ).

%% ∀ ?v0:A$ ?v1:A_set$ ?v2:A$ ?v3:A_set$ ((member$g(?v0, ?v1) ∧ member$g(?v2, ?v3)) ⇒ member$g(fun_app$k(fun_app$l(times$, ?v0), ?v2), times$n(?v1, ?v3)))
tff(axiom462,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A_set$',A__questionmark_v2: 'A$',A__questionmark_v3: 'A_set$'] :
      ( ( 'member$g'(A__questionmark_v0,A__questionmark_v1)
        & 'member$g'(A__questionmark_v2,A__questionmark_v3) )
     => 'member$g'('fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2),'times$n'(A__questionmark_v1,A__questionmark_v3)) ) ).

%% ∀ ?v0:A$ ?v1:Nat_a_fun$ ?v2:Nat_set$ (fun_app$k(fun_app$l(times$, ?v0), sum$d(?v1, ?v2)) = sum$d(uvr$(?v0, ?v1), ?v2))
tff(axiom463,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'Nat_a_fun$',A__questionmark_v2: 'Nat_set$'] : 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),'sum$d'(A__questionmark_v1,A__questionmark_v2)) = 'sum$d'('uvr$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) ).

%% ∀ ?v0:A$ ?v1:N_n_fun_a_fun$ ?v2:N_n_fun_set$ (fun_app$k(fun_app$l(times$, ?v0), sum$c(?v1, ?v2)) = sum$c(uvs$(?v0, ?v1), ?v2))
tff(axiom464,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'N_n_fun_a_fun$',A__questionmark_v2: 'N_n_fun_set$'] : 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),'sum$c'(A__questionmark_v1,A__questionmark_v2)) = 'sum$c'('uvs$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N_a_n_vec_n_vec_fun$ ?v2:N_set$ (times$a(?v0, sum$b(?v1, ?v2)) = sum$b(uwp$(?v0, ?v1), ?v2))
tff(axiom465,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N_a_n_vec_n_vec_fun$',A__questionmark_v2: 'N_set$'] : 'times$a'(A__questionmark_v0,'sum$b'(A__questionmark_v1,A__questionmark_v2)) = 'sum$b'('uwp$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) ).

%% ∀ ?v0:A_n_vec$ ?v1:N_a_n_vec_fun$ ?v2:N_set$ (fun_app$b(times$b(?v0), sum$(?v1, ?v2)) = sum$(uwq$(?v0, ?v1), ?v2))
tff(axiom466,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N_set$'] : 'fun_app$b'('times$b'(A__questionmark_v0),'sum$'(A__questionmark_v1,A__questionmark_v2)) = 'sum$'('uwq$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) ).

%% ∀ ?v0:A$ ?v1:N_a_fun$ ?v2:N_set$ (fun_app$k(fun_app$l(times$, ?v0), sum$a(?v1, ?v2)) = sum$a(uvt$(?v0, ?v1), ?v2))
tff(axiom467,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N_set$'] : 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),'sum$a'(A__questionmark_v1,A__questionmark_v2)) = 'sum$a'('uvt$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) ).

%% ∀ ?v0:Nat_a_fun$ ?v1:Nat_set$ ?v2:A$ (fun_app$k(fun_app$l(times$, sum$d(?v0, ?v1)), ?v2) = sum$d(uvo$(?v0, ?v2), ?v1))
tff(axiom468,axiom,
    ! [A__questionmark_v0: 'Nat_a_fun$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'A$'] : 'fun_app$k'('fun_app$l'('times$','sum$d'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$d'('uvo$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_fun_a_fun$ ?v1:N_n_fun_set$ ?v2:A$ (fun_app$k(fun_app$l(times$, sum$c(?v0, ?v1)), ?v2) = sum$c(uvp$(?v0, ?v2), ?v1))
tff(axiom469,axiom,
    ! [A__questionmark_v0: 'N_n_fun_a_fun$',A__questionmark_v1: 'N_n_fun_set$',A__questionmark_v2: 'A$'] : 'fun_app$k'('fun_app$l'('times$','sum$c'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$c'('uvp$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_a_n_vec_n_vec_fun$ ?v1:N_set$ ?v2:A_n_vec_n_vec$ (times$a(sum$b(?v0, ?v1), ?v2) = sum$b(uwr$(?v0, ?v2), ?v1))
tff(axiom470,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_n_vec_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'A_n_vec_n_vec$'] : 'times$a'('sum$b'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$b'('uwr$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_a_n_vec_fun$ ?v1:N_set$ ?v2:A_n_vec$ (fun_app$b(times$b(sum$(?v0, ?v1)), ?v2) = sum$(uws$(?v0, ?v2), ?v1))
tff(axiom471,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'A_n_vec$'] : 'fun_app$b'('times$b'('sum$'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$'('uws$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_set$ ?v2:A$ (fun_app$k(fun_app$l(times$, sum$a(?v0, ?v1)), ?v2) = sum$a(uvq$(?v0, ?v2), ?v1))
tff(axiom472,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'A$'] : 'fun_app$k'('fun_app$l'('times$','sum$a'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$a'('uvq$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_set$ ?v2:N_a_fun$ ?v3:N_set$ (fun_app$k(fun_app$l(times$, sum$a(?v0, ?v1)), sum$a(?v2, ?v3)) = sum$a(uwu$(?v0, ?v2, ?v3), ?v1))
tff(axiom473,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_a_fun$',A__questionmark_v3: 'N_set$'] : 'fun_app$k'('fun_app$l'('times$','sum$a'(A__questionmark_v0,A__questionmark_v1)),'sum$a'(A__questionmark_v2,A__questionmark_v3)) = 'sum$a'('uwu$'(A__questionmark_v0,A__questionmark_v2,A__questionmark_v3),A__questionmark_v1) ).

%% ∀ ?v0:N_a_n_vec_fun$ ?v1:N_set$ ?v2:N_a_n_vec_fun$ ?v3:N_set$ (fun_app$b(times$b(sum$(?v0, ?v1)), sum$(?v2, ?v3)) = sum$(uww$(?v0, ?v2, ?v3), ?v1))
tff(axiom474,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_a_n_vec_fun$',A__questionmark_v3: 'N_set$'] : 'fun_app$b'('times$b'('sum$'(A__questionmark_v0,A__questionmark_v1)),'sum$'(A__questionmark_v2,A__questionmark_v3)) = 'sum$'('uww$'(A__questionmark_v0,A__questionmark_v2,A__questionmark_v3),A__questionmark_v1) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_set$ ?v2:Nat_a_fun$ ?v3:Nat_set$ (fun_app$k(fun_app$l(times$, sum$a(?v0, ?v1)), sum$d(?v2, ?v3)) = sum$a(uwy$(?v0, ?v2, ?v3), ?v1))
tff(axiom475,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'Nat_a_fun$',A__questionmark_v3: 'Nat_set$'] : 'fun_app$k'('fun_app$l'('times$','sum$a'(A__questionmark_v0,A__questionmark_v1)),'sum$d'(A__questionmark_v2,A__questionmark_v3)) = 'sum$a'('uwy$'(A__questionmark_v0,A__questionmark_v2,A__questionmark_v3),A__questionmark_v1) ).

%% ∀ ?v0:Nat_a_fun$ ?v1:Nat_set$ ?v2:N_a_fun$ ?v3:N_set$ (fun_app$k(fun_app$l(times$, sum$d(?v0, ?v1)), sum$a(?v2, ?v3)) = sum$d(uxa$(?v0, ?v2, ?v3), ?v1))
tff(axiom476,axiom,
    ! [A__questionmark_v0: 'Nat_a_fun$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'N_a_fun$',A__questionmark_v3: 'N_set$'] : 'fun_app$k'('fun_app$l'('times$','sum$d'(A__questionmark_v0,A__questionmark_v1)),'sum$a'(A__questionmark_v2,A__questionmark_v3)) = 'sum$d'('uxa$'(A__questionmark_v0,A__questionmark_v2,A__questionmark_v3),A__questionmark_v1) ).

%% ∀ ?v0:Nat_a_fun$ ?v1:Nat_set$ ?v2:Nat_a_fun$ ?v3:Nat_set$ (fun_app$k(fun_app$l(times$, sum$d(?v0, ?v1)), sum$d(?v2, ?v3)) = sum$d(uxc$(?v0, ?v2, ?v3), ?v1))
tff(axiom477,axiom,
    ! [A__questionmark_v0: 'Nat_a_fun$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'Nat_a_fun$',A__questionmark_v3: 'Nat_set$'] : 'fun_app$k'('fun_app$l'('times$','sum$d'(A__questionmark_v0,A__questionmark_v1)),'sum$d'(A__questionmark_v2,A__questionmark_v3)) = 'sum$d'('uxc$'(A__questionmark_v0,A__questionmark_v2,A__questionmark_v3),A__questionmark_v1) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_set$ ?v2:N_n_fun_a_fun$ ?v3:N_n_fun_set$ (fun_app$k(fun_app$l(times$, sum$a(?v0, ?v1)), sum$c(?v2, ?v3)) = sum$a(uxe$(?v0, ?v2, ?v3), ?v1))
tff(axiom478,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_n_fun_a_fun$',A__questionmark_v3: 'N_n_fun_set$'] : 'fun_app$k'('fun_app$l'('times$','sum$a'(A__questionmark_v0,A__questionmark_v1)),'sum$c'(A__questionmark_v2,A__questionmark_v3)) = 'sum$a'('uxe$'(A__questionmark_v0,A__questionmark_v2,A__questionmark_v3),A__questionmark_v1) ).

%% ∀ ?v0:Nat_a_fun$ ?v1:Nat_set$ ?v2:N_n_fun_a_fun$ ?v3:N_n_fun_set$ (fun_app$k(fun_app$l(times$, sum$d(?v0, ?v1)), sum$c(?v2, ?v3)) = sum$d(uxg$(?v0, ?v2, ?v3), ?v1))
tff(axiom479,axiom,
    ! [A__questionmark_v0: 'Nat_a_fun$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'N_n_fun_a_fun$',A__questionmark_v3: 'N_n_fun_set$'] : 'fun_app$k'('fun_app$l'('times$','sum$d'(A__questionmark_v0,A__questionmark_v1)),'sum$c'(A__questionmark_v2,A__questionmark_v3)) = 'sum$d'('uxg$'(A__questionmark_v0,A__questionmark_v2,A__questionmark_v3),A__questionmark_v1) ).

%% ∀ ?v0:N_n_fun_a_fun$ ?v1:N_n_fun_set$ ?v2:N_a_fun$ ?v3:N_set$ (fun_app$k(fun_app$l(times$, sum$c(?v0, ?v1)), sum$a(?v2, ?v3)) = sum$c(uxi$(?v0, ?v2, ?v3), ?v1))
tff(axiom480,axiom,
    ! [A__questionmark_v0: 'N_n_fun_a_fun$',A__questionmark_v1: 'N_n_fun_set$',A__questionmark_v2: 'N_a_fun$',A__questionmark_v3: 'N_set$'] : 'fun_app$k'('fun_app$l'('times$','sum$c'(A__questionmark_v0,A__questionmark_v1)),'sum$a'(A__questionmark_v2,A__questionmark_v3)) = 'sum$c'('uxi$'(A__questionmark_v0,A__questionmark_v2,A__questionmark_v3),A__questionmark_v1) ).

%% ∀ ?v0:N_n_fun_a_fun$ ?v1:N_n_fun_set$ ?v2:Nat_a_fun$ ?v3:Nat_set$ (fun_app$k(fun_app$l(times$, sum$c(?v0, ?v1)), sum$d(?v2, ?v3)) = sum$c(uxk$(?v0, ?v2, ?v3), ?v1))
tff(axiom481,axiom,
    ! [A__questionmark_v0: 'N_n_fun_a_fun$',A__questionmark_v1: 'N_n_fun_set$',A__questionmark_v2: 'Nat_a_fun$',A__questionmark_v3: 'Nat_set$'] : 'fun_app$k'('fun_app$l'('times$','sum$c'(A__questionmark_v0,A__questionmark_v1)),'sum$d'(A__questionmark_v2,A__questionmark_v3)) = 'sum$c'('uxk$'(A__questionmark_v0,A__questionmark_v2,A__questionmark_v3),A__questionmark_v1) ).

%% ∀ ?v0:N_n_fun_a_fun$ ?v1:N_n_fun_set$ ?v2:N_n_fun_a_fun$ ?v3:N_n_fun_set$ (fun_app$k(fun_app$l(times$, sum$c(?v0, ?v1)), sum$c(?v2, ?v3)) = sum$c(uxm$(?v0, ?v2, ?v3), ?v1))
tff(axiom482,axiom,
    ! [A__questionmark_v0: 'N_n_fun_a_fun$',A__questionmark_v1: 'N_n_fun_set$',A__questionmark_v2: 'N_n_fun_a_fun$',A__questionmark_v3: 'N_n_fun_set$'] : 'fun_app$k'('fun_app$l'('times$','sum$c'(A__questionmark_v0,A__questionmark_v1)),'sum$c'(A__questionmark_v2,A__questionmark_v3)) = 'sum$c'('uxm$'(A__questionmark_v0,A__questionmark_v2,A__questionmark_v3),A__questionmark_v1) ).

%% ∀ ?v0:A_n_vec_n_vec$ (is_basis$(set_of_vector$(?v0)) ⇒ (top$k = collect$d(uxn$(?v0))))
tff(axiom483,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$'] :
      ( 'is_basis$'('set_of_vector$'(A__questionmark_v0))
     => ( 'top$k' = 'collect$d'('uxn$'(A__questionmark_v0)) ) ) ).

%% ∀ ?v0:Nat$ fun_app$m(top$g, ?v0)
tff(axiom484,axiom,
    ! [A__questionmark_v0: 'Nat$'] : 'fun_app$m'('top$g',A__questionmark_v0) ).

%% ∀ ?v0:N$ fun_app$t(top$i, ?v0)
tff(axiom485,axiom,
    ! [A__questionmark_v0: 'N$'] : 'fun_app$t'('top$i',A__questionmark_v0) ).

%% ∀ ?v0:N_a_n_vec_fun$ ?v1:N_a_n_vec_fun_set$ ?v2:N_a_n_vec_fun_set$ ((member$c(?v0, times$h(?v1, ?v2)) ∧ ∀ ?v3:N_a_n_vec_fun$ ?v4:N_a_n_vec_fun$ (((?v0 = times$g(?v3, ?v4)) ∧ (member$c(?v3, ?v1) ∧ member$c(?v4, ?v2))) ⇒ false)) ⇒ false)
tff(axiom486,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$',A__questionmark_v1: 'N_a_n_vec_fun_set$',A__questionmark_v2: 'N_a_n_vec_fun_set$'] :
      ( ( 'member$c'(A__questionmark_v0,'times$h'(A__questionmark_v1,A__questionmark_v2))
        & ! [A__questionmark_v3: 'N_a_n_vec_fun$',A__questionmark_v4: 'N_a_n_vec_fun$'] :
            ( ( ( A__questionmark_v0 = 'times$g'(A__questionmark_v3,A__questionmark_v4) )
              & 'member$c'(A__questionmark_v3,A__questionmark_v1)
              & 'member$c'(A__questionmark_v4,A__questionmark_v2) )
           => $false ) )
     => $false ) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_a_fun_set$ ?v2:N_a_fun_set$ ((member$e(?v0, times$j(?v1, ?v2)) ∧ ∀ ?v3:N_a_fun$ ?v4:N_a_fun$ (((?v0 = times$i(?v3, ?v4)) ∧ (member$e(?v3, ?v1) ∧ member$e(?v4, ?v2))) ⇒ false)) ⇒ false)
tff(axiom487,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_a_fun_set$',A__questionmark_v2: 'N_a_fun_set$'] :
      ( ( 'member$e'(A__questionmark_v0,'times$j'(A__questionmark_v1,A__questionmark_v2))
        & ! [A__questionmark_v3: 'N_a_fun$',A__questionmark_v4: 'N_a_fun$'] :
            ( ( ( A__questionmark_v0 = 'times$i'(A__questionmark_v3,A__questionmark_v4) )
              & 'member$e'(A__questionmark_v3,A__questionmark_v1)
              & 'member$e'(A__questionmark_v4,A__questionmark_v2) )
           => $false ) )
     => $false ) ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec_set$ ?v2:A_n_vec_set$ ((member$(?v0, times$l(?v1, ?v2)) ∧ ∀ ?v3:A_n_vec$ ?v4:A_n_vec$ (((?v0 = fun_app$b(times$b(?v3), ?v4)) ∧ (member$(?v3, ?v1) ∧ member$(?v4, ?v2))) ⇒ false)) ⇒ false)
tff(axiom488,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec_set$',A__questionmark_v2: 'A_n_vec_set$'] :
      ( ( 'member$'(A__questionmark_v0,'times$l'(A__questionmark_v1,A__questionmark_v2))
        & ! [A__questionmark_v3: 'A_n_vec$',A__questionmark_v4: 'A_n_vec$'] :
            ( ( ( A__questionmark_v0 = 'fun_app$b'('times$b'(A__questionmark_v3),A__questionmark_v4) )
              & 'member$'(A__questionmark_v3,A__questionmark_v1)
              & 'member$'(A__questionmark_v4,A__questionmark_v2) )
           => $false ) )
     => $false ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec_set$ ?v2:A_n_vec_n_vec_set$ ((member$j(?v0, times$m(?v1, ?v2)) ∧ ∀ ?v3:A_n_vec_n_vec$ ?v4:A_n_vec_n_vec$ (((?v0 = times$a(?v3, ?v4)) ∧ (member$j(?v3, ?v1) ∧ member$j(?v4, ?v2))) ⇒ false)) ⇒ false)
tff(axiom489,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_set$',A__questionmark_v2: 'A_n_vec_n_vec_set$'] :
      ( ( 'member$j'(A__questionmark_v0,'times$m'(A__questionmark_v1,A__questionmark_v2))
        & ! [A__questionmark_v3: 'A_n_vec_n_vec$',A__questionmark_v4: 'A_n_vec_n_vec$'] :
            ( ( ( A__questionmark_v0 = 'times$a'(A__questionmark_v3,A__questionmark_v4) )
              & 'member$j'(A__questionmark_v3,A__questionmark_v1)
              & 'member$j'(A__questionmark_v4,A__questionmark_v2) )
           => $false ) )
     => $false ) ).

%% ∀ ?v0:A_set$ ?v1:A_set_set$ ?v2:A_set_set$ ((member$k(?v0, times$o(?v1, ?v2)) ∧ ∀ ?v3:A_set$ ?v4:A_set$ (((?v0 = times$n(?v3, ?v4)) ∧ (member$k(?v3, ?v1) ∧ member$k(?v4, ?v2))) ⇒ false)) ⇒ false)
tff(axiom490,axiom,
    ! [A__questionmark_v0: 'A_set$',A__questionmark_v1: 'A_set_set$',A__questionmark_v2: 'A_set_set$'] :
      ( ( 'member$k'(A__questionmark_v0,'times$o'(A__questionmark_v1,A__questionmark_v2))
        & ! [A__questionmark_v3: 'A_set$',A__questionmark_v4: 'A_set$'] :
            ( ( ( A__questionmark_v0 = 'times$n'(A__questionmark_v3,A__questionmark_v4) )
              & 'member$k'(A__questionmark_v3,A__questionmark_v1)
              & 'member$k'(A__questionmark_v4,A__questionmark_v2) )
           => $false ) )
     => $false ) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_set_set$ ?v2:Nat_set_set$ ((member$l(?v0, times$p(?v1, ?v2)) ∧ ∀ ?v3:Nat_set$ ?v4:Nat_set$ (((?v0 = times$k(?v3, ?v4)) ∧ (member$l(?v3, ?v1) ∧ member$l(?v4, ?v2))) ⇒ false)) ⇒ false)
tff(axiom491,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_set_set$',A__questionmark_v2: 'Nat_set_set$'] :
      ( ( 'member$l'(A__questionmark_v0,'times$p'(A__questionmark_v1,A__questionmark_v2))
        & ! [A__questionmark_v3: 'Nat_set$',A__questionmark_v4: 'Nat_set$'] :
            ( ( ( A__questionmark_v0 = 'times$k'(A__questionmark_v3,A__questionmark_v4) )
              & 'member$l'(A__questionmark_v3,A__questionmark_v1)
              & 'member$l'(A__questionmark_v4,A__questionmark_v2) )
           => $false ) )
     => $false ) ).

%% ∀ ?v0:Int ?v1:Int_set$ ?v2:Int_set$ ((member$m(?v0, times$q(?v1, ?v2)) ∧ ∀ ?v3:Int ?v4:Int (((?v0 = fun_app$aq(times$d(?v3), ?v4)) ∧ (member$m(?v3, ?v1) ∧ member$m(?v4, ?v2))) ⇒ false)) ⇒ false)
tff(axiom492,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: 'Int_set$',A__questionmark_v2: 'Int_set$'] :
      ( ( 'member$m'(A__questionmark_v0,'times$q'(A__questionmark_v1,A__questionmark_v2))
        & ! [A__questionmark_v3: $int,A__questionmark_v4: $int] :
            ( ( ( A__questionmark_v0 = 'fun_app$aq'('times$d'(A__questionmark_v3),A__questionmark_v4) )
              & 'member$m'(A__questionmark_v3,A__questionmark_v1)
              & 'member$m'(A__questionmark_v4,A__questionmark_v2) )
           => $false ) )
     => $false ) ).

%% ∀ ?v0:Nat$ ?v1:Nat_set$ ?v2:Nat_set$ ((member$a(?v0, times$k(?v1, ?v2)) ∧ ∀ ?v3:Nat$ ?v4:Nat$ (((?v0 = fun_app$v(fun_app$ao(times$c, ?v3), ?v4)) ∧ (member$a(?v3, ?v1) ∧ member$a(?v4, ?v2))) ⇒ false)) ⇒ false)
tff(axiom493,axiom,
    ! [A__questionmark_v0: 'Nat$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'Nat_set$'] :
      ( ( 'member$a'(A__questionmark_v0,'times$k'(A__questionmark_v1,A__questionmark_v2))
        & ! [A__questionmark_v3: 'Nat$',A__questionmark_v4: 'Nat$'] :
            ( ( ( A__questionmark_v0 = 'fun_app$v'('fun_app$ao'('times$c',A__questionmark_v3),A__questionmark_v4) )
              & 'member$a'(A__questionmark_v3,A__questionmark_v1)
              & 'member$a'(A__questionmark_v4,A__questionmark_v2) )
           => $false ) )
     => $false ) ).

%% ∀ ?v0:A$ ?v1:A_set$ ?v2:A_set$ ((member$g(?v0, times$n(?v1, ?v2)) ∧ ∀ ?v3:A$ ?v4:A$ (((?v0 = fun_app$k(fun_app$l(times$, ?v3), ?v4)) ∧ (member$g(?v3, ?v1) ∧ member$g(?v4, ?v2))) ⇒ false)) ⇒ false)
tff(axiom494,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A_set$',A__questionmark_v2: 'A_set$'] :
      ( ( 'member$g'(A__questionmark_v0,'times$n'(A__questionmark_v1,A__questionmark_v2))
        & ! [A__questionmark_v3: 'A$',A__questionmark_v4: 'A$'] :
            ( ( ( A__questionmark_v0 = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v3),A__questionmark_v4) )
              & 'member$g'(A__questionmark_v3,A__questionmark_v1)
              & 'member$g'(A__questionmark_v4,A__questionmark_v2) )
           => $false ) )
     => $false ) ).

%% ∀ ?v0:N_set$ ?v1:N_n_fun$ ?v2:N_n_fun$ ?v3:N_set$ ?v4:N_a_fun$ ?v5:N_a_fun$ ((∀ ?v6:N$ (member$f(?v6, ?v0) ⇒ (fun_app$y(?v1, fun_app$y(?v2, ?v6)) = ?v6)) ∧ (∀ ?v6:N$ (member$f(?v6, ?v0) ⇒ member$f(fun_app$y(?v2, ?v6), ?v3)) ∧ (∀ ?v6:N$ (member$f(?v6, ?v3) ⇒ (fun_app$y(?v2, fun_app$y(?v1, ?v6)) = ?v6)) ∧ (∀ ?v6:N$ (member$f(?v6, ?v3) ⇒ member$f(fun_app$y(?v1, ?v6), ?v0)) ∧ ∀ ?v6:N$ (member$f(?v6, ?v0) ⇒ (fun_app$d(?v4, fun_app$y(?v2, ?v6)) = fun_app$d(?v5, ?v6))))))) ⇒ (sum$a(?v5, ?v0) = sum$a(?v4, ?v3)))
tff(axiom495,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_n_fun$',A__questionmark_v2: 'N_n_fun$',A__questionmark_v3: 'N_set$',A__questionmark_v4: 'N_a_fun$',A__questionmark_v5: 'N_a_fun$'] :
      ( ( ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v0)
           => ( 'fun_app$y'(A__questionmark_v1,'fun_app$y'(A__questionmark_v2,A__questionmark_v6)) = A__questionmark_v6 ) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v0)
           => 'member$f'('fun_app$y'(A__questionmark_v2,A__questionmark_v6),A__questionmark_v3) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v3)
           => ( 'fun_app$y'(A__questionmark_v2,'fun_app$y'(A__questionmark_v1,A__questionmark_v6)) = A__questionmark_v6 ) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v3)
           => 'member$f'('fun_app$y'(A__questionmark_v1,A__questionmark_v6),A__questionmark_v0) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v0)
           => ( 'fun_app$d'(A__questionmark_v4,'fun_app$y'(A__questionmark_v2,A__questionmark_v6)) = 'fun_app$d'(A__questionmark_v5,A__questionmark_v6) ) ) )
     => ( 'sum$a'(A__questionmark_v5,A__questionmark_v0) = 'sum$a'(A__questionmark_v4,A__questionmark_v3) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_n_fun$ ?v2:N_n_fun$ ?v3:N_set$ ?v4:N_a_n_vec_fun$ ?v5:N_a_n_vec_fun$ ((∀ ?v6:N$ (member$f(?v6, ?v0) ⇒ (fun_app$y(?v1, fun_app$y(?v2, ?v6)) = ?v6)) ∧ (∀ ?v6:N$ (member$f(?v6, ?v0) ⇒ member$f(fun_app$y(?v2, ?v6), ?v3)) ∧ (∀ ?v6:N$ (member$f(?v6, ?v3) ⇒ (fun_app$y(?v2, fun_app$y(?v1, ?v6)) = ?v6)) ∧ (∀ ?v6:N$ (member$f(?v6, ?v3) ⇒ member$f(fun_app$y(?v1, ?v6), ?v0)) ∧ ∀ ?v6:N$ (member$f(?v6, ?v0) ⇒ (fun_app$a(?v4, fun_app$y(?v2, ?v6)) = fun_app$a(?v5, ?v6))))))) ⇒ (sum$(?v5, ?v0) = sum$(?v4, ?v3)))
tff(axiom496,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_n_fun$',A__questionmark_v2: 'N_n_fun$',A__questionmark_v3: 'N_set$',A__questionmark_v4: 'N_a_n_vec_fun$',A__questionmark_v5: 'N_a_n_vec_fun$'] :
      ( ( ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v0)
           => ( 'fun_app$y'(A__questionmark_v1,'fun_app$y'(A__questionmark_v2,A__questionmark_v6)) = A__questionmark_v6 ) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v0)
           => 'member$f'('fun_app$y'(A__questionmark_v2,A__questionmark_v6),A__questionmark_v3) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v3)
           => ( 'fun_app$y'(A__questionmark_v2,'fun_app$y'(A__questionmark_v1,A__questionmark_v6)) = A__questionmark_v6 ) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v3)
           => 'member$f'('fun_app$y'(A__questionmark_v1,A__questionmark_v6),A__questionmark_v0) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v0)
           => ( 'fun_app$a'(A__questionmark_v4,'fun_app$y'(A__questionmark_v2,A__questionmark_v6)) = 'fun_app$a'(A__questionmark_v5,A__questionmark_v6) ) ) )
     => ( 'sum$'(A__questionmark_v5,A__questionmark_v0) = 'sum$'(A__questionmark_v4,A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_set$ ?v1:N_a_fun$ ?v2:A_n_fun$ ?v3:N_set$ ?v4:N_a_fun$ ?v5:A_a_fun$ ((∀ ?v6:A$ (member$g(?v6, ?v0) ⇒ (fun_app$d(?v1, fun_app$bf(?v2, ?v6)) = ?v6)) ∧ (∀ ?v6:A$ (member$g(?v6, ?v0) ⇒ member$f(fun_app$bf(?v2, ?v6), ?v3)) ∧ (∀ ?v6:N$ (member$f(?v6, ?v3) ⇒ (fun_app$bf(?v2, fun_app$d(?v1, ?v6)) = ?v6)) ∧ (∀ ?v6:N$ (member$f(?v6, ?v3) ⇒ member$g(fun_app$d(?v1, ?v6), ?v0)) ∧ ∀ ?v6:A$ (member$g(?v6, ?v0) ⇒ (fun_app$d(?v4, fun_app$bf(?v2, ?v6)) = fun_app$k(?v5, ?v6))))))) ⇒ (sum$n(?v5, ?v0) = sum$a(?v4, ?v3)))
tff(axiom497,axiom,
    ! [A__questionmark_v0: 'A_set$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'A_n_fun$',A__questionmark_v3: 'N_set$',A__questionmark_v4: 'N_a_fun$',A__questionmark_v5: 'A_a_fun$'] :
      ( ( ! [A__questionmark_v6: 'A$'] :
            ( 'member$g'(A__questionmark_v6,A__questionmark_v0)
           => ( 'fun_app$d'(A__questionmark_v1,'fun_app$bf'(A__questionmark_v2,A__questionmark_v6)) = A__questionmark_v6 ) )
        & ! [A__questionmark_v6: 'A$'] :
            ( 'member$g'(A__questionmark_v6,A__questionmark_v0)
           => 'member$f'('fun_app$bf'(A__questionmark_v2,A__questionmark_v6),A__questionmark_v3) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v3)
           => ( 'fun_app$bf'(A__questionmark_v2,'fun_app$d'(A__questionmark_v1,A__questionmark_v6)) = A__questionmark_v6 ) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v3)
           => 'member$g'('fun_app$d'(A__questionmark_v1,A__questionmark_v6),A__questionmark_v0) )
        & ! [A__questionmark_v6: 'A$'] :
            ( 'member$g'(A__questionmark_v6,A__questionmark_v0)
           => ( 'fun_app$d'(A__questionmark_v4,'fun_app$bf'(A__questionmark_v2,A__questionmark_v6)) = 'fun_app$k'(A__questionmark_v5,A__questionmark_v6) ) ) )
     => ( 'sum$n'(A__questionmark_v5,A__questionmark_v0) = 'sum$a'(A__questionmark_v4,A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_set$ ?v1:Nat_a_fun$ ?v2:A_nat_fun$ ?v3:Nat_set$ ?v4:Nat_a_fun$ ?v5:A_a_fun$ ((∀ ?v6:A$ (member$g(?v6, ?v0) ⇒ (fun_app$aa(?v1, fun_app$bc(?v2, ?v6)) = ?v6)) ∧ (∀ ?v6:A$ (member$g(?v6, ?v0) ⇒ member$a(fun_app$bc(?v2, ?v6), ?v3)) ∧ (∀ ?v6:Nat$ (member$a(?v6, ?v3) ⇒ (fun_app$bc(?v2, fun_app$aa(?v1, ?v6)) = ?v6)) ∧ (∀ ?v6:Nat$ (member$a(?v6, ?v3) ⇒ member$g(fun_app$aa(?v1, ?v6), ?v0)) ∧ ∀ ?v6:A$ (member$g(?v6, ?v0) ⇒ (fun_app$aa(?v4, fun_app$bc(?v2, ?v6)) = fun_app$k(?v5, ?v6))))))) ⇒ (sum$n(?v5, ?v0) = sum$d(?v4, ?v3)))
tff(axiom498,axiom,
    ! [A__questionmark_v0: 'A_set$',A__questionmark_v1: 'Nat_a_fun$',A__questionmark_v2: 'A_nat_fun$',A__questionmark_v3: 'Nat_set$',A__questionmark_v4: 'Nat_a_fun$',A__questionmark_v5: 'A_a_fun$'] :
      ( ( ! [A__questionmark_v6: 'A$'] :
            ( 'member$g'(A__questionmark_v6,A__questionmark_v0)
           => ( 'fun_app$aa'(A__questionmark_v1,'fun_app$bc'(A__questionmark_v2,A__questionmark_v6)) = A__questionmark_v6 ) )
        & ! [A__questionmark_v6: 'A$'] :
            ( 'member$g'(A__questionmark_v6,A__questionmark_v0)
           => 'member$a'('fun_app$bc'(A__questionmark_v2,A__questionmark_v6),A__questionmark_v3) )
        & ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v3)
           => ( 'fun_app$bc'(A__questionmark_v2,'fun_app$aa'(A__questionmark_v1,A__questionmark_v6)) = A__questionmark_v6 ) )
        & ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v3)
           => 'member$g'('fun_app$aa'(A__questionmark_v1,A__questionmark_v6),A__questionmark_v0) )
        & ! [A__questionmark_v6: 'A$'] :
            ( 'member$g'(A__questionmark_v6,A__questionmark_v0)
           => ( 'fun_app$aa'(A__questionmark_v4,'fun_app$bc'(A__questionmark_v2,A__questionmark_v6)) = 'fun_app$k'(A__questionmark_v5,A__questionmark_v6) ) ) )
     => ( 'sum$n'(A__questionmark_v5,A__questionmark_v0) = 'sum$d'(A__questionmark_v4,A__questionmark_v3) ) ) ).

%% ∀ ?v0:N_set$ ?v1:A_n_fun$ ?v2:N_a_fun$ ?v3:A_set$ ?v4:A_a_fun$ ?v5:N_a_fun$ ((∀ ?v6:N$ (member$f(?v6, ?v0) ⇒ (fun_app$bf(?v1, fun_app$d(?v2, ?v6)) = ?v6)) ∧ (∀ ?v6:N$ (member$f(?v6, ?v0) ⇒ member$g(fun_app$d(?v2, ?v6), ?v3)) ∧ (∀ ?v6:A$ (member$g(?v6, ?v3) ⇒ (fun_app$d(?v2, fun_app$bf(?v1, ?v6)) = ?v6)) ∧ (∀ ?v6:A$ (member$g(?v6, ?v3) ⇒ member$f(fun_app$bf(?v1, ?v6), ?v0)) ∧ ∀ ?v6:N$ (member$f(?v6, ?v0) ⇒ (fun_app$k(?v4, fun_app$d(?v2, ?v6)) = fun_app$d(?v5, ?v6))))))) ⇒ (sum$a(?v5, ?v0) = sum$n(?v4, ?v3)))
tff(axiom499,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'A_n_fun$',A__questionmark_v2: 'N_a_fun$',A__questionmark_v3: 'A_set$',A__questionmark_v4: 'A_a_fun$',A__questionmark_v5: 'N_a_fun$'] :
      ( ( ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v0)
           => ( 'fun_app$bf'(A__questionmark_v1,'fun_app$d'(A__questionmark_v2,A__questionmark_v6)) = A__questionmark_v6 ) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v0)
           => 'member$g'('fun_app$d'(A__questionmark_v2,A__questionmark_v6),A__questionmark_v3) )
        & ! [A__questionmark_v6: 'A$'] :
            ( 'member$g'(A__questionmark_v6,A__questionmark_v3)
           => ( 'fun_app$d'(A__questionmark_v2,'fun_app$bf'(A__questionmark_v1,A__questionmark_v6)) = A__questionmark_v6 ) )
        & ! [A__questionmark_v6: 'A$'] :
            ( 'member$g'(A__questionmark_v6,A__questionmark_v3)
           => 'member$f'('fun_app$bf'(A__questionmark_v1,A__questionmark_v6),A__questionmark_v0) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v0)
           => ( 'fun_app$k'(A__questionmark_v4,'fun_app$d'(A__questionmark_v2,A__questionmark_v6)) = 'fun_app$d'(A__questionmark_v5,A__questionmark_v6) ) ) )
     => ( 'sum$a'(A__questionmark_v5,A__questionmark_v0) = 'sum$n'(A__questionmark_v4,A__questionmark_v3) ) ) ).

%% ∀ ?v0:N_set$ ?v1:Nat_n_fun$ ?v2:N_nat_fun$ ?v3:Nat_set$ ?v4:Nat_a_fun$ ?v5:N_a_fun$ ((∀ ?v6:N$ (member$f(?v6, ?v0) ⇒ (fun_app$bg(?v1, fun_app$h(?v2, ?v6)) = ?v6)) ∧ (∀ ?v6:N$ (member$f(?v6, ?v0) ⇒ member$a(fun_app$h(?v2, ?v6), ?v3)) ∧ (∀ ?v6:Nat$ (member$a(?v6, ?v3) ⇒ (fun_app$h(?v2, fun_app$bg(?v1, ?v6)) = ?v6)) ∧ (∀ ?v6:Nat$ (member$a(?v6, ?v3) ⇒ member$f(fun_app$bg(?v1, ?v6), ?v0)) ∧ ∀ ?v6:N$ (member$f(?v6, ?v0) ⇒ (fun_app$aa(?v4, fun_app$h(?v2, ?v6)) = fun_app$d(?v5, ?v6))))))) ⇒ (sum$a(?v5, ?v0) = sum$d(?v4, ?v3)))
tff(axiom500,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'Nat_n_fun$',A__questionmark_v2: 'N_nat_fun$',A__questionmark_v3: 'Nat_set$',A__questionmark_v4: 'Nat_a_fun$',A__questionmark_v5: 'N_a_fun$'] :
      ( ( ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v0)
           => ( 'fun_app$bg'(A__questionmark_v1,'fun_app$h'(A__questionmark_v2,A__questionmark_v6)) = A__questionmark_v6 ) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v0)
           => 'member$a'('fun_app$h'(A__questionmark_v2,A__questionmark_v6),A__questionmark_v3) )
        & ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v3)
           => ( 'fun_app$h'(A__questionmark_v2,'fun_app$bg'(A__questionmark_v1,A__questionmark_v6)) = A__questionmark_v6 ) )
        & ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v3)
           => 'member$f'('fun_app$bg'(A__questionmark_v1,A__questionmark_v6),A__questionmark_v0) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v0)
           => ( 'fun_app$aa'(A__questionmark_v4,'fun_app$h'(A__questionmark_v2,A__questionmark_v6)) = 'fun_app$d'(A__questionmark_v5,A__questionmark_v6) ) ) )
     => ( 'sum$a'(A__questionmark_v5,A__questionmark_v0) = 'sum$d'(A__questionmark_v4,A__questionmark_v3) ) ) ).

%% ∀ ?v0:Nat_set$ ?v1:A_nat_fun$ ?v2:Nat_a_fun$ ?v3:A_set$ ?v4:A_a_fun$ ?v5:Nat_a_fun$ ((∀ ?v6:Nat$ (member$a(?v6, ?v0) ⇒ (fun_app$bc(?v1, fun_app$aa(?v2, ?v6)) = ?v6)) ∧ (∀ ?v6:Nat$ (member$a(?v6, ?v0) ⇒ member$g(fun_app$aa(?v2, ?v6), ?v3)) ∧ (∀ ?v6:A$ (member$g(?v6, ?v3) ⇒ (fun_app$aa(?v2, fun_app$bc(?v1, ?v6)) = ?v6)) ∧ (∀ ?v6:A$ (member$g(?v6, ?v3) ⇒ member$a(fun_app$bc(?v1, ?v6), ?v0)) ∧ ∀ ?v6:Nat$ (member$a(?v6, ?v0) ⇒ (fun_app$k(?v4, fun_app$aa(?v2, ?v6)) = fun_app$aa(?v5, ?v6))))))) ⇒ (sum$d(?v5, ?v0) = sum$n(?v4, ?v3)))
tff(axiom501,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'A_nat_fun$',A__questionmark_v2: 'Nat_a_fun$',A__questionmark_v3: 'A_set$',A__questionmark_v4: 'A_a_fun$',A__questionmark_v5: 'Nat_a_fun$'] :
      ( ( ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v0)
           => ( 'fun_app$bc'(A__questionmark_v1,'fun_app$aa'(A__questionmark_v2,A__questionmark_v6)) = A__questionmark_v6 ) )
        & ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v0)
           => 'member$g'('fun_app$aa'(A__questionmark_v2,A__questionmark_v6),A__questionmark_v3) )
        & ! [A__questionmark_v6: 'A$'] :
            ( 'member$g'(A__questionmark_v6,A__questionmark_v3)
           => ( 'fun_app$aa'(A__questionmark_v2,'fun_app$bc'(A__questionmark_v1,A__questionmark_v6)) = A__questionmark_v6 ) )
        & ! [A__questionmark_v6: 'A$'] :
            ( 'member$g'(A__questionmark_v6,A__questionmark_v3)
           => 'member$a'('fun_app$bc'(A__questionmark_v1,A__questionmark_v6),A__questionmark_v0) )
        & ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v0)
           => ( 'fun_app$k'(A__questionmark_v4,'fun_app$aa'(A__questionmark_v2,A__questionmark_v6)) = 'fun_app$aa'(A__questionmark_v5,A__questionmark_v6) ) ) )
     => ( 'sum$d'(A__questionmark_v5,A__questionmark_v0) = 'sum$n'(A__questionmark_v4,A__questionmark_v3) ) ) ).

%% ∀ ?v0:Nat_set$ ?v1:N_nat_fun$ ?v2:Nat_n_fun$ ?v3:N_set$ ?v4:N_a_fun$ ?v5:Nat_a_fun$ ((∀ ?v6:Nat$ (member$a(?v6, ?v0) ⇒ (fun_app$h(?v1, fun_app$bg(?v2, ?v6)) = ?v6)) ∧ (∀ ?v6:Nat$ (member$a(?v6, ?v0) ⇒ member$f(fun_app$bg(?v2, ?v6), ?v3)) ∧ (∀ ?v6:N$ (member$f(?v6, ?v3) ⇒ (fun_app$bg(?v2, fun_app$h(?v1, ?v6)) = ?v6)) ∧ (∀ ?v6:N$ (member$f(?v6, ?v3) ⇒ member$a(fun_app$h(?v1, ?v6), ?v0)) ∧ ∀ ?v6:Nat$ (member$a(?v6, ?v0) ⇒ (fun_app$d(?v4, fun_app$bg(?v2, ?v6)) = fun_app$aa(?v5, ?v6))))))) ⇒ (sum$d(?v5, ?v0) = sum$a(?v4, ?v3)))
tff(axiom502,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'N_nat_fun$',A__questionmark_v2: 'Nat_n_fun$',A__questionmark_v3: 'N_set$',A__questionmark_v4: 'N_a_fun$',A__questionmark_v5: 'Nat_a_fun$'] :
      ( ( ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v0)
           => ( 'fun_app$h'(A__questionmark_v1,'fun_app$bg'(A__questionmark_v2,A__questionmark_v6)) = A__questionmark_v6 ) )
        & ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v0)
           => 'member$f'('fun_app$bg'(A__questionmark_v2,A__questionmark_v6),A__questionmark_v3) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v3)
           => ( 'fun_app$bg'(A__questionmark_v2,'fun_app$h'(A__questionmark_v1,A__questionmark_v6)) = A__questionmark_v6 ) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v3)
           => 'member$a'('fun_app$h'(A__questionmark_v1,A__questionmark_v6),A__questionmark_v0) )
        & ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v0)
           => ( 'fun_app$d'(A__questionmark_v4,'fun_app$bg'(A__questionmark_v2,A__questionmark_v6)) = 'fun_app$aa'(A__questionmark_v5,A__questionmark_v6) ) ) )
     => ( 'sum$d'(A__questionmark_v5,A__questionmark_v0) = 'sum$a'(A__questionmark_v4,A__questionmark_v3) ) ) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_nat_fun$ ?v2:Nat_nat_fun$ ?v3:Nat_set$ ?v4:Nat_a_fun$ ?v5:Nat_a_fun$ ((∀ ?v6:Nat$ (member$a(?v6, ?v0) ⇒ (fun_app$v(?v1, fun_app$v(?v2, ?v6)) = ?v6)) ∧ (∀ ?v6:Nat$ (member$a(?v6, ?v0) ⇒ member$a(fun_app$v(?v2, ?v6), ?v3)) ∧ (∀ ?v6:Nat$ (member$a(?v6, ?v3) ⇒ (fun_app$v(?v2, fun_app$v(?v1, ?v6)) = ?v6)) ∧ (∀ ?v6:Nat$ (member$a(?v6, ?v3) ⇒ member$a(fun_app$v(?v1, ?v6), ?v0)) ∧ ∀ ?v6:Nat$ (member$a(?v6, ?v0) ⇒ (fun_app$aa(?v4, fun_app$v(?v2, ?v6)) = fun_app$aa(?v5, ?v6))))))) ⇒ (sum$d(?v5, ?v0) = sum$d(?v4, ?v3)))
tff(axiom503,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_nat_fun$',A__questionmark_v2: 'Nat_nat_fun$',A__questionmark_v3: 'Nat_set$',A__questionmark_v4: 'Nat_a_fun$',A__questionmark_v5: 'Nat_a_fun$'] :
      ( ( ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v0)
           => ( 'fun_app$v'(A__questionmark_v1,'fun_app$v'(A__questionmark_v2,A__questionmark_v6)) = A__questionmark_v6 ) )
        & ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v0)
           => 'member$a'('fun_app$v'(A__questionmark_v2,A__questionmark_v6),A__questionmark_v3) )
        & ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v3)
           => ( 'fun_app$v'(A__questionmark_v2,'fun_app$v'(A__questionmark_v1,A__questionmark_v6)) = A__questionmark_v6 ) )
        & ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v3)
           => 'member$a'('fun_app$v'(A__questionmark_v1,A__questionmark_v6),A__questionmark_v0) )
        & ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v0)
           => ( 'fun_app$aa'(A__questionmark_v4,'fun_app$v'(A__questionmark_v2,A__questionmark_v6)) = 'fun_app$aa'(A__questionmark_v5,A__questionmark_v6) ) ) )
     => ( 'sum$d'(A__questionmark_v5,A__questionmark_v0) = 'sum$d'(A__questionmark_v4,A__questionmark_v3) ) ) ).

%% ∀ ?v0:Nat_set$ ?v1:N_nat_fun$ ?v2:Nat_n_fun$ ?v3:N_set$ ?v4:N_a_set_fun$ ?v5:Nat_a_set_fun$ ((∀ ?v6:Nat$ (member$a(?v6, ?v0) ⇒ (fun_app$h(?v1, fun_app$bg(?v2, ?v6)) = ?v6)) ∧ (∀ ?v6:Nat$ (member$a(?v6, ?v0) ⇒ member$f(fun_app$bg(?v2, ?v6), ?v3)) ∧ (∀ ?v6:N$ (member$f(?v6, ?v3) ⇒ (fun_app$bg(?v2, fun_app$h(?v1, ?v6)) = ?v6)) ∧ (∀ ?v6:N$ (member$f(?v6, ?v3) ⇒ member$a(fun_app$h(?v1, ?v6), ?v0)) ∧ ∀ ?v6:Nat$ (member$a(?v6, ?v0) ⇒ (fun_app$am(?v4, fun_app$bg(?v2, ?v6)) = fun_app$bh(?v5, ?v6))))))) ⇒ (sum$o(?v5, ?v0) = sum$e(?v4, ?v3)))
tff(axiom504,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'N_nat_fun$',A__questionmark_v2: 'Nat_n_fun$',A__questionmark_v3: 'N_set$',A__questionmark_v4: 'N_a_set_fun$',A__questionmark_v5: 'Nat_a_set_fun$'] :
      ( ( ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v0)
           => ( 'fun_app$h'(A__questionmark_v1,'fun_app$bg'(A__questionmark_v2,A__questionmark_v6)) = A__questionmark_v6 ) )
        & ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v0)
           => 'member$f'('fun_app$bg'(A__questionmark_v2,A__questionmark_v6),A__questionmark_v3) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v3)
           => ( 'fun_app$bg'(A__questionmark_v2,'fun_app$h'(A__questionmark_v1,A__questionmark_v6)) = A__questionmark_v6 ) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v3)
           => 'member$a'('fun_app$h'(A__questionmark_v1,A__questionmark_v6),A__questionmark_v0) )
        & ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v0)
           => ( 'fun_app$am'(A__questionmark_v4,'fun_app$bg'(A__questionmark_v2,A__questionmark_v6)) = 'fun_app$bh'(A__questionmark_v5,A__questionmark_v6) ) ) )
     => ( 'sum$o'(A__questionmark_v5,A__questionmark_v0) = 'sum$e'(A__questionmark_v4,A__questionmark_v3) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_n_fun$ ?v2:N_set$ ?v3:N_n_fun$ ?v4:N_a_fun$ ?v5:N_a_fun$ ((∀ ?v6:N$ (member$f(?v6, ?v0) ⇒ (member$f(fun_app$y(?v1, ?v6), ?v2) ∧ (fun_app$y(?v3, fun_app$y(?v1, ?v6)) = ?v6))) ∧ ∀ ?v6:N$ (member$f(?v6, ?v2) ⇒ (member$f(fun_app$y(?v3, ?v6), ?v0) ∧ ((fun_app$y(?v1, fun_app$y(?v3, ?v6)) = ?v6) ∧ (fun_app$d(?v4, fun_app$y(?v3, ?v6)) = fun_app$d(?v5, ?v6)))))) ⇒ (sum$a(?v5, ?v2) = sum$a(?v4, ?v0)))
tff(axiom505,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_n_fun$',A__questionmark_v2: 'N_set$',A__questionmark_v3: 'N_n_fun$',A__questionmark_v4: 'N_a_fun$',A__questionmark_v5: 'N_a_fun$'] :
      ( ( ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v0)
           => ( 'member$f'('fun_app$y'(A__questionmark_v1,A__questionmark_v6),A__questionmark_v2)
              & ( 'fun_app$y'(A__questionmark_v3,'fun_app$y'(A__questionmark_v1,A__questionmark_v6)) = A__questionmark_v6 ) ) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v2)
           => ( 'member$f'('fun_app$y'(A__questionmark_v3,A__questionmark_v6),A__questionmark_v0)
              & ( 'fun_app$y'(A__questionmark_v1,'fun_app$y'(A__questionmark_v3,A__questionmark_v6)) = A__questionmark_v6 )
              & ( 'fun_app$d'(A__questionmark_v4,'fun_app$y'(A__questionmark_v3,A__questionmark_v6)) = 'fun_app$d'(A__questionmark_v5,A__questionmark_v6) ) ) ) )
     => ( 'sum$a'(A__questionmark_v5,A__questionmark_v2) = 'sum$a'(A__questionmark_v4,A__questionmark_v0) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_n_fun$ ?v2:N_set$ ?v3:N_n_fun$ ?v4:N_a_n_vec_fun$ ?v5:N_a_n_vec_fun$ ((∀ ?v6:N$ (member$f(?v6, ?v0) ⇒ (member$f(fun_app$y(?v1, ?v6), ?v2) ∧ (fun_app$y(?v3, fun_app$y(?v1, ?v6)) = ?v6))) ∧ ∀ ?v6:N$ (member$f(?v6, ?v2) ⇒ (member$f(fun_app$y(?v3, ?v6), ?v0) ∧ ((fun_app$y(?v1, fun_app$y(?v3, ?v6)) = ?v6) ∧ (fun_app$a(?v4, fun_app$y(?v3, ?v6)) = fun_app$a(?v5, ?v6)))))) ⇒ (sum$(?v5, ?v2) = sum$(?v4, ?v0)))
tff(axiom506,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_n_fun$',A__questionmark_v2: 'N_set$',A__questionmark_v3: 'N_n_fun$',A__questionmark_v4: 'N_a_n_vec_fun$',A__questionmark_v5: 'N_a_n_vec_fun$'] :
      ( ( ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v0)
           => ( 'member$f'('fun_app$y'(A__questionmark_v1,A__questionmark_v6),A__questionmark_v2)
              & ( 'fun_app$y'(A__questionmark_v3,'fun_app$y'(A__questionmark_v1,A__questionmark_v6)) = A__questionmark_v6 ) ) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v2)
           => ( 'member$f'('fun_app$y'(A__questionmark_v3,A__questionmark_v6),A__questionmark_v0)
              & ( 'fun_app$y'(A__questionmark_v1,'fun_app$y'(A__questionmark_v3,A__questionmark_v6)) = A__questionmark_v6 )
              & ( 'fun_app$a'(A__questionmark_v4,'fun_app$y'(A__questionmark_v3,A__questionmark_v6)) = 'fun_app$a'(A__questionmark_v5,A__questionmark_v6) ) ) ) )
     => ( 'sum$'(A__questionmark_v5,A__questionmark_v2) = 'sum$'(A__questionmark_v4,A__questionmark_v0) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_a_fun$ ?v2:A_set$ ?v3:A_n_fun$ ?v4:N_a_fun$ ?v5:A_a_fun$ ((∀ ?v6:N$ (member$f(?v6, ?v0) ⇒ (member$g(fun_app$d(?v1, ?v6), ?v2) ∧ (fun_app$bf(?v3, fun_app$d(?v1, ?v6)) = ?v6))) ∧ ∀ ?v6:A$ (member$g(?v6, ?v2) ⇒ (member$f(fun_app$bf(?v3, ?v6), ?v0) ∧ ((fun_app$d(?v1, fun_app$bf(?v3, ?v6)) = ?v6) ∧ (fun_app$d(?v4, fun_app$bf(?v3, ?v6)) = fun_app$k(?v5, ?v6)))))) ⇒ (sum$n(?v5, ?v2) = sum$a(?v4, ?v0)))
tff(axiom507,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'A_set$',A__questionmark_v3: 'A_n_fun$',A__questionmark_v4: 'N_a_fun$',A__questionmark_v5: 'A_a_fun$'] :
      ( ( ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v0)
           => ( 'member$g'('fun_app$d'(A__questionmark_v1,A__questionmark_v6),A__questionmark_v2)
              & ( 'fun_app$bf'(A__questionmark_v3,'fun_app$d'(A__questionmark_v1,A__questionmark_v6)) = A__questionmark_v6 ) ) )
        & ! [A__questionmark_v6: 'A$'] :
            ( 'member$g'(A__questionmark_v6,A__questionmark_v2)
           => ( 'member$f'('fun_app$bf'(A__questionmark_v3,A__questionmark_v6),A__questionmark_v0)
              & ( 'fun_app$d'(A__questionmark_v1,'fun_app$bf'(A__questionmark_v3,A__questionmark_v6)) = A__questionmark_v6 )
              & ( 'fun_app$d'(A__questionmark_v4,'fun_app$bf'(A__questionmark_v3,A__questionmark_v6)) = 'fun_app$k'(A__questionmark_v5,A__questionmark_v6) ) ) ) )
     => ( 'sum$n'(A__questionmark_v5,A__questionmark_v2) = 'sum$a'(A__questionmark_v4,A__questionmark_v0) ) ) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_a_fun$ ?v2:A_set$ ?v3:A_nat_fun$ ?v4:Nat_a_fun$ ?v5:A_a_fun$ ((∀ ?v6:Nat$ (member$a(?v6, ?v0) ⇒ (member$g(fun_app$aa(?v1, ?v6), ?v2) ∧ (fun_app$bc(?v3, fun_app$aa(?v1, ?v6)) = ?v6))) ∧ ∀ ?v6:A$ (member$g(?v6, ?v2) ⇒ (member$a(fun_app$bc(?v3, ?v6), ?v0) ∧ ((fun_app$aa(?v1, fun_app$bc(?v3, ?v6)) = ?v6) ∧ (fun_app$aa(?v4, fun_app$bc(?v3, ?v6)) = fun_app$k(?v5, ?v6)))))) ⇒ (sum$n(?v5, ?v2) = sum$d(?v4, ?v0)))
tff(axiom508,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_a_fun$',A__questionmark_v2: 'A_set$',A__questionmark_v3: 'A_nat_fun$',A__questionmark_v4: 'Nat_a_fun$',A__questionmark_v5: 'A_a_fun$'] :
      ( ( ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v0)
           => ( 'member$g'('fun_app$aa'(A__questionmark_v1,A__questionmark_v6),A__questionmark_v2)
              & ( 'fun_app$bc'(A__questionmark_v3,'fun_app$aa'(A__questionmark_v1,A__questionmark_v6)) = A__questionmark_v6 ) ) )
        & ! [A__questionmark_v6: 'A$'] :
            ( 'member$g'(A__questionmark_v6,A__questionmark_v2)
           => ( 'member$a'('fun_app$bc'(A__questionmark_v3,A__questionmark_v6),A__questionmark_v0)
              & ( 'fun_app$aa'(A__questionmark_v1,'fun_app$bc'(A__questionmark_v3,A__questionmark_v6)) = A__questionmark_v6 )
              & ( 'fun_app$aa'(A__questionmark_v4,'fun_app$bc'(A__questionmark_v3,A__questionmark_v6)) = 'fun_app$k'(A__questionmark_v5,A__questionmark_v6) ) ) ) )
     => ( 'sum$n'(A__questionmark_v5,A__questionmark_v2) = 'sum$d'(A__questionmark_v4,A__questionmark_v0) ) ) ).

%% ∀ ?v0:A_set$ ?v1:A_n_fun$ ?v2:N_set$ ?v3:N_a_fun$ ?v4:A_a_fun$ ?v5:N_a_fun$ ((∀ ?v6:A$ (member$g(?v6, ?v0) ⇒ (member$f(fun_app$bf(?v1, ?v6), ?v2) ∧ (fun_app$d(?v3, fun_app$bf(?v1, ?v6)) = ?v6))) ∧ ∀ ?v6:N$ (member$f(?v6, ?v2) ⇒ (member$g(fun_app$d(?v3, ?v6), ?v0) ∧ ((fun_app$bf(?v1, fun_app$d(?v3, ?v6)) = ?v6) ∧ (fun_app$k(?v4, fun_app$d(?v3, ?v6)) = fun_app$d(?v5, ?v6)))))) ⇒ (sum$a(?v5, ?v2) = sum$n(?v4, ?v0)))
tff(axiom509,axiom,
    ! [A__questionmark_v0: 'A_set$',A__questionmark_v1: 'A_n_fun$',A__questionmark_v2: 'N_set$',A__questionmark_v3: 'N_a_fun$',A__questionmark_v4: 'A_a_fun$',A__questionmark_v5: 'N_a_fun$'] :
      ( ( ! [A__questionmark_v6: 'A$'] :
            ( 'member$g'(A__questionmark_v6,A__questionmark_v0)
           => ( 'member$f'('fun_app$bf'(A__questionmark_v1,A__questionmark_v6),A__questionmark_v2)
              & ( 'fun_app$d'(A__questionmark_v3,'fun_app$bf'(A__questionmark_v1,A__questionmark_v6)) = A__questionmark_v6 ) ) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v2)
           => ( 'member$g'('fun_app$d'(A__questionmark_v3,A__questionmark_v6),A__questionmark_v0)
              & ( 'fun_app$bf'(A__questionmark_v1,'fun_app$d'(A__questionmark_v3,A__questionmark_v6)) = A__questionmark_v6 )
              & ( 'fun_app$k'(A__questionmark_v4,'fun_app$d'(A__questionmark_v3,A__questionmark_v6)) = 'fun_app$d'(A__questionmark_v5,A__questionmark_v6) ) ) ) )
     => ( 'sum$a'(A__questionmark_v5,A__questionmark_v2) = 'sum$n'(A__questionmark_v4,A__questionmark_v0) ) ) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_n_fun$ ?v2:N_set$ ?v3:N_nat_fun$ ?v4:Nat_a_fun$ ?v5:N_a_fun$ ((∀ ?v6:Nat$ (member$a(?v6, ?v0) ⇒ (member$f(fun_app$bg(?v1, ?v6), ?v2) ∧ (fun_app$h(?v3, fun_app$bg(?v1, ?v6)) = ?v6))) ∧ ∀ ?v6:N$ (member$f(?v6, ?v2) ⇒ (member$a(fun_app$h(?v3, ?v6), ?v0) ∧ ((fun_app$bg(?v1, fun_app$h(?v3, ?v6)) = ?v6) ∧ (fun_app$aa(?v4, fun_app$h(?v3, ?v6)) = fun_app$d(?v5, ?v6)))))) ⇒ (sum$a(?v5, ?v2) = sum$d(?v4, ?v0)))
tff(axiom510,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_n_fun$',A__questionmark_v2: 'N_set$',A__questionmark_v3: 'N_nat_fun$',A__questionmark_v4: 'Nat_a_fun$',A__questionmark_v5: 'N_a_fun$'] :
      ( ( ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v0)
           => ( 'member$f'('fun_app$bg'(A__questionmark_v1,A__questionmark_v6),A__questionmark_v2)
              & ( 'fun_app$h'(A__questionmark_v3,'fun_app$bg'(A__questionmark_v1,A__questionmark_v6)) = A__questionmark_v6 ) ) )
        & ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v2)
           => ( 'member$a'('fun_app$h'(A__questionmark_v3,A__questionmark_v6),A__questionmark_v0)
              & ( 'fun_app$bg'(A__questionmark_v1,'fun_app$h'(A__questionmark_v3,A__questionmark_v6)) = A__questionmark_v6 )
              & ( 'fun_app$aa'(A__questionmark_v4,'fun_app$h'(A__questionmark_v3,A__questionmark_v6)) = 'fun_app$d'(A__questionmark_v5,A__questionmark_v6) ) ) ) )
     => ( 'sum$a'(A__questionmark_v5,A__questionmark_v2) = 'sum$d'(A__questionmark_v4,A__questionmark_v0) ) ) ).

%% ∀ ?v0:A_set$ ?v1:A_nat_fun$ ?v2:Nat_set$ ?v3:Nat_a_fun$ ?v4:A_a_fun$ ?v5:Nat_a_fun$ ((∀ ?v6:A$ (member$g(?v6, ?v0) ⇒ (member$a(fun_app$bc(?v1, ?v6), ?v2) ∧ (fun_app$aa(?v3, fun_app$bc(?v1, ?v6)) = ?v6))) ∧ ∀ ?v6:Nat$ (member$a(?v6, ?v2) ⇒ (member$g(fun_app$aa(?v3, ?v6), ?v0) ∧ ((fun_app$bc(?v1, fun_app$aa(?v3, ?v6)) = ?v6) ∧ (fun_app$k(?v4, fun_app$aa(?v3, ?v6)) = fun_app$aa(?v5, ?v6)))))) ⇒ (sum$d(?v5, ?v2) = sum$n(?v4, ?v0)))
tff(axiom511,axiom,
    ! [A__questionmark_v0: 'A_set$',A__questionmark_v1: 'A_nat_fun$',A__questionmark_v2: 'Nat_set$',A__questionmark_v3: 'Nat_a_fun$',A__questionmark_v4: 'A_a_fun$',A__questionmark_v5: 'Nat_a_fun$'] :
      ( ( ! [A__questionmark_v6: 'A$'] :
            ( 'member$g'(A__questionmark_v6,A__questionmark_v0)
           => ( 'member$a'('fun_app$bc'(A__questionmark_v1,A__questionmark_v6),A__questionmark_v2)
              & ( 'fun_app$aa'(A__questionmark_v3,'fun_app$bc'(A__questionmark_v1,A__questionmark_v6)) = A__questionmark_v6 ) ) )
        & ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v2)
           => ( 'member$g'('fun_app$aa'(A__questionmark_v3,A__questionmark_v6),A__questionmark_v0)
              & ( 'fun_app$bc'(A__questionmark_v1,'fun_app$aa'(A__questionmark_v3,A__questionmark_v6)) = A__questionmark_v6 )
              & ( 'fun_app$k'(A__questionmark_v4,'fun_app$aa'(A__questionmark_v3,A__questionmark_v6)) = 'fun_app$aa'(A__questionmark_v5,A__questionmark_v6) ) ) ) )
     => ( 'sum$d'(A__questionmark_v5,A__questionmark_v2) = 'sum$n'(A__questionmark_v4,A__questionmark_v0) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_nat_fun$ ?v2:Nat_set$ ?v3:Nat_n_fun$ ?v4:N_a_fun$ ?v5:Nat_a_fun$ ((∀ ?v6:N$ (member$f(?v6, ?v0) ⇒ (member$a(fun_app$h(?v1, ?v6), ?v2) ∧ (fun_app$bg(?v3, fun_app$h(?v1, ?v6)) = ?v6))) ∧ ∀ ?v6:Nat$ (member$a(?v6, ?v2) ⇒ (member$f(fun_app$bg(?v3, ?v6), ?v0) ∧ ((fun_app$h(?v1, fun_app$bg(?v3, ?v6)) = ?v6) ∧ (fun_app$d(?v4, fun_app$bg(?v3, ?v6)) = fun_app$aa(?v5, ?v6)))))) ⇒ (sum$d(?v5, ?v2) = sum$a(?v4, ?v0)))
tff(axiom512,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_nat_fun$',A__questionmark_v2: 'Nat_set$',A__questionmark_v3: 'Nat_n_fun$',A__questionmark_v4: 'N_a_fun$',A__questionmark_v5: 'Nat_a_fun$'] :
      ( ( ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v0)
           => ( 'member$a'('fun_app$h'(A__questionmark_v1,A__questionmark_v6),A__questionmark_v2)
              & ( 'fun_app$bg'(A__questionmark_v3,'fun_app$h'(A__questionmark_v1,A__questionmark_v6)) = A__questionmark_v6 ) ) )
        & ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v2)
           => ( 'member$f'('fun_app$bg'(A__questionmark_v3,A__questionmark_v6),A__questionmark_v0)
              & ( 'fun_app$h'(A__questionmark_v1,'fun_app$bg'(A__questionmark_v3,A__questionmark_v6)) = A__questionmark_v6 )
              & ( 'fun_app$d'(A__questionmark_v4,'fun_app$bg'(A__questionmark_v3,A__questionmark_v6)) = 'fun_app$aa'(A__questionmark_v5,A__questionmark_v6) ) ) ) )
     => ( 'sum$d'(A__questionmark_v5,A__questionmark_v2) = 'sum$a'(A__questionmark_v4,A__questionmark_v0) ) ) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_nat_fun$ ?v2:Nat_set$ ?v3:Nat_nat_fun$ ?v4:Nat_a_fun$ ?v5:Nat_a_fun$ ((∀ ?v6:Nat$ (member$a(?v6, ?v0) ⇒ (member$a(fun_app$v(?v1, ?v6), ?v2) ∧ (fun_app$v(?v3, fun_app$v(?v1, ?v6)) = ?v6))) ∧ ∀ ?v6:Nat$ (member$a(?v6, ?v2) ⇒ (member$a(fun_app$v(?v3, ?v6), ?v0) ∧ ((fun_app$v(?v1, fun_app$v(?v3, ?v6)) = ?v6) ∧ (fun_app$aa(?v4, fun_app$v(?v3, ?v6)) = fun_app$aa(?v5, ?v6)))))) ⇒ (sum$d(?v5, ?v2) = sum$d(?v4, ?v0)))
tff(axiom513,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_nat_fun$',A__questionmark_v2: 'Nat_set$',A__questionmark_v3: 'Nat_nat_fun$',A__questionmark_v4: 'Nat_a_fun$',A__questionmark_v5: 'Nat_a_fun$'] :
      ( ( ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v0)
           => ( 'member$a'('fun_app$v'(A__questionmark_v1,A__questionmark_v6),A__questionmark_v2)
              & ( 'fun_app$v'(A__questionmark_v3,'fun_app$v'(A__questionmark_v1,A__questionmark_v6)) = A__questionmark_v6 ) ) )
        & ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v2)
           => ( 'member$a'('fun_app$v'(A__questionmark_v3,A__questionmark_v6),A__questionmark_v0)
              & ( 'fun_app$v'(A__questionmark_v1,'fun_app$v'(A__questionmark_v3,A__questionmark_v6)) = A__questionmark_v6 )
              & ( 'fun_app$aa'(A__questionmark_v4,'fun_app$v'(A__questionmark_v3,A__questionmark_v6)) = 'fun_app$aa'(A__questionmark_v5,A__questionmark_v6) ) ) ) )
     => ( 'sum$d'(A__questionmark_v5,A__questionmark_v2) = 'sum$d'(A__questionmark_v4,A__questionmark_v0) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_nat_fun$ ?v2:Nat_set$ ?v3:Nat_n_fun$ ?v4:N_a_set_fun$ ?v5:Nat_a_set_fun$ ((∀ ?v6:N$ (member$f(?v6, ?v0) ⇒ (member$a(fun_app$h(?v1, ?v6), ?v2) ∧ (fun_app$bg(?v3, fun_app$h(?v1, ?v6)) = ?v6))) ∧ ∀ ?v6:Nat$ (member$a(?v6, ?v2) ⇒ (member$f(fun_app$bg(?v3, ?v6), ?v0) ∧ ((fun_app$h(?v1, fun_app$bg(?v3, ?v6)) = ?v6) ∧ (fun_app$am(?v4, fun_app$bg(?v3, ?v6)) = fun_app$bh(?v5, ?v6)))))) ⇒ (sum$o(?v5, ?v2) = sum$e(?v4, ?v0)))
tff(axiom514,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_nat_fun$',A__questionmark_v2: 'Nat_set$',A__questionmark_v3: 'Nat_n_fun$',A__questionmark_v4: 'N_a_set_fun$',A__questionmark_v5: 'Nat_a_set_fun$'] :
      ( ( ! [A__questionmark_v6: 'N$'] :
            ( 'member$f'(A__questionmark_v6,A__questionmark_v0)
           => ( 'member$a'('fun_app$h'(A__questionmark_v1,A__questionmark_v6),A__questionmark_v2)
              & ( 'fun_app$bg'(A__questionmark_v3,'fun_app$h'(A__questionmark_v1,A__questionmark_v6)) = A__questionmark_v6 ) ) )
        & ! [A__questionmark_v6: 'Nat$'] :
            ( 'member$a'(A__questionmark_v6,A__questionmark_v2)
           => ( 'member$f'('fun_app$bg'(A__questionmark_v3,A__questionmark_v6),A__questionmark_v0)
              & ( 'fun_app$h'(A__questionmark_v1,'fun_app$bg'(A__questionmark_v3,A__questionmark_v6)) = A__questionmark_v6 )
              & ( 'fun_app$am'(A__questionmark_v4,'fun_app$bg'(A__questionmark_v3,A__questionmark_v6)) = 'fun_app$bh'(A__questionmark_v5,A__questionmark_v6) ) ) ) )
     => ( 'sum$o'(A__questionmark_v5,A__questionmark_v2) = 'sum$e'(A__questionmark_v4,A__questionmark_v0) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_set$ ?v2:N_n_fun$ ?v3:N_a_fun$ ?v4:N_a_fun$ ((∀ ?v5:N$ (member$f(?v5, ?v0) ⇒ ∃ ?v6:N$ ((member$f(?v6, ?v1) ∧ (fun_app$y(?v2, ?v6) = ?v5)) ∧ ∀ ?v7:N$ ((member$f(?v7, ?v1) ∧ (fun_app$y(?v2, ?v7) = ?v5)) ⇒ (?v7 = ?v6)))) ∧ ∀ ?v5:N$ (member$f(?v5, ?v1) ⇒ (member$f(fun_app$y(?v2, ?v5), ?v0) ∧ (fun_app$d(?v3, fun_app$y(?v2, ?v5)) = fun_app$d(?v4, ?v5))))) ⇒ (sum$a(?v4, ?v1) = sum$a(?v3, ?v0)))
tff(axiom515,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_n_fun$',A__questionmark_v3: 'N_a_fun$',A__questionmark_v4: 'N_a_fun$'] :
      ( ( ! [A__questionmark_v5: 'N$'] :
            ( 'member$f'(A__questionmark_v5,A__questionmark_v0)
           => ? [A__questionmark_v6: 'N$'] :
                ( 'member$f'(A__questionmark_v6,A__questionmark_v1)
                & ( 'fun_app$y'(A__questionmark_v2,A__questionmark_v6) = A__questionmark_v5 )
                & ! [A__questionmark_v7: 'N$'] :
                    ( ( 'member$f'(A__questionmark_v7,A__questionmark_v1)
                      & ( 'fun_app$y'(A__questionmark_v2,A__questionmark_v7) = A__questionmark_v5 ) )
                   => ( A__questionmark_v7 = A__questionmark_v6 ) ) ) )
        & ! [A__questionmark_v5: 'N$'] :
            ( 'member$f'(A__questionmark_v5,A__questionmark_v1)
           => ( 'member$f'('fun_app$y'(A__questionmark_v2,A__questionmark_v5),A__questionmark_v0)
              & ( 'fun_app$d'(A__questionmark_v3,'fun_app$y'(A__questionmark_v2,A__questionmark_v5)) = 'fun_app$d'(A__questionmark_v4,A__questionmark_v5) ) ) ) )
     => ( 'sum$a'(A__questionmark_v4,A__questionmark_v1) = 'sum$a'(A__questionmark_v3,A__questionmark_v0) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_set$ ?v2:N_n_fun$ ?v3:N_a_n_vec_fun$ ?v4:N_a_n_vec_fun$ ((∀ ?v5:N$ (member$f(?v5, ?v0) ⇒ ∃ ?v6:N$ ((member$f(?v6, ?v1) ∧ (fun_app$y(?v2, ?v6) = ?v5)) ∧ ∀ ?v7:N$ ((member$f(?v7, ?v1) ∧ (fun_app$y(?v2, ?v7) = ?v5)) ⇒ (?v7 = ?v6)))) ∧ ∀ ?v5:N$ (member$f(?v5, ?v1) ⇒ (member$f(fun_app$y(?v2, ?v5), ?v0) ∧ (fun_app$a(?v3, fun_app$y(?v2, ?v5)) = fun_app$a(?v4, ?v5))))) ⇒ (sum$(?v4, ?v1) = sum$(?v3, ?v0)))
tff(axiom516,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_n_fun$',A__questionmark_v3: 'N_a_n_vec_fun$',A__questionmark_v4: 'N_a_n_vec_fun$'] :
      ( ( ! [A__questionmark_v5: 'N$'] :
            ( 'member$f'(A__questionmark_v5,A__questionmark_v0)
           => ? [A__questionmark_v6: 'N$'] :
                ( 'member$f'(A__questionmark_v6,A__questionmark_v1)
                & ( 'fun_app$y'(A__questionmark_v2,A__questionmark_v6) = A__questionmark_v5 )
                & ! [A__questionmark_v7: 'N$'] :
                    ( ( 'member$f'(A__questionmark_v7,A__questionmark_v1)
                      & ( 'fun_app$y'(A__questionmark_v2,A__questionmark_v7) = A__questionmark_v5 ) )
                   => ( A__questionmark_v7 = A__questionmark_v6 ) ) ) )
        & ! [A__questionmark_v5: 'N$'] :
            ( 'member$f'(A__questionmark_v5,A__questionmark_v1)
           => ( 'member$f'('fun_app$y'(A__questionmark_v2,A__questionmark_v5),A__questionmark_v0)
              & ( 'fun_app$a'(A__questionmark_v3,'fun_app$y'(A__questionmark_v2,A__questionmark_v5)) = 'fun_app$a'(A__questionmark_v4,A__questionmark_v5) ) ) ) )
     => ( 'sum$'(A__questionmark_v4,A__questionmark_v1) = 'sum$'(A__questionmark_v3,A__questionmark_v0) ) ) ).

%% ∀ ?v0:N_set$ ?v1:A_set$ ?v2:A_n_fun$ ?v3:N_a_fun$ ?v4:A_a_fun$ ((∀ ?v5:N$ (member$f(?v5, ?v0) ⇒ ∃ ?v6:A$ ((member$g(?v6, ?v1) ∧ (fun_app$bf(?v2, ?v6) = ?v5)) ∧ ∀ ?v7:A$ ((member$g(?v7, ?v1) ∧ (fun_app$bf(?v2, ?v7) = ?v5)) ⇒ (?v7 = ?v6)))) ∧ ∀ ?v5:A$ (member$g(?v5, ?v1) ⇒ (member$f(fun_app$bf(?v2, ?v5), ?v0) ∧ (fun_app$d(?v3, fun_app$bf(?v2, ?v5)) = fun_app$k(?v4, ?v5))))) ⇒ (sum$n(?v4, ?v1) = sum$a(?v3, ?v0)))
tff(axiom517,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'A_set$',A__questionmark_v2: 'A_n_fun$',A__questionmark_v3: 'N_a_fun$',A__questionmark_v4: 'A_a_fun$'] :
      ( ( ! [A__questionmark_v5: 'N$'] :
            ( 'member$f'(A__questionmark_v5,A__questionmark_v0)
           => ? [A__questionmark_v6: 'A$'] :
                ( 'member$g'(A__questionmark_v6,A__questionmark_v1)
                & ( 'fun_app$bf'(A__questionmark_v2,A__questionmark_v6) = A__questionmark_v5 )
                & ! [A__questionmark_v7: 'A$'] :
                    ( ( 'member$g'(A__questionmark_v7,A__questionmark_v1)
                      & ( 'fun_app$bf'(A__questionmark_v2,A__questionmark_v7) = A__questionmark_v5 ) )
                   => ( A__questionmark_v7 = A__questionmark_v6 ) ) ) )
        & ! [A__questionmark_v5: 'A$'] :
            ( 'member$g'(A__questionmark_v5,A__questionmark_v1)
           => ( 'member$f'('fun_app$bf'(A__questionmark_v2,A__questionmark_v5),A__questionmark_v0)
              & ( 'fun_app$d'(A__questionmark_v3,'fun_app$bf'(A__questionmark_v2,A__questionmark_v5)) = 'fun_app$k'(A__questionmark_v4,A__questionmark_v5) ) ) ) )
     => ( 'sum$n'(A__questionmark_v4,A__questionmark_v1) = 'sum$a'(A__questionmark_v3,A__questionmark_v0) ) ) ).

%% ∀ ?v0:Nat_set$ ?v1:A_set$ ?v2:A_nat_fun$ ?v3:Nat_a_fun$ ?v4:A_a_fun$ ((∀ ?v5:Nat$ (member$a(?v5, ?v0) ⇒ ∃ ?v6:A$ ((member$g(?v6, ?v1) ∧ (fun_app$bc(?v2, ?v6) = ?v5)) ∧ ∀ ?v7:A$ ((member$g(?v7, ?v1) ∧ (fun_app$bc(?v2, ?v7) = ?v5)) ⇒ (?v7 = ?v6)))) ∧ ∀ ?v5:A$ (member$g(?v5, ?v1) ⇒ (member$a(fun_app$bc(?v2, ?v5), ?v0) ∧ (fun_app$aa(?v3, fun_app$bc(?v2, ?v5)) = fun_app$k(?v4, ?v5))))) ⇒ (sum$n(?v4, ?v1) = sum$d(?v3, ?v0)))
tff(axiom518,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'A_set$',A__questionmark_v2: 'A_nat_fun$',A__questionmark_v3: 'Nat_a_fun$',A__questionmark_v4: 'A_a_fun$'] :
      ( ( ! [A__questionmark_v5: 'Nat$'] :
            ( 'member$a'(A__questionmark_v5,A__questionmark_v0)
           => ? [A__questionmark_v6: 'A$'] :
                ( 'member$g'(A__questionmark_v6,A__questionmark_v1)
                & ( 'fun_app$bc'(A__questionmark_v2,A__questionmark_v6) = A__questionmark_v5 )
                & ! [A__questionmark_v7: 'A$'] :
                    ( ( 'member$g'(A__questionmark_v7,A__questionmark_v1)
                      & ( 'fun_app$bc'(A__questionmark_v2,A__questionmark_v7) = A__questionmark_v5 ) )
                   => ( A__questionmark_v7 = A__questionmark_v6 ) ) ) )
        & ! [A__questionmark_v5: 'A$'] :
            ( 'member$g'(A__questionmark_v5,A__questionmark_v1)
           => ( 'member$a'('fun_app$bc'(A__questionmark_v2,A__questionmark_v5),A__questionmark_v0)
              & ( 'fun_app$aa'(A__questionmark_v3,'fun_app$bc'(A__questionmark_v2,A__questionmark_v5)) = 'fun_app$k'(A__questionmark_v4,A__questionmark_v5) ) ) ) )
     => ( 'sum$n'(A__questionmark_v4,A__questionmark_v1) = 'sum$d'(A__questionmark_v3,A__questionmark_v0) ) ) ).

%% ∀ ?v0:A_set$ ?v1:N_set$ ?v2:N_a_fun$ ?v3:A_a_fun$ ?v4:N_a_fun$ ((∀ ?v5:A$ (member$g(?v5, ?v0) ⇒ ∃ ?v6:N$ ((member$f(?v6, ?v1) ∧ (fun_app$d(?v2, ?v6) = ?v5)) ∧ ∀ ?v7:N$ ((member$f(?v7, ?v1) ∧ (fun_app$d(?v2, ?v7) = ?v5)) ⇒ (?v7 = ?v6)))) ∧ ∀ ?v5:N$ (member$f(?v5, ?v1) ⇒ (member$g(fun_app$d(?v2, ?v5), ?v0) ∧ (fun_app$k(?v3, fun_app$d(?v2, ?v5)) = fun_app$d(?v4, ?v5))))) ⇒ (sum$a(?v4, ?v1) = sum$n(?v3, ?v0)))
tff(axiom519,axiom,
    ! [A__questionmark_v0: 'A_set$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_a_fun$',A__questionmark_v3: 'A_a_fun$',A__questionmark_v4: 'N_a_fun$'] :
      ( ( ! [A__questionmark_v5: 'A$'] :
            ( 'member$g'(A__questionmark_v5,A__questionmark_v0)
           => ? [A__questionmark_v6: 'N$'] :
                ( 'member$f'(A__questionmark_v6,A__questionmark_v1)
                & ( 'fun_app$d'(A__questionmark_v2,A__questionmark_v6) = A__questionmark_v5 )
                & ! [A__questionmark_v7: 'N$'] :
                    ( ( 'member$f'(A__questionmark_v7,A__questionmark_v1)
                      & ( 'fun_app$d'(A__questionmark_v2,A__questionmark_v7) = A__questionmark_v5 ) )
                   => ( A__questionmark_v7 = A__questionmark_v6 ) ) ) )
        & ! [A__questionmark_v5: 'N$'] :
            ( 'member$f'(A__questionmark_v5,A__questionmark_v1)
           => ( 'member$g'('fun_app$d'(A__questionmark_v2,A__questionmark_v5),A__questionmark_v0)
              & ( 'fun_app$k'(A__questionmark_v3,'fun_app$d'(A__questionmark_v2,A__questionmark_v5)) = 'fun_app$d'(A__questionmark_v4,A__questionmark_v5) ) ) ) )
     => ( 'sum$a'(A__questionmark_v4,A__questionmark_v1) = 'sum$n'(A__questionmark_v3,A__questionmark_v0) ) ) ).

%% ∀ ?v0:Nat_set$ ?v1:N_set$ ?v2:N_nat_fun$ ?v3:Nat_a_fun$ ?v4:N_a_fun$ ((∀ ?v5:Nat$ (member$a(?v5, ?v0) ⇒ ∃ ?v6:N$ ((member$f(?v6, ?v1) ∧ (fun_app$h(?v2, ?v6) = ?v5)) ∧ ∀ ?v7:N$ ((member$f(?v7, ?v1) ∧ (fun_app$h(?v2, ?v7) = ?v5)) ⇒ (?v7 = ?v6)))) ∧ ∀ ?v5:N$ (member$f(?v5, ?v1) ⇒ (member$a(fun_app$h(?v2, ?v5), ?v0) ∧ (fun_app$aa(?v3, fun_app$h(?v2, ?v5)) = fun_app$d(?v4, ?v5))))) ⇒ (sum$a(?v4, ?v1) = sum$d(?v3, ?v0)))
tff(axiom520,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_nat_fun$',A__questionmark_v3: 'Nat_a_fun$',A__questionmark_v4: 'N_a_fun$'] :
      ( ( ! [A__questionmark_v5: 'Nat$'] :
            ( 'member$a'(A__questionmark_v5,A__questionmark_v0)
           => ? [A__questionmark_v6: 'N$'] :
                ( 'member$f'(A__questionmark_v6,A__questionmark_v1)
                & ( 'fun_app$h'(A__questionmark_v2,A__questionmark_v6) = A__questionmark_v5 )
                & ! [A__questionmark_v7: 'N$'] :
                    ( ( 'member$f'(A__questionmark_v7,A__questionmark_v1)
                      & ( 'fun_app$h'(A__questionmark_v2,A__questionmark_v7) = A__questionmark_v5 ) )
                   => ( A__questionmark_v7 = A__questionmark_v6 ) ) ) )
        & ! [A__questionmark_v5: 'N$'] :
            ( 'member$f'(A__questionmark_v5,A__questionmark_v1)
           => ( 'member$a'('fun_app$h'(A__questionmark_v2,A__questionmark_v5),A__questionmark_v0)
              & ( 'fun_app$aa'(A__questionmark_v3,'fun_app$h'(A__questionmark_v2,A__questionmark_v5)) = 'fun_app$d'(A__questionmark_v4,A__questionmark_v5) ) ) ) )
     => ( 'sum$a'(A__questionmark_v4,A__questionmark_v1) = 'sum$d'(A__questionmark_v3,A__questionmark_v0) ) ) ).

%% ∀ ?v0:A_set$ ?v1:Nat_set$ ?v2:Nat_a_fun$ ?v3:A_a_fun$ ?v4:Nat_a_fun$ ((∀ ?v5:A$ (member$g(?v5, ?v0) ⇒ ∃ ?v6:Nat$ ((member$a(?v6, ?v1) ∧ (fun_app$aa(?v2, ?v6) = ?v5)) ∧ ∀ ?v7:Nat$ ((member$a(?v7, ?v1) ∧ (fun_app$aa(?v2, ?v7) = ?v5)) ⇒ (?v7 = ?v6)))) ∧ ∀ ?v5:Nat$ (member$a(?v5, ?v1) ⇒ (member$g(fun_app$aa(?v2, ?v5), ?v0) ∧ (fun_app$k(?v3, fun_app$aa(?v2, ?v5)) = fun_app$aa(?v4, ?v5))))) ⇒ (sum$d(?v4, ?v1) = sum$n(?v3, ?v0)))
tff(axiom521,axiom,
    ! [A__questionmark_v0: 'A_set$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'Nat_a_fun$',A__questionmark_v3: 'A_a_fun$',A__questionmark_v4: 'Nat_a_fun$'] :
      ( ( ! [A__questionmark_v5: 'A$'] :
            ( 'member$g'(A__questionmark_v5,A__questionmark_v0)
           => ? [A__questionmark_v6: 'Nat$'] :
                ( 'member$a'(A__questionmark_v6,A__questionmark_v1)
                & ( 'fun_app$aa'(A__questionmark_v2,A__questionmark_v6) = A__questionmark_v5 )
                & ! [A__questionmark_v7: 'Nat$'] :
                    ( ( 'member$a'(A__questionmark_v7,A__questionmark_v1)
                      & ( 'fun_app$aa'(A__questionmark_v2,A__questionmark_v7) = A__questionmark_v5 ) )
                   => ( A__questionmark_v7 = A__questionmark_v6 ) ) ) )
        & ! [A__questionmark_v5: 'Nat$'] :
            ( 'member$a'(A__questionmark_v5,A__questionmark_v1)
           => ( 'member$g'('fun_app$aa'(A__questionmark_v2,A__questionmark_v5),A__questionmark_v0)
              & ( 'fun_app$k'(A__questionmark_v3,'fun_app$aa'(A__questionmark_v2,A__questionmark_v5)) = 'fun_app$aa'(A__questionmark_v4,A__questionmark_v5) ) ) ) )
     => ( 'sum$d'(A__questionmark_v4,A__questionmark_v1) = 'sum$n'(A__questionmark_v3,A__questionmark_v0) ) ) ).

%% ∀ ?v0:N_set$ ?v1:Nat_set$ ?v2:Nat_n_fun$ ?v3:N_a_fun$ ?v4:Nat_a_fun$ ((∀ ?v5:N$ (member$f(?v5, ?v0) ⇒ ∃ ?v6:Nat$ ((member$a(?v6, ?v1) ∧ (fun_app$bg(?v2, ?v6) = ?v5)) ∧ ∀ ?v7:Nat$ ((member$a(?v7, ?v1) ∧ (fun_app$bg(?v2, ?v7) = ?v5)) ⇒ (?v7 = ?v6)))) ∧ ∀ ?v5:Nat$ (member$a(?v5, ?v1) ⇒ (member$f(fun_app$bg(?v2, ?v5), ?v0) ∧ (fun_app$d(?v3, fun_app$bg(?v2, ?v5)) = fun_app$aa(?v4, ?v5))))) ⇒ (sum$d(?v4, ?v1) = sum$a(?v3, ?v0)))
tff(axiom522,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'Nat_n_fun$',A__questionmark_v3: 'N_a_fun$',A__questionmark_v4: 'Nat_a_fun$'] :
      ( ( ! [A__questionmark_v5: 'N$'] :
            ( 'member$f'(A__questionmark_v5,A__questionmark_v0)
           => ? [A__questionmark_v6: 'Nat$'] :
                ( 'member$a'(A__questionmark_v6,A__questionmark_v1)
                & ( 'fun_app$bg'(A__questionmark_v2,A__questionmark_v6) = A__questionmark_v5 )
                & ! [A__questionmark_v7: 'Nat$'] :
                    ( ( 'member$a'(A__questionmark_v7,A__questionmark_v1)
                      & ( 'fun_app$bg'(A__questionmark_v2,A__questionmark_v7) = A__questionmark_v5 ) )
                   => ( A__questionmark_v7 = A__questionmark_v6 ) ) ) )
        & ! [A__questionmark_v5: 'Nat$'] :
            ( 'member$a'(A__questionmark_v5,A__questionmark_v1)
           => ( 'member$f'('fun_app$bg'(A__questionmark_v2,A__questionmark_v5),A__questionmark_v0)
              & ( 'fun_app$d'(A__questionmark_v3,'fun_app$bg'(A__questionmark_v2,A__questionmark_v5)) = 'fun_app$aa'(A__questionmark_v4,A__questionmark_v5) ) ) ) )
     => ( 'sum$d'(A__questionmark_v4,A__questionmark_v1) = 'sum$a'(A__questionmark_v3,A__questionmark_v0) ) ) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_set$ ?v2:Nat_nat_fun$ ?v3:Nat_a_fun$ ?v4:Nat_a_fun$ ((∀ ?v5:Nat$ (member$a(?v5, ?v0) ⇒ ∃ ?v6:Nat$ ((member$a(?v6, ?v1) ∧ (fun_app$v(?v2, ?v6) = ?v5)) ∧ ∀ ?v7:Nat$ ((member$a(?v7, ?v1) ∧ (fun_app$v(?v2, ?v7) = ?v5)) ⇒ (?v7 = ?v6)))) ∧ ∀ ?v5:Nat$ (member$a(?v5, ?v1) ⇒ (member$a(fun_app$v(?v2, ?v5), ?v0) ∧ (fun_app$aa(?v3, fun_app$v(?v2, ?v5)) = fun_app$aa(?v4, ?v5))))) ⇒ (sum$d(?v4, ?v1) = sum$d(?v3, ?v0)))
tff(axiom523,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'Nat_nat_fun$',A__questionmark_v3: 'Nat_a_fun$',A__questionmark_v4: 'Nat_a_fun$'] :
      ( ( ! [A__questionmark_v5: 'Nat$'] :
            ( 'member$a'(A__questionmark_v5,A__questionmark_v0)
           => ? [A__questionmark_v6: 'Nat$'] :
                ( 'member$a'(A__questionmark_v6,A__questionmark_v1)
                & ( 'fun_app$v'(A__questionmark_v2,A__questionmark_v6) = A__questionmark_v5 )
                & ! [A__questionmark_v7: 'Nat$'] :
                    ( ( 'member$a'(A__questionmark_v7,A__questionmark_v1)
                      & ( 'fun_app$v'(A__questionmark_v2,A__questionmark_v7) = A__questionmark_v5 ) )
                   => ( A__questionmark_v7 = A__questionmark_v6 ) ) ) )
        & ! [A__questionmark_v5: 'Nat$'] :
            ( 'member$a'(A__questionmark_v5,A__questionmark_v1)
           => ( 'member$a'('fun_app$v'(A__questionmark_v2,A__questionmark_v5),A__questionmark_v0)
              & ( 'fun_app$aa'(A__questionmark_v3,'fun_app$v'(A__questionmark_v2,A__questionmark_v5)) = 'fun_app$aa'(A__questionmark_v4,A__questionmark_v5) ) ) ) )
     => ( 'sum$d'(A__questionmark_v4,A__questionmark_v1) = 'sum$d'(A__questionmark_v3,A__questionmark_v0) ) ) ).

%% ∀ ?v0:N_set$ ?v1:Nat_set$ ?v2:Nat_n_fun$ ?v3:N_a_set_fun$ ?v4:Nat_a_set_fun$ ((∀ ?v5:N$ (member$f(?v5, ?v0) ⇒ ∃ ?v6:Nat$ ((member$a(?v6, ?v1) ∧ (fun_app$bg(?v2, ?v6) = ?v5)) ∧ ∀ ?v7:Nat$ ((member$a(?v7, ?v1) ∧ (fun_app$bg(?v2, ?v7) = ?v5)) ⇒ (?v7 = ?v6)))) ∧ ∀ ?v5:Nat$ (member$a(?v5, ?v1) ⇒ (member$f(fun_app$bg(?v2, ?v5), ?v0) ∧ (fun_app$am(?v3, fun_app$bg(?v2, ?v5)) = fun_app$bh(?v4, ?v5))))) ⇒ (sum$o(?v4, ?v1) = sum$e(?v3, ?v0)))
tff(axiom524,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'Nat_n_fun$',A__questionmark_v3: 'N_a_set_fun$',A__questionmark_v4: 'Nat_a_set_fun$'] :
      ( ( ! [A__questionmark_v5: 'N$'] :
            ( 'member$f'(A__questionmark_v5,A__questionmark_v0)
           => ? [A__questionmark_v6: 'Nat$'] :
                ( 'member$a'(A__questionmark_v6,A__questionmark_v1)
                & ( 'fun_app$bg'(A__questionmark_v2,A__questionmark_v6) = A__questionmark_v5 )
                & ! [A__questionmark_v7: 'Nat$'] :
                    ( ( 'member$a'(A__questionmark_v7,A__questionmark_v1)
                      & ( 'fun_app$bg'(A__questionmark_v2,A__questionmark_v7) = A__questionmark_v5 ) )
                   => ( A__questionmark_v7 = A__questionmark_v6 ) ) ) )
        & ! [A__questionmark_v5: 'Nat$'] :
            ( 'member$a'(A__questionmark_v5,A__questionmark_v1)
           => ( 'member$f'('fun_app$bg'(A__questionmark_v2,A__questionmark_v5),A__questionmark_v0)
              & ( 'fun_app$am'(A__questionmark_v3,'fun_app$bg'(A__questionmark_v2,A__questionmark_v5)) = 'fun_app$bh'(A__questionmark_v4,A__questionmark_v5) ) ) ) )
     => ( 'sum$o'(A__questionmark_v4,A__questionmark_v1) = 'sum$e'(A__questionmark_v3,A__questionmark_v0) ) ) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_set$ ?v2:Nat_a_fun$ ?v3:Nat_a_fun$ (((?v0 = ?v1) ∧ ∀ ?v4:Nat$ (member$a(?v4, ?v1) ⇒ (fun_app$aa(?v2, ?v4) = fun_app$aa(?v3, ?v4)))) ⇒ (sum$d(?v2, ?v0) = sum$d(?v3, ?v1)))
tff(axiom525,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'Nat_a_fun$',A__questionmark_v3: 'Nat_a_fun$'] :
      ( ( ( A__questionmark_v0 = A__questionmark_v1 )
        & ! [A__questionmark_v4: 'Nat$'] :
            ( 'member$a'(A__questionmark_v4,A__questionmark_v1)
           => ( 'fun_app$aa'(A__questionmark_v2,A__questionmark_v4) = 'fun_app$aa'(A__questionmark_v3,A__questionmark_v4) ) ) )
     => ( 'sum$d'(A__questionmark_v2,A__questionmark_v0) = 'sum$d'(A__questionmark_v3,A__questionmark_v1) ) ) ).

%% ∀ ?v0:N_n_fun_set$ ?v1:N_n_fun_set$ ?v2:N_n_fun_a_fun$ ?v3:N_n_fun_a_fun$ (((?v0 = ?v1) ∧ ∀ ?v4:N_n_fun$ (member$d(?v4, ?v1) ⇒ (fun_app$i(?v2, ?v4) = fun_app$i(?v3, ?v4)))) ⇒ (sum$c(?v2, ?v0) = sum$c(?v3, ?v1)))
tff(axiom526,axiom,
    ! [A__questionmark_v0: 'N_n_fun_set$',A__questionmark_v1: 'N_n_fun_set$',A__questionmark_v2: 'N_n_fun_a_fun$',A__questionmark_v3: 'N_n_fun_a_fun$'] :
      ( ( ( A__questionmark_v0 = A__questionmark_v1 )
        & ! [A__questionmark_v4: 'N_n_fun$'] :
            ( 'member$d'(A__questionmark_v4,A__questionmark_v1)
           => ( 'fun_app$i'(A__questionmark_v2,A__questionmark_v4) = 'fun_app$i'(A__questionmark_v3,A__questionmark_v4) ) ) )
     => ( 'sum$c'(A__questionmark_v2,A__questionmark_v0) = 'sum$c'(A__questionmark_v3,A__questionmark_v1) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_set$ ?v2:N_a_n_vec_n_vec_fun$ ?v3:N_a_n_vec_n_vec_fun$ (((?v0 = ?v1) ∧ ∀ ?v4:N$ (member$f(?v4, ?v1) ⇒ (fun_app$f(?v2, ?v4) = fun_app$f(?v3, ?v4)))) ⇒ (sum$b(?v2, ?v0) = sum$b(?v3, ?v1)))
tff(axiom527,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_a_n_vec_n_vec_fun$',A__questionmark_v3: 'N_a_n_vec_n_vec_fun$'] :
      ( ( ( A__questionmark_v0 = A__questionmark_v1 )
        & ! [A__questionmark_v4: 'N$'] :
            ( 'member$f'(A__questionmark_v4,A__questionmark_v1)
           => ( 'fun_app$f'(A__questionmark_v2,A__questionmark_v4) = 'fun_app$f'(A__questionmark_v3,A__questionmark_v4) ) ) )
     => ( 'sum$b'(A__questionmark_v2,A__questionmark_v0) = 'sum$b'(A__questionmark_v3,A__questionmark_v1) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_set$ ?v2:N_a_n_vec_set_fun$ ?v3:N_a_n_vec_set_fun$ (((?v0 = ?v1) ∧ ∀ ?v4:N$ (member$f(?v4, ?v1) ⇒ (fun_app$au(?v2, ?v4) = fun_app$au(?v3, ?v4)))) ⇒ (sum$j(?v2, ?v0) = sum$j(?v3, ?v1)))
tff(axiom528,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_a_n_vec_set_fun$',A__questionmark_v3: 'N_a_n_vec_set_fun$'] :
      ( ( ( A__questionmark_v0 = A__questionmark_v1 )
        & ! [A__questionmark_v4: 'N$'] :
            ( 'member$f'(A__questionmark_v4,A__questionmark_v1)
           => ( 'fun_app$au'(A__questionmark_v2,A__questionmark_v4) = 'fun_app$au'(A__questionmark_v3,A__questionmark_v4) ) ) )
     => ( 'sum$j'(A__questionmark_v2,A__questionmark_v0) = 'sum$j'(A__questionmark_v3,A__questionmark_v1) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_set$ ?v2:N_a_set_fun$ ?v3:N_a_set_fun$ (((?v0 = ?v1) ∧ ∀ ?v4:N$ (member$f(?v4, ?v1) ⇒ (fun_app$am(?v2, ?v4) = fun_app$am(?v3, ?v4)))) ⇒ (sum$e(?v2, ?v0) = sum$e(?v3, ?v1)))
tff(axiom529,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_a_set_fun$',A__questionmark_v3: 'N_a_set_fun$'] :
      ( ( ( A__questionmark_v0 = A__questionmark_v1 )
        & ! [A__questionmark_v4: 'N$'] :
            ( 'member$f'(A__questionmark_v4,A__questionmark_v1)
           => ( 'fun_app$am'(A__questionmark_v2,A__questionmark_v4) = 'fun_app$am'(A__questionmark_v3,A__questionmark_v4) ) ) )
     => ( 'sum$e'(A__questionmark_v2,A__questionmark_v0) = 'sum$e'(A__questionmark_v3,A__questionmark_v1) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_set$ ?v2:N_a_n_vec_fun$ ?v3:N_a_n_vec_fun$ (((?v0 = ?v1) ∧ ∀ ?v4:N$ (member$f(?v4, ?v1) ⇒ (fun_app$a(?v2, ?v4) = fun_app$a(?v3, ?v4)))) ⇒ (sum$(?v2, ?v0) = sum$(?v3, ?v1)))
tff(axiom530,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_a_n_vec_fun$',A__questionmark_v3: 'N_a_n_vec_fun$'] :
      ( ( ( A__questionmark_v0 = A__questionmark_v1 )
        & ! [A__questionmark_v4: 'N$'] :
            ( 'member$f'(A__questionmark_v4,A__questionmark_v1)
           => ( 'fun_app$a'(A__questionmark_v2,A__questionmark_v4) = 'fun_app$a'(A__questionmark_v3,A__questionmark_v4) ) ) )
     => ( 'sum$'(A__questionmark_v2,A__questionmark_v0) = 'sum$'(A__questionmark_v3,A__questionmark_v1) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_set$ ?v2:N_a_fun$ ?v3:N_a_fun$ (((?v0 = ?v1) ∧ ∀ ?v4:N$ (member$f(?v4, ?v1) ⇒ (fun_app$d(?v2, ?v4) = fun_app$d(?v3, ?v4)))) ⇒ (sum$a(?v2, ?v0) = sum$a(?v3, ?v1)))
tff(axiom531,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_a_fun$',A__questionmark_v3: 'N_a_fun$'] :
      ( ( ( A__questionmark_v0 = A__questionmark_v1 )
        & ! [A__questionmark_v4: 'N$'] :
            ( 'member$f'(A__questionmark_v4,A__questionmark_v1)
           => ( 'fun_app$d'(A__questionmark_v2,A__questionmark_v4) = 'fun_app$d'(A__questionmark_v3,A__questionmark_v4) ) ) )
     => ( 'sum$a'(A__questionmark_v2,A__questionmark_v0) = 'sum$a'(A__questionmark_v3,A__questionmark_v1) ) ) ).

%% ∀ ?v0:N_n_vec$ (set_of_vector$a(?v0) = collect$(uxo$(?v0)))
tff(axiom532,axiom,
    ! [A__questionmark_v0: 'N_n_vec$'] : 'set_of_vector$a'(A__questionmark_v0) = 'collect$'('uxo$'(A__questionmark_v0)) ).

%% ∀ ?v0:N_n_fun_n_vec$ (set_of_vector$b(?v0) = collect$f(uxp$(?v0)))
tff(axiom533,axiom,
    ! [A__questionmark_v0: 'N_n_fun_n_vec$'] : 'set_of_vector$b'(A__questionmark_v0) = 'collect$f'('uxp$'(A__questionmark_v0)) ).

%% ∀ ?v0:Nat_nat_fun_n_vec$ (set_of_vector$c(?v0) = collect$g(uxq$(?v0)))
tff(axiom534,axiom,
    ! [A__questionmark_v0: 'Nat_nat_fun_n_vec$'] : 'set_of_vector$c'(A__questionmark_v0) = 'collect$g'('uxq$'(A__questionmark_v0)) ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ (set_of_vector$d(?v0) = collect$h(uxr$(?v0)))
tff(axiom535,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$'] : 'set_of_vector$d'(A__questionmark_v0) = 'collect$h'('uxr$'(A__questionmark_v0)) ).

%% ∀ ?v0:Nat_n_vec$ (set_of_vector$e(?v0) = collect$a(uxs$(?v0)))
tff(axiom536,axiom,
    ! [A__questionmark_v0: 'Nat_n_vec$'] : 'set_of_vector$e'(A__questionmark_v0) = 'collect$a'('uxs$'(A__questionmark_v0)) ).

%% ∀ ?v0:A_n_vec_n_vec$ (set_of_vector$(?v0) = collect$d(uxt$(?v0)))
tff(axiom537,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$'] : 'set_of_vector$'(A__questionmark_v0) = 'collect$d'('uxt$'(A__questionmark_v0)) ).

%% ∀ ?v0:A_n_vec$ (set_of_vector$f(?v0) = collect$e(uxu$(?v0)))
tff(axiom538,axiom,
    ! [A__questionmark_v0: 'A_n_vec$'] : 'set_of_vector$f'(A__questionmark_v0) = 'collect$e'('uxu$'(A__questionmark_v0)) ).

%% ∀ ?v0:N_n_a_fun_fun$ ?v1:N_set$ ?v2:N_set$ (sum$a(uxv$(?v0, ?v1), ?v2) = sum$a(uxx$(?v0, ?v2), ?v1))
tff(axiom539,axiom,
    ! [A__questionmark_v0: 'N_n_a_fun_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_set$'] : 'sum$a'('uxv$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$a'('uxx$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_a_n_vec_fun_fun$ ?v1:N_set$ ?v2:N_set$ (sum$(uxy$(?v0, ?v1), ?v2) = sum$(uya$(?v0, ?v2), ?v1))
tff(axiom540,axiom,
    ! [A__questionmark_v0: 'N_n_a_n_vec_fun_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_set$'] : 'sum$'('uxy$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$'('uya$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_nat_a_fun_fun$ ?v1:Nat_set$ ?v2:N_set$ (sum$a(uyb$(?v0, ?v1), ?v2) = sum$d(uyd$(?v0, ?v2), ?v1))
tff(axiom541,axiom,
    ! [A__questionmark_v0: 'N_nat_a_fun_fun$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'N_set$'] : 'sum$a'('uyb$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$d'('uyd$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:Nat_n_a_fun_fun$ ?v1:N_set$ ?v2:Nat_set$ (sum$d(uye$(?v0, ?v1), ?v2) = sum$a(uyg$(?v0, ?v2), ?v1))
tff(axiom542,axiom,
    ! [A__questionmark_v0: 'Nat_n_a_fun_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'Nat_set$'] : 'sum$d'('uye$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$a'('uyg$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:Nat_nat_a_fun_fun$ ?v1:Nat_set$ ?v2:Nat_set$ (sum$d(uyh$(?v0, ?v1), ?v2) = sum$d(uyj$(?v0, ?v2), ?v1))
tff(axiom543,axiom,
    ! [A__questionmark_v0: 'Nat_nat_a_fun_fun$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'Nat_set$'] : 'sum$d'('uyh$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$d'('uyj$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_a_set_fun_fun$ ?v1:N_set$ ?v2:N_set$ (sum$e(uyk$(?v0, ?v1), ?v2) = sum$e(uym$(?v0, ?v2), ?v1))
tff(axiom544,axiom,
    ! [A__questionmark_v0: 'N_n_a_set_fun_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_set$'] : 'sum$e'('uyk$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$e'('uym$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_n_fun_a_fun_fun$ ?v1:N_n_fun_set$ ?v2:N_set$ (sum$a(uyn$(?v0, ?v1), ?v2) = sum$c(uyp$(?v0, ?v2), ?v1))
tff(axiom545,axiom,
    ! [A__questionmark_v0: 'N_n_n_fun_a_fun_fun$',A__questionmark_v1: 'N_n_fun_set$',A__questionmark_v2: 'N_set$'] : 'sum$a'('uyn$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$c'('uyp$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:Nat_n_n_fun_a_fun_fun$ ?v1:N_n_fun_set$ ?v2:Nat_set$ (sum$d(uyq$(?v0, ?v1), ?v2) = sum$c(uys$(?v0, ?v2), ?v1))
tff(axiom546,axiom,
    ! [A__questionmark_v0: 'Nat_n_n_fun_a_fun_fun$',A__questionmark_v1: 'N_n_fun_set$',A__questionmark_v2: 'Nat_set$'] : 'sum$d'('uyq$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$c'('uys$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_fun_n_a_fun_fun$ ?v1:N_set$ ?v2:N_n_fun_set$ (sum$c(uyt$(?v0, ?v1), ?v2) = sum$a(uyv$(?v0, ?v2), ?v1))
tff(axiom547,axiom,
    ! [A__questionmark_v0: 'N_n_fun_n_a_fun_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_n_fun_set$'] : 'sum$c'('uyt$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$a'('uyv$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_n_fun_nat_a_fun_fun$ ?v1:Nat_set$ ?v2:N_n_fun_set$ (sum$c(uyw$(?v0, ?v1), ?v2) = sum$d(uyy$(?v0, ?v2), ?v1))
tff(axiom548,axiom,
    ! [A__questionmark_v0: 'N_n_fun_nat_a_fun_fun$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'N_n_fun_set$'] : 'sum$c'('uyw$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'sum$d'('uyy$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:N_a_n_vec_fun$ (fun_app$r(top$p, ?v0) = member$c(?v0, top$c))
tff(axiom549,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$'] :
      ( 'fun_app$r'('top$p',A__questionmark_v0)
    <=> 'member$c'(A__questionmark_v0,'top$c') ) ).

%% ∀ ?v0:N_a_fun$ (fun_app$(top$q, ?v0) = member$e(?v0, top$d))
tff(axiom550,axiom,
    ! [A__questionmark_v0: 'N_a_fun$'] :
      ( 'fun_app$'('top$q',A__questionmark_v0)
    <=> 'member$e'(A__questionmark_v0,'top$d') ) ).

%% ∀ ?v0:A$ (fun_app$u(top$r, ?v0) = member$g(?v0, top$f))
tff(axiom551,axiom,
    ! [A__questionmark_v0: 'A$'] :
      ( 'fun_app$u'('top$r',A__questionmark_v0)
    <=> 'member$g'(A__questionmark_v0,'top$f') ) ).

%% ∀ ?v0:Nat$ (fun_app$m(top$g, ?v0) = member$a(?v0, top$e))
tff(axiom552,axiom,
    ! [A__questionmark_v0: 'Nat$'] :
      ( 'fun_app$m'('top$g',A__questionmark_v0)
    <=> 'member$a'(A__questionmark_v0,'top$e') ) ).

%% ∀ ?v0:N$ (fun_app$t(top$i, ?v0) = member$f(?v0, top$))
tff(axiom553,axiom,
    ! [A__questionmark_v0: 'N$'] :
      ( 'fun_app$t'('top$i',A__questionmark_v0)
    <=> 'member$f'(A__questionmark_v0,'top$') ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_a_fun$ (is_basis$(set_of_vector$(?v0)) ⇒ (sum$l(uvu$(?v1), set_of_vector$(?v0)) = sum$(uyz$(?v0, ?v1), top$)))
tff(axiom554,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_a_fun$'] :
      ( 'is_basis$'('set_of_vector$'(A__questionmark_v0))
     => ( 'sum$l'('uvu$'(A__questionmark_v1),'set_of_vector$'(A__questionmark_v0)) = 'sum$'('uyz$'(A__questionmark_v0,A__questionmark_v1),'top$') ) ) ).

%% ∀ ?v0:Nat_n_vec$ ?v1:Nat_n_vec_n_vec$ ?v2:N$ (fun_app$h(vec_nth$d(vector_matrix_mult$(?v0, ?v1)), ?v2) = sum$k(uza$(?v0, ?v1, ?v2), top$))
tff(axiom555,axiom,
    ! [A__questionmark_v0: 'Nat_n_vec$',A__questionmark_v1: 'Nat_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$h'('vec_nth$d'('vector_matrix_mult$'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$k'('uza$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),'top$') ).

%% ∀ ?v0:A_n_n_fun_vec$ ?v1:A_n_vec_n_n_fun_vec$ ?v2:N$ (fun_app$d(vec_nth$a(vector_matrix_mult$a(?v0, ?v1)), ?v2) = sum$c(fun_app$aj(uzb$(?v0, ?v1), ?v2), top$j))
tff(axiom556,axiom,
    ! [A__questionmark_v0: 'A_n_n_fun_vec$',A__questionmark_v1: 'A_n_vec_n_n_fun_vec$',A__questionmark_v2: 'N$'] : 'fun_app$d'('vec_nth$a'('vector_matrix_mult$a'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$c'('fun_app$aj'('uzb$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),'top$j') ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec_n_vec$ ?v2:N$ (fun_app$f(vec_nth$b(vector_matrix_mult$b(?v0, ?v1)), ?v2) = sum$b(uzc$(?v0, ?v1, ?v2), top$))
tff(axiom557,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$f'('vec_nth$b'('vector_matrix_mult$b'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$b'('uzc$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),'top$') ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec$ ?v2:N$ (fun_app$a(vec_nth$(vector_matrix_mult$c(?v0, ?v1)), ?v2) = sum$(fun_app$z(uzd$(?v0, ?v1), ?v2), top$))
tff(axiom558,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vec_nth$'('vector_matrix_mult$c'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$'('fun_app$z'('uzd$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),'top$') ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ (fun_app$d(vec_nth$a(vector_matrix_mult$d(?v0, ?v1)), ?v2) = sum$a(fun_app$e(uze$(?v0, ?v1), ?v2), top$))
tff(axiom559,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$d'('vec_nth$a'('vector_matrix_mult$d'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$a'('fun_app$e'('uze$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),'top$') ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec_n_vec$ ?v1:N$ ?v2:N$ (fun_app$f(vec_nth$b(fun_app$g(transpose_row$(?v0), ?v1)), ?v2) = fun_app$f(vec_nth$b(fun_app$g(vec_nth$c(?v0), ?v2)), ?v1))
tff(axiom560,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'fun_app$f'('vec_nth$b'('fun_app$g'('transpose_row$'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$f'('vec_nth$b'('fun_app$g'('vec_nth$c'(A__questionmark_v0),A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:Nat_n_vec_n_vec$ ?v1:N$ ?v2:N$ (fun_app$h(vec_nth$d(transpose_row$a(?v0, ?v1)), ?v2) = fun_app$h(vec_nth$d(vec_nth$e(?v0, ?v2)), ?v1))
tff(axiom561,axiom,
    ! [A__questionmark_v0: 'Nat_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'fun_app$h'('vec_nth$d'('transpose_row$a'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'fun_app$h'('vec_nth$d'('vec_nth$e'(A__questionmark_v0,A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ ?v1:N$ ?v2:N$ (fun_app$a(vec_nth$(fun_app$f(transpose_row$b(?v0), ?v1)), ?v2) = fun_app$a(vec_nth$(fun_app$f(vec_nth$b(?v0), ?v2)), ?v1))
tff(axiom562,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vec_nth$'('fun_app$f'('transpose_row$b'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$a'('vec_nth$'('fun_app$f'('vec_nth$b'(A__questionmark_v0),A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ (fun_app$d(vec_nth$a(fun_app$a(transpose_row$c(?v0), ?v1)), ?v2) = fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v2)), ?v1))
tff(axiom563,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'fun_app$d'('vec_nth$a'('fun_app$a'('transpose_row$c'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec$ ?v2:N$ (fun_app$f(mat_mult_row$(?v0, ?v1), ?v2) = vec_lambda$a(fun_app$z(uzf$(?v0, ?v1), ?v2)))
tff(axiom564,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$f'('mat_mult_row$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'vec_lambda$a'('fun_app$z'('uzf$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ (fun_app$a(mat_mult_row$a(?v0, ?v1), ?v2) = vec_lambda$(fun_app$e(uzg$(?v0, ?v1), ?v2)))
tff(axiom565,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$a'('mat_mult_row$a'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'vec_lambda$'('fun_app$e'('uzg$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ ?v1:N$ ?v2:N$ (fun_app$f(vec_nth$b(fun_app$g(columnvector_row$(?v0), ?v1)), ?v2) = fun_app$f(vec_nth$b(?v0), ?v1))
tff(axiom566,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'fun_app$f'('vec_nth$b'('fun_app$g'('columnvector_row$'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$f'('vec_nth$b'(A__questionmark_v0),A__questionmark_v1) ).

%% ∀ ?v0:Nat_n_vec$ ?v1:N$ ?v2:N$ (fun_app$h(vec_nth$d(columnvector_row$a(?v0, ?v1)), ?v2) = fun_app$h(vec_nth$d(?v0), ?v1))
tff(axiom567,axiom,
    ! [A__questionmark_v0: 'Nat_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'fun_app$h'('vec_nth$d'('columnvector_row$a'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'fun_app$h'('vec_nth$d'(A__questionmark_v0),A__questionmark_v1) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ (fun_app$a(vec_nth$(fun_app$f(columnvector_row$b(?v0), ?v1)), ?v2) = fun_app$a(vec_nth$(?v0), ?v1))
tff(axiom568,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vec_nth$'('fun_app$f'('columnvector_row$b'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v1) ).

%% ∀ ?v0:A_n_vec$ ?v1:N$ ?v2:N$ (fun_app$d(vec_nth$a(fun_app$a(columnvector_row$c(?v0), ?v1)), ?v2) = fun_app$d(vec_nth$a(?v0), ?v1))
tff(axiom569,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'fun_app$d'('vec_nth$a'('fun_app$a'('columnvector_row$c'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$d'('vec_nth$a'(A__questionmark_v0),A__questionmark_v1) ).

%% ∀ ?v0:Nat_n_vec_n_vec$ ?v1:Nat_n_vec$ ?v2:N$ (fun_app$h(vec_nth$d(matrix_vector_mult$a(?v0, ?v1)), ?v2) = sum$k(uzh$(?v0, ?v1, ?v2), top$))
tff(axiom570,axiom,
    ! [A__questionmark_v0: 'Nat_n_vec_n_vec$',A__questionmark_v1: 'Nat_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$h'('vec_nth$d'('matrix_vector_mult$a'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$k'('uzh$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),'top$') ).

%% ∀ ?v0:A_n_n_fun_vec_n_vec$ ?v1:A_n_n_fun_vec$ ?v2:N$ (fun_app$d(vec_nth$a(matrix_vector_mult$b(?v0, ?v1)), ?v2) = sum$c(fun_app$aj(uzi$(?v0, ?v1), ?v2), top$j))
tff(axiom571,axiom,
    ! [A__questionmark_v0: 'A_n_n_fun_vec_n_vec$',A__questionmark_v1: 'A_n_n_fun_vec$',A__questionmark_v2: 'N$'] : 'fun_app$d'('vec_nth$a'('matrix_vector_mult$b'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$c'('fun_app$aj'('uzi$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),'top$j') ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec$ ?v2:N$ (fun_app$f(vec_nth$b(matrix_vector_mult$c(?v0, ?v1)), ?v2) = sum$b(uzj$(?v0, ?v1, ?v2), top$))
tff(axiom572,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$f'('vec_nth$b'('matrix_vector_mult$c'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$b'('uzj$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),'top$') ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ (fun_app$a(vec_nth$(matrix_vector_mult$d(?v0, ?v1)), ?v2) = sum$(fun_app$z(uzk$(?v0, ?v1), ?v2), top$))
tff(axiom573,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vec_nth$'('matrix_vector_mult$d'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$'('fun_app$z'('uzk$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),'top$') ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec$ ?v2:N$ (fun_app$d(vec_nth$a(fun_app$b(matrix_vector_mult$(?v0), ?v1)), ?v2) = sum$a(fun_app$e(uzl$(?v0, ?v1), ?v2), top$))
tff(axiom574,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$d'('vec_nth$a'('fun_app$b'('matrix_vector_mult$'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'sum$a'('fun_app$e'('uzl$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),'top$') ).

%% ∀ ?v0:Bool ?v1:Nat$ ((?v0 ∧ fun_app$m(top$g, ?v1)) = ?v0)
tff(axiom575,axiom,
    ! [A__questionmark_v0: tlbool,A__questionmark_v1: 'Nat$'] :
      ( ( ( A__questionmark_v0 = tltrue )
        & 'fun_app$m'('top$g',A__questionmark_v1) )
    <=> ( A__questionmark_v0 = tltrue ) ) ).

%% ∀ ?v0:Bool ?v1:N$ ((?v0 ∧ fun_app$t(top$i, ?v1)) = ?v0)
tff(axiom576,axiom,
    ! [A__questionmark_v0: tlbool,A__questionmark_v1: 'N$'] :
      ( ( ( A__questionmark_v0 = tltrue )
        & 'fun_app$t'('top$i',A__questionmark_v1) )
    <=> ( A__questionmark_v0 = tltrue ) ) ).

%% ∀ ?v0:N_nat_fun$ ?v1:N$ (fun_app$h(vec_nth$d(vec_lambda$b(?v0)), ?v1) = fun_app$h(?v0, ?v1))
tff(axiom577,axiom,
    ! [A__questionmark_v0: 'N_nat_fun$',A__questionmark_v1: 'N$'] : 'fun_app$h'('vec_nth$d'('vec_lambda$b'(A__questionmark_v0)),A__questionmark_v1) = 'fun_app$h'(A__questionmark_v0,A__questionmark_v1) ).

%% ∀ ?v0:N_a_n_vec_n_vec_fun$ ?v1:N$ (fun_app$f(vec_nth$b(vec_lambda$c(?v0)), ?v1) = fun_app$f(?v0, ?v1))
tff(axiom578,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_n_vec_fun$',A__questionmark_v1: 'N$'] : 'fun_app$f'('vec_nth$b'('vec_lambda$c'(A__questionmark_v0)),A__questionmark_v1) = 'fun_app$f'(A__questionmark_v0,A__questionmark_v1) ).

%% ∀ ?v0:N_a_n_vec_fun$ ?v1:N$ (fun_app$a(vec_nth$(vec_lambda$a(?v0)), ?v1) = fun_app$a(?v0, ?v1))
tff(axiom579,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$',A__questionmark_v1: 'N$'] : 'fun_app$a'('vec_nth$'('vec_lambda$a'(A__questionmark_v0)),A__questionmark_v1) = 'fun_app$a'(A__questionmark_v0,A__questionmark_v1) ).

%% ∀ ?v0:N_a_fun$ ?v1:N$ (fun_app$d(vec_nth$a(vec_lambda$(?v0)), ?v1) = fun_app$d(?v0, ?v1))
tff(axiom580,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N$'] : 'fun_app$d'('vec_nth$a'('vec_lambda$'(A__questionmark_v0)),A__questionmark_v1) = 'fun_app$d'(A__questionmark_v0,A__questionmark_v1) ).

%% ∀ ?v0:Nat_n_vec$ (vec_lambda$b(vec_nth$d(?v0)) = ?v0)
tff(axiom581,axiom,
    ! [A__questionmark_v0: 'Nat_n_vec$'] : 'vec_lambda$b'('vec_nth$d'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ (vec_lambda$c(vec_nth$b(?v0)) = ?v0)
tff(axiom582,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$'] : 'vec_lambda$c'('vec_nth$b'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:A_n_vec_n_vec$ (vec_lambda$a(vec_nth$(?v0)) = ?v0)
tff(axiom583,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$'] : 'vec_lambda$a'('vec_nth$'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:A_n_vec$ (vec_lambda$(vec_nth$a(?v0)) = ?v0)
tff(axiom584,axiom,
    ! [A__questionmark_v0: 'A_n_vec$'] : 'vec_lambda$'('vec_nth$a'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:A$ ?v1:N_a_n_vec_fun$ ?v2:N$ (fun_app$d(comp$(uzm$(?v0), ?v1), ?v2) = ?v0)
tff(axiom585,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N$'] : 'fun_app$d'('comp$'('uzm$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = A__questionmark_v0 ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec_a_n_vec_fun$ ?v2:A_n_vec$ (fun_app$b(comp$a(uzn$(?v0), ?v1), ?v2) = ?v0)
tff(axiom586,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec_a_n_vec_fun$',A__questionmark_v2: 'A_n_vec$'] : 'fun_app$b'('comp$a'('uzn$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = A__questionmark_v0 ).

%% ∀ ?v0:A_n_vec$ ?v1:N_a_fun$ ?v2:N$ (fun_app$a(comp$b(uzo$(?v0), ?v1), ?v2) = ?v0)
tff(axiom587,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N$'] : 'fun_app$a'('comp$b'('uzo$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = A__questionmark_v0 ).

%% ∀ ?v0:A$ ?v1:N_a_fun$ ?v2:N$ (fun_app$d(comp$c(uzp$(?v0), ?v1), ?v2) = ?v0)
tff(axiom588,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N$'] : 'fun_app$d'('comp$c'('uzp$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = A__questionmark_v0 ).

%% ∀ ?v0:A_n_vec$ ?v1:N_a_n_vec_fun$ ?v2:N$ (fun_app$a(comp$d(uzn$(?v0), ?v1), ?v2) = ?v0)
tff(axiom589,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N$'] : 'fun_app$a'('comp$d'('uzn$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = A__questionmark_v0 ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec$ ((?v0 = ?v1) = ∀ ?v2:A_n_vec_n_vec$ (matrix_vector_mult$d(?v0, ?v2) = matrix_vector_mult$d(?v1, ?v2)))
tff(axiom590,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$'] :
      ( ( A__questionmark_v0 = A__questionmark_v1 )
    <=> ! [A__questionmark_v2: 'A_n_vec_n_vec$'] : 'matrix_vector_mult$d'(A__questionmark_v0,A__questionmark_v2) = 'matrix_vector_mult$d'(A__questionmark_v1,A__questionmark_v2) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A$ ?v2:A_n_vec$ (fun_app$b(matrix_vector_mult$(?v0), fun_app$b(fun_app$c(vector_scalar_mult$, ?v1), ?v2)) = fun_app$b(fun_app$c(vector_scalar_mult$, ?v1), fun_app$b(matrix_vector_mult$(?v0), ?v2)))
tff(axiom591,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A_n_vec$'] : 'fun_app$b'('matrix_vector_mult$'(A__questionmark_v0),'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v1),A__questionmark_v2)) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v1),'fun_app$b'('matrix_vector_mult$'(A__questionmark_v0),A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A$ ?v2:A_n_vec$ (fun_app$b(matrix_vector_mult$(?v0), fun_app$b(fun_app$c(vector_scalar_mult$, ?v1), ?v2)) = fun_app$b(fun_app$c(vector_scalar_mult$, ?v1), fun_app$b(matrix_vector_mult$(?v0), ?v2)))
tff(axiom592,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A_n_vec$'] : 'fun_app$b'('matrix_vector_mult$'(A__questionmark_v0),'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v1),A__questionmark_v2)) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v1),'fun_app$b'('matrix_vector_mult$'(A__questionmark_v0),A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_n_vec$ (vec_lambda$a(vec_nth$(?v0)) = ?v0)
tff(axiom593,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$'] : 'vec_lambda$a'('vec_nth$'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:A_n_vec$ (vec_lambda$(vec_nth$a(?v0)) = ?v0)
tff(axiom594,axiom,
    ! [A__questionmark_v0: 'A_n_vec$'] : 'vec_lambda$'('vec_nth$a'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N_a_n_vec_fun$ (∀ ?v2:N$ (fun_app$a(vec_nth$(?v0), ?v2) = fun_app$a(?v1, ?v2)) = (vec_lambda$a(?v1) = ?v0))
tff(axiom595,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N_a_n_vec_fun$'] :
      ( ! [A__questionmark_v2: 'N$'] : 'fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v2) = 'fun_app$a'(A__questionmark_v1,A__questionmark_v2)
    <=> ( 'vec_lambda$a'(A__questionmark_v1) = A__questionmark_v0 ) ) ).

%% ∀ ?v0:A_n_vec$ ?v1:N_a_fun$ (∀ ?v2:N$ (fun_app$d(vec_nth$a(?v0), ?v2) = fun_app$d(?v1, ?v2)) = (vec_lambda$(?v1) = ?v0))
tff(axiom596,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'N_a_fun$'] :
      ( ! [A__questionmark_v2: 'N$'] : 'fun_app$d'('vec_nth$a'(A__questionmark_v0),A__questionmark_v2) = 'fun_app$d'(A__questionmark_v1,A__questionmark_v2)
    <=> ( 'vec_lambda$'(A__questionmark_v1) = A__questionmark_v0 ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N_a_n_vec_fun$ ?v2:N_set$ (fun_app$b(matrix_vector_mult$(?v0), sum$(?v1, ?v2)) = sum$(uzq$(?v0, ?v1), ?v2))
tff(axiom597,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N_set$'] : 'fun_app$b'('matrix_vector_mult$'(A__questionmark_v0),'sum$'(A__questionmark_v1,A__questionmark_v2)) = 'sum$'('uzq$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) ).

%% ∀ ?v0:A$ ?v1:A_n_vec$ ?v2:A_n_vec_n_vec$ (vector_matrix_mult$d(fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), ?v1), ?v2) = fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), vector_matrix_mult$d(?v1, ?v2)))
tff(axiom598,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'A_n_vec_n_vec$'] : 'vector_matrix_mult$d'('fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),'vector_matrix_mult$d'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ (fun_app$a(transpose_row$c(?v0), ?v1) = vec_lambda$(fun_app$e(uzr$(?v0), ?v1)))
tff(axiom599,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$'] : 'fun_app$a'('transpose_row$c'(A__questionmark_v0),A__questionmark_v1) = 'vec_lambda$'('fun_app$e'('uzr$'(A__questionmark_v0),A__questionmark_v1)) ).

%% ∀ ?v0:N_a_n_vec_fun$ (member$c(?v0, top$c) ⇒ (vec_nth$(vec_lambda$a(?v0)) = ?v0))
tff(axiom600,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$'] :
      ( 'member$c'(A__questionmark_v0,'top$c')
     => ( 'vec_nth$'('vec_lambda$a'(A__questionmark_v0)) = A__questionmark_v0 ) ) ).

%% ∀ ?v0:N_a_fun$ (member$e(?v0, top$d) ⇒ (vec_nth$a(vec_lambda$(?v0)) = ?v0))
tff(axiom601,axiom,
    ! [A__questionmark_v0: 'N_a_fun$'] :
      ( 'member$e'(A__questionmark_v0,'top$d')
     => ( 'vec_nth$a'('vec_lambda$'(A__questionmark_v0)) = A__questionmark_v0 ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec$ (fun_app$b(matrix_vector_mult$(?v0), ?v1) = vec_lambda$(uzs$(?v0, ?v1)))
tff(axiom602,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec$'] : 'fun_app$b'('matrix_vector_mult$'(A__questionmark_v0),A__questionmark_v1) = 'vec_lambda$'('uzs$'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec$ (vector_matrix_mult$c(?v0, ?v1) = vec_lambda$a(uzt$(?v0, ?v1)))
tff(axiom603,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$'] : 'vector_matrix_mult$c'(A__questionmark_v0,A__questionmark_v1) = 'vec_lambda$a'('uzt$'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec_n_vec$ (vector_matrix_mult$d(?v0, ?v1) = vec_lambda$(uzu$(?v0, ?v1)))
tff(axiom604,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$'] : 'vector_matrix_mult$d'(A__questionmark_v0,A__questionmark_v1) = 'vec_lambda$'('uzu$'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec_n_vec$ (vector_scalar_mult$a(?v0, ?v1) = vec_lambda$a(uzv$(?v0, ?v1)))
tff(axiom605,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$'] : 'vector_scalar_mult$a'(A__questionmark_v0,A__questionmark_v1) = 'vec_lambda$a'('uzv$'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:A$ ?v1:A_n_vec$ (fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), ?v1) = vec_lambda$(uzw$(?v0, ?v1)))
tff(axiom606,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A_n_vec$'] : 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),A__questionmark_v1) = 'vec_lambda$'('uzw$'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:N_a_n_vec_n_vec_fun$ ?v1:N_set$ (sum$b(?v0, ?v1) = vec_lambda$a(uzx$(?v0, ?v1)))
tff(axiom607,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_n_vec_fun$',A__questionmark_v1: 'N_set$'] : 'sum$b'(A__questionmark_v0,A__questionmark_v1) = 'vec_lambda$a'('uzx$'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:N_a_n_vec_fun$ ?v1:N_set$ (sum$(?v0, ?v1) = vec_lambda$(uzy$(?v0, ?v1)))
tff(axiom608,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$',A__questionmark_v1: 'N_set$'] : 'sum$'(A__questionmark_v0,A__questionmark_v1) = 'vec_lambda$'('uzy$'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ (times$a(?v0, ?v1) = vec_lambda$a(uwj$(?v0, ?v1)))
tff(axiom609,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$'] : 'times$a'(A__questionmark_v0,A__questionmark_v1) = 'vec_lambda$a'('uwj$'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec$ (fun_app$b(times$b(?v0), ?v1) = vec_lambda$(uwk$(?v0, ?v1)))
tff(axiom610,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec$'] : 'fun_app$b'('times$b'(A__questionmark_v0),A__questionmark_v1) = 'vec_lambda$'('uwk$'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec$ (fun_app$b(coord$(?v0), ?v1) = vec_lambda$(the$(uzz$(?v0, ?v1))))
tff(axiom611,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec$'] : 'fun_app$b'('coord$'(A__questionmark_v0),A__questionmark_v1) = 'vec_lambda$'('the$'('uzz$'(A__questionmark_v0,A__questionmark_v1))) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:A_n_vec_a_n_vec_fun$ (matrix$(?v0, ?v1, ?v2) = vec_lambda$a(vab$(?v0, ?v1, ?v2)))
tff(axiom612,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'A_n_vec_a_n_vec_fun$'] : 'matrix$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2) = 'vec_lambda$a'('vab$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec$ (fun_app$b(matrix_vector_mult$(?v0), ?v1) = sum$(vac$(?v0, ?v1), top$))
tff(axiom613,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec$'] : 'fun_app$b'('matrix_vector_mult$'(A__questionmark_v0),A__questionmark_v1) = 'sum$'('vac$'(A__questionmark_v0,A__questionmark_v1),'top$') ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec$ (fun_app$b(matrix_vector_mult$(?v0), ?v1) = sum$(vad$(?v0, ?v1), top$))
tff(axiom614,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec$'] : 'fun_app$b'('matrix_vector_mult$'(A__questionmark_v0),A__questionmark_v1) = 'sum$'('vad$'(A__questionmark_v0,A__questionmark_v1),'top$') ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:A$ ?v3:N$ (fun_app$a(mult_row_row$(?v0, ?v1, ?v2), ?v3) = vec_lambda$(fun_app$e(vae$(?v0, ?v1, ?v2), ?v3)))
tff(axiom615,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'A$',A__questionmark_v3: 'N$'] : 'fun_app$a'('mult_row_row$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'vec_lambda$'('fun_app$e'('vae$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:A$ ?v3:N$ (fun_app$a(mult_column_row$(?v0, ?v1, ?v2), ?v3) = vec_lambda$(fun_app$e(vaf$(?v0, ?v1, ?v2), ?v3)))
tff(axiom616,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'A$',A__questionmark_v3: 'N$'] : 'fun_app$a'('mult_column_row$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'vec_lambda$'('fun_app$e'('vaf$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_n_vec$ (vec_nth$(transpose$(?v0)) = transpose_row$c(?v0))
tff(axiom617,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$'] : 'vec_nth$'('transpose$'(A__questionmark_v0)) = 'transpose_row$c'(A__questionmark_v0) ).

%% ∀ ?v0:A_n_vec_n_vec$ (transpose$(?v0) = vec_lambda$a(vag$(?v0)))
tff(axiom618,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$'] : 'transpose$'(A__questionmark_v0) = 'vec_lambda$a'('vag$'(A__questionmark_v0)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:A$ ?v3:N$ ?v4:N$ (fun_app$d(vec_nth$a(fun_app$a(mult_column_row$(?v0, ?v1, ?v2), ?v3)), ?v4) = (if (?v4 = ?v1) fun_app$k(fun_app$l(times$, fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v3)), ?v4)), ?v2) else fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v3)), ?v4)))
tff(axiom619,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'A$',A__questionmark_v3: 'N$',A__questionmark_v4: 'N$'] :
      ( ( ( A__questionmark_v4 = A__questionmark_v1 )
       => ( 'fun_app$d'('vec_nth$a'('fun_app$a'('mult_column_row$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3)),A__questionmark_v4) = 'fun_app$k'('fun_app$l'('times$','fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v3)),A__questionmark_v4)),A__questionmark_v2) ) )
      & ( ( A__questionmark_v4 != A__questionmark_v1 )
       => ( 'fun_app$d'('vec_nth$a'('fun_app$a'('mult_column_row$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3)),A__questionmark_v4) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v3)),A__questionmark_v4) ) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:A$ ?v3:N$ ?v4:N$ (fun_app$d(vec_nth$a(fun_app$a(mult_row_row$(?v0, ?v1, ?v2), ?v3)), ?v4) = (if (?v3 = ?v1) fun_app$k(fun_app$l(times$, ?v2), fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v1)), ?v4)) else fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v3)), ?v4)))
tff(axiom620,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'A$',A__questionmark_v3: 'N$',A__questionmark_v4: 'N$'] :
      ( ( ( A__questionmark_v3 = A__questionmark_v1 )
       => ( 'fun_app$d'('vec_nth$a'('fun_app$a'('mult_row_row$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3)),A__questionmark_v4) = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v2),'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v4)) ) )
      & ( ( A__questionmark_v3 != A__questionmark_v1 )
       => ( 'fun_app$d'('vec_nth$a'('fun_app$a'('mult_row_row$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3)),A__questionmark_v4) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v3)),A__questionmark_v4) ) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec$ ?v2:A_n_vec$ ((is_basis$(set_of_vector$(?v0)) ∧ (fun_app$b(coord$(?v0), ?v1) = fun_app$b(coord$(?v0), ?v2))) ⇒ (?v1 = ?v2))
tff(axiom621,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'A_n_vec$'] :
      ( ( 'is_basis$'('set_of_vector$'(A__questionmark_v0))
        & ( 'fun_app$b'('coord$'(A__questionmark_v0),A__questionmark_v1) = 'fun_app$b'('coord$'(A__questionmark_v0),A__questionmark_v2) ) )
     => ( A__questionmark_v1 = A__questionmark_v2 ) ) ).

%% ∀ ?v0:N$ ?v1:A_n_vec_n_vec$ (column$(?v0, ?v1) = vec_lambda$(vah$(?v0, ?v1)))
tff(axiom622,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'A_n_vec_n_vec$'] : 'column$'(A__questionmark_v0,A__questionmark_v1) = 'vec_lambda$'('vah$'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ (matrix_change_of_basis$(?v0, ?v1) = vec_lambda$a(vaj$(?v0, ?v1)))
tff(axiom623,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$'] : 'matrix_change_of_basis$'(A__questionmark_v0,A__questionmark_v1) = 'vec_lambda$a'('vaj$'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:A$ (fun_app$be(mult_column$(?v0, ?v1), ?v2) = vec_lambda$a(vak$(?v0, ?v1, ?v2)))
tff(axiom624,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'A$'] : 'fun_app$be'('mult_column$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'vec_lambda$a'('vak$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ ?v3:N$ (fun_app$a(fun_app$z(interchange_columns_row$(?v0, ?v1), ?v2), ?v3) = vec_lambda$(fun_app$e(val$(?v0, ?v1, ?v2), ?v3)))
tff(axiom625,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$a'('fun_app$z'('interchange_columns_row$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'vec_lambda$'('fun_app$e'('val$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ ?v3:N$ (fun_app$a(fun_app$z(interchange_rows_row$(?v0, ?v1), ?v2), ?v3) = vec_lambda$(fun_app$e(vam$(?v0, ?v1, ?v2), ?v3)))
tff(axiom626,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$'] : 'fun_app$a'('fun_app$z'('interchange_rows_row$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3) = 'vec_lambda$'('fun_app$e'('vam$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:A$ (fun_app$be(mult_row$(?v0, ?v1), ?v2) = vec_lambda$a(van$(?v0, ?v1, ?v2)))
tff(axiom627,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'A$'] : 'fun_app$be'('mult_row$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'vec_lambda$a'('van$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ (fun_app$f(interchange_columns$(?v0, ?v1), ?v2) = vec_lambda$a(fun_app$z(vao$(?v0, ?v1), ?v2)))
tff(axiom628,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'fun_app$f'('interchange_columns$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'vec_lambda$a'('fun_app$z'('vao$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ (vec_nth$(fun_app$f(interchange_columns$(?v0, ?v1), ?v2)) = fun_app$z(interchange_columns_row$(?v0, ?v1), ?v2))
tff(axiom629,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'vec_nth$'('fun_app$f'('interchange_columns$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)) = 'fun_app$z'('interchange_columns_row$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:A$ (vec_nth$(fun_app$be(mult_row$(?v0, ?v1), ?v2)) = mult_row_row$(?v0, ?v1, ?v2))
tff(axiom630,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'A$'] : 'vec_nth$'('fun_app$be'('mult_row$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)) = 'mult_row_row$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:A$ (vec_nth$(fun_app$be(mult_column$(?v0, ?v1), ?v2)) = mult_column_row$(?v0, ?v1, ?v2))
tff(axiom631,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'A$'] : 'vec_nth$'('fun_app$be'('mult_column$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)) = 'mult_column_row$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ ?v3:N$ ?v4:N$ (fun_app$d(vec_nth$a(fun_app$a(fun_app$z(interchange_rows_row$(?v0, ?v1), ?v2), ?v3)), ?v4) = (if (?v3 = ?v1) fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v2)), ?v4) else (if (?v3 = ?v2) fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v1)), ?v4) else fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v3)), ?v4))))
tff(axiom632,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$',A__questionmark_v4: 'N$'] :
      ( ( ( A__questionmark_v3 = A__questionmark_v1 )
       => ( 'fun_app$d'('vec_nth$a'('fun_app$a'('fun_app$z'('interchange_rows_row$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3)),A__questionmark_v4) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v2)),A__questionmark_v4) ) )
      & ( ( A__questionmark_v3 != A__questionmark_v1 )
       => ( ( ( A__questionmark_v3 = A__questionmark_v2 )
           => ( 'fun_app$d'('vec_nth$a'('fun_app$a'('fun_app$z'('interchange_rows_row$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3)),A__questionmark_v4) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v4) ) )
          & ( ( A__questionmark_v3 != A__questionmark_v2 )
           => ( 'fun_app$d'('vec_nth$a'('fun_app$a'('fun_app$z'('interchange_rows_row$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3)),A__questionmark_v4) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v3)),A__questionmark_v4) ) ) ) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ ?v3:N$ ?v4:N$ (fun_app$d(vec_nth$a(fun_app$a(fun_app$z(interchange_columns_row$(?v0, ?v1), ?v2), ?v3)), ?v4) = (if (?v4 = ?v1) fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v3)), ?v2) else (if (?v4 = ?v2) fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v3)), ?v1) else fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v3)), ?v4))))
tff(axiom633,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$',A__questionmark_v3: 'N$',A__questionmark_v4: 'N$'] :
      ( ( ( A__questionmark_v4 = A__questionmark_v1 )
       => ( 'fun_app$d'('vec_nth$a'('fun_app$a'('fun_app$z'('interchange_columns_row$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3)),A__questionmark_v4) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v3)),A__questionmark_v2) ) )
      & ( ( A__questionmark_v4 != A__questionmark_v1 )
       => ( ( ( A__questionmark_v4 = A__questionmark_v2 )
           => ( 'fun_app$d'('vec_nth$a'('fun_app$a'('fun_app$z'('interchange_columns_row$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3)),A__questionmark_v4) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v3)),A__questionmark_v1) ) )
          & ( ( A__questionmark_v4 != A__questionmark_v2 )
           => ( 'fun_app$d'('vec_nth$a'('fun_app$a'('fun_app$z'('interchange_columns_row$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2),A__questionmark_v3)),A__questionmark_v4) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v3)),A__questionmark_v4) ) ) ) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ (matrix_matrix_mult$(?v0, ?v1) = vec_lambda$a(vap$(?v0, ?v1)))
tff(axiom634,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$'] : 'matrix_matrix_mult$'(A__questionmark_v0,A__questionmark_v1) = 'vec_lambda$a'('vap$'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:N$ ?v1:A_n_vec_n_vec$ ?v2:A_n_vec$ (fun_app$w(det$, vec_lambda$a(var$(?v0, ?v1, ?v2))) = fun_app$k(fun_app$l(times$, fun_app$d(vec_nth$a(?v2), ?v0)), fun_app$w(det$, ?v1)))
tff(axiom635,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'A_n_vec$'] : 'fun_app$w'('det$','vec_lambda$a'('var$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2))) = 'fun_app$k'('fun_app$l'('times$','fun_app$d'('vec_nth$a'(A__questionmark_v2),A__questionmark_v0)),'fun_app$w'('det$',A__questionmark_v1)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ (fun_app$f(interchange_rows$(?v0, ?v1), ?v2) = vec_lambda$a(fun_app$z(vas$(?v0, ?v1), ?v2)))
tff(axiom636,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'fun_app$f'('interchange_rows$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'vec_lambda$a'('fun_app$z'('vas$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:A_n_vec_a_n_vec_fun$ ?v3:A_n_vec$ ((is_basis$(set_of_vector$(?v0)) ∧ (is_basis$(set_of_vector$(?v1)) ∧ linear$(vector_scalar_mult$, vector_scalar_mult$, ?v2))) ⇒ (fun_app$b(coord$(?v1), fun_app$b(?v2, ?v3)) = fun_app$b(matrix_vector_mult$(matrix$(?v0, ?v1, ?v2)), fun_app$b(coord$(?v0), ?v3))))
tff(axiom637,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'A_n_vec_a_n_vec_fun$',A__questionmark_v3: 'A_n_vec$'] :
      ( ( 'is_basis$'('set_of_vector$'(A__questionmark_v0))
        & 'is_basis$'('set_of_vector$'(A__questionmark_v1))
        & 'linear$'('vector_scalar_mult$','vector_scalar_mult$',A__questionmark_v2) )
     => ( 'fun_app$b'('coord$'(A__questionmark_v1),'fun_app$b'(A__questionmark_v2,A__questionmark_v3)) = 'fun_app$b'('matrix_vector_mult$'('matrix$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2)),'fun_app$b'('coord$'(A__questionmark_v0),A__questionmark_v3)) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ ?v1:A_n_vec_n_vec_n_vec$ (matrix_matrix_mult$a(?v0, ?v1) = vec_lambda$c(vau$(?v0, ?v1)))
tff(axiom638,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec_n_vec$'] : 'matrix_matrix_mult$a'(A__questionmark_v0,A__questionmark_v1) = 'vec_lambda$c'('vau$'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ (matrix_matrix_mult$(?v0, ?v1) = vec_lambda$a(vaw$(?v0, ?v1)))
tff(axiom639,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$'] : 'matrix_matrix_mult$'(A__questionmark_v0,A__questionmark_v1) = 'vec_lambda$a'('vaw$'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ (fun_app$a(vec_nth$(fun_app$f(interchange_rows$(?v0, ?v1), ?v2)), ?v2) = fun_app$a(vec_nth$(?v0), ?v1))
tff(axiom640,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vec_nth$'('fun_app$f'('interchange_rows$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)),A__questionmark_v2) = 'fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v1) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ (fun_app$a(vec_nth$(fun_app$f(interchange_rows$(?v0, ?v1), ?v2)), ?v1) = fun_app$a(vec_nth$(?v0), ?v2))
tff(axiom641,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vec_nth$'('fun_app$f'('interchange_rows$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)),A__questionmark_v1) = 'fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v2) ).

%% ∀ ?v0:A_n_vec_n_vec$ linear$(vector_scalar_mult$, vector_scalar_mult$, matrix_vector_mult$(?v0))
tff(axiom642,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$'] : 'linear$'('vector_scalar_mult$','vector_scalar_mult$','matrix_vector_mult$'(A__questionmark_v0)) ).

%% ∀ ?v0:A_a_fun$ ((linear$a(times$, times$, ?v0) ∧ ∀ ?v1:A$ ((?v0 = vax$(?v1)) ⇒ false)) ⇒ false)
tff(axiom643,axiom,
    ! [A__questionmark_v0: 'A_a_fun$'] :
      ( ( 'linear$a'('times$','times$',A__questionmark_v0)
        & ! [A__questionmark_v1: 'A$'] :
            ( ( A__questionmark_v0 = 'vax$'(A__questionmark_v1) )
           => $false ) )
     => $false ) ).

%% ∀ ?v0:A_n_vec_a_fun$ ?v1:A_n_vec$ (linear$b(vector_scalar_mult$, times$, ?v0) ⇒ linear$(vector_scalar_mult$, vector_scalar_mult$, vay$(?v0, ?v1)))
tff(axiom644,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_fun$',A__questionmark_v1: 'A_n_vec$'] :
      ( 'linear$b'('vector_scalar_mult$','times$',A__questionmark_v0)
     => 'linear$'('vector_scalar_mult$','vector_scalar_mult$','vay$'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:A_n_vec_a_n_vec_fun$ ?v1:A$ ?v2:A_n_vec$ (linear$(vector_scalar_mult$, vector_scalar_mult$, ?v0) ⇒ (fun_app$b(?v0, fun_app$b(fun_app$c(vector_scalar_mult$, ?v1), ?v2)) = fun_app$b(fun_app$c(vector_scalar_mult$, ?v1), fun_app$b(?v0, ?v2))))
tff(axiom645,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_n_vec_fun$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A_n_vec$'] :
      ( 'linear$'('vector_scalar_mult$','vector_scalar_mult$',A__questionmark_v0)
     => ( 'fun_app$b'(A__questionmark_v0,'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v1),A__questionmark_v2)) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v1),'fun_app$b'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:A$ linear$a(times$, times$, fun_app$l(times$, ?v0))
tff(axiom646,axiom,
    ! [A__questionmark_v0: 'A$'] : 'linear$a'('times$','times$','fun_app$l'('times$',A__questionmark_v0)) ).

%% ∀ ?v0:A$ linear$a(times$, times$, vax$(?v0))
tff(axiom647,axiom,
    ! [A__questionmark_v0: 'A$'] : 'linear$a'('times$','times$','vax$'(A__questionmark_v0)) ).

%% linear$a(times$, times$, vaz$)
tff(axiom648,axiom,
    'linear$a'('times$','times$','vaz$') ).

%% ∀ ?v0:A_n_vec_a_n_vec_fun$ ?v1:A$ (linear$(vector_scalar_mult$, vector_scalar_mult$, ?v0) ⇒ linear$(vector_scalar_mult$, vector_scalar_mult$, vba$(?v0, ?v1)))
tff(axiom649,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_n_vec_fun$',A__questionmark_v1: 'A$'] :
      ( 'linear$'('vector_scalar_mult$','vector_scalar_mult$',A__questionmark_v0)
     => 'linear$'('vector_scalar_mult$','vector_scalar_mult$','vba$'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:A$ linear$(vector_scalar_mult$, vector_scalar_mult$, fun_app$c(vector_scalar_mult$, ?v0))
tff(axiom650,axiom,
    ! [A__questionmark_v0: 'A$'] : 'linear$'('vector_scalar_mult$','vector_scalar_mult$','fun_app$c'('vector_scalar_mult$',A__questionmark_v0)) ).

%% linear$(vector_scalar_mult$, vector_scalar_mult$, vbb$)
tff(axiom651,axiom,
    'linear$'('vector_scalar_mult$','vector_scalar_mult$','vbb$') ).

%% ∀ ?v0:A_a_n_vec_fun$ ((linear$c(times$, vector_scalar_mult$, ?v0) ∧ ∀ ?v1:A_n_vec$ ((?v0 = vbc$(?v1)) ⇒ false)) ⇒ false)
tff(axiom652,axiom,
    ! [A__questionmark_v0: 'A_a_n_vec_fun$'] :
      ( ( 'linear$c'('times$','vector_scalar_mult$',A__questionmark_v0)
        & ! [A__questionmark_v1: 'A_n_vec$'] :
            ( ( A__questionmark_v0 = 'vbc$'(A__questionmark_v1) )
           => $false ) )
     => $false ) ).

%% ∀ ?v0:N$ ?v1:N$ ?v2:N$ ?v3:A_n_vec_n_vec$ ((¬(?v0 = ?v1) ∧ ¬(?v2 = ?v1)) ⇒ (fun_app$a(vec_nth$(fun_app$f(interchange_rows$(?v3, ?v0), ?v2)), ?v1) = fun_app$a(vec_nth$(?v3), ?v1)))
tff(axiom653,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$',A__questionmark_v3: 'A_n_vec_n_vec$'] :
      ( ( ( A__questionmark_v0 != A__questionmark_v1 )
        & ( A__questionmark_v2 != A__questionmark_v1 ) )
     => ( 'fun_app$a'('vec_nth$'('fun_app$f'('interchange_rows$'(A__questionmark_v3,A__questionmark_v0),A__questionmark_v2)),A__questionmark_v1) = 'fun_app$a'('vec_nth$'(A__questionmark_v3),A__questionmark_v1) ) ) ).

%% ∀ ?v0:A_n_vec$ linear$c(times$, vector_scalar_mult$, vbc$(?v0))
tff(axiom654,axiom,
    ! [A__questionmark_v0: 'A_n_vec$'] : 'linear$c'('times$','vector_scalar_mult$','vbc$'(A__questionmark_v0)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:A_n_vec_n_vec$ ?v3:A_n_vec_a_n_vec_fun$ ?v4:A_n_vec_a_n_vec_fun$ ((is_basis$(set_of_vector$(?v0)) ∧ (is_basis$(set_of_vector$(?v1)) ∧ (is_basis$(set_of_vector$(?v2)) ∧ (linear$(vector_scalar_mult$, vector_scalar_mult$, ?v3) ∧ linear$(vector_scalar_mult$, vector_scalar_mult$, ?v4))))) ⇒ (matrix$(?v0, ?v2, comp$a(?v4, ?v3)) = matrix_matrix_mult$(matrix$(?v1, ?v2, ?v4), matrix$(?v0, ?v1, ?v3))))
tff(axiom655,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'A_n_vec_n_vec$',A__questionmark_v3: 'A_n_vec_a_n_vec_fun$',A__questionmark_v4: 'A_n_vec_a_n_vec_fun$'] :
      ( ( 'is_basis$'('set_of_vector$'(A__questionmark_v0))
        & 'is_basis$'('set_of_vector$'(A__questionmark_v1))
        & 'is_basis$'('set_of_vector$'(A__questionmark_v2))
        & 'linear$'('vector_scalar_mult$','vector_scalar_mult$',A__questionmark_v3)
        & 'linear$'('vector_scalar_mult$','vector_scalar_mult$',A__questionmark_v4) )
     => ( 'matrix$'(A__questionmark_v0,A__questionmark_v2,'comp$a'(A__questionmark_v4,A__questionmark_v3)) = 'matrix_matrix_mult$'('matrix$'(A__questionmark_v1,A__questionmark_v2,A__questionmark_v4),'matrix$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v3)) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_a_n_vec_a_n_vec_fun_fun$ (∀ ?v2:N$ (member$f(?v2, ?v0) ⇒ linear$(vector_scalar_mult$, vector_scalar_mult$, fun_app$al(?v1, ?v2))) ⇒ linear$(vector_scalar_mult$, vector_scalar_mult$, vbe$(?v0, ?v1)))
tff(axiom656,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_a_n_vec_a_n_vec_fun_fun$'] :
      ( ! [A__questionmark_v2: 'N$'] :
          ( 'member$f'(A__questionmark_v2,A__questionmark_v0)
         => 'linear$'('vector_scalar_mult$','vector_scalar_mult$','fun_app$al'(A__questionmark_v1,A__questionmark_v2)) )
     => 'linear$'('vector_scalar_mult$','vector_scalar_mult$','vbe$'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:A_n_vec_a_n_vec_fun$ ?v1:N_a_n_vec_fun$ ?v2:N_set$ (linear$(vector_scalar_mult$, vector_scalar_mult$, ?v0) ⇒ (fun_app$b(?v0, sum$(?v1, ?v2)) = sum$(vbf$(?v0, ?v1), ?v2)))
tff(axiom657,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_n_vec_fun$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N_set$'] :
      ( 'linear$'('vector_scalar_mult$','vector_scalar_mult$',A__questionmark_v0)
     => ( 'fun_app$b'(A__questionmark_v0,'sum$'(A__questionmark_v1,A__questionmark_v2)) = 'sum$'('vbf$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) ) ) ).

%% ∀ ?v0:N$ ?v1:A$ ?v2:N_a_n_vec_fun$ ?v3:N_a_n_vec_fun$ (fun_app$w(det$, vec_lambda$a(vbg$(?v0, ?v1, ?v2, ?v3))) = fun_app$k(fun_app$l(times$, ?v1), fun_app$w(det$, vec_lambda$a(vbh$(?v0, ?v2, ?v3)))))
tff(axiom658,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'A$',A__questionmark_v2: 'N_a_n_vec_fun$',A__questionmark_v3: 'N_a_n_vec_fun$'] : 'fun_app$w'('det$','vec_lambda$a'('vbg$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3))) = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v1),'fun_app$w'('det$','vec_lambda$a'('vbh$'(A__questionmark_v0,A__questionmark_v2,A__questionmark_v3)))) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:A_n_vec_n_vec$ ((is_basis$(set_of_vector$(?v0)) ∧ is_basis$(set_of_vector$(?v1))) ⇒ ∃ ?v3:A_n_vec_a_n_vec_fun$ ((matrix$(?v0, ?v1, ?v3) = ?v2) ∧ linear$(vector_scalar_mult$, vector_scalar_mult$, ?v3)))
tff(axiom659,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'A_n_vec_n_vec$'] :
      ( ( 'is_basis$'('set_of_vector$'(A__questionmark_v0))
        & 'is_basis$'('set_of_vector$'(A__questionmark_v1)) )
     => ? [A__questionmark_v3: 'A_n_vec_a_n_vec_fun$'] :
          ( ( 'matrix$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v3) = A__questionmark_v2 )
          & 'linear$'('vector_scalar_mult$','vector_scalar_mult$',A__questionmark_v3) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ (is_basis$(set_of_vector$(?v0)) ⇒ linear$(vector_scalar_mult$, vector_scalar_mult$, coord$(?v0)))
tff(axiom660,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$'] :
      ( 'is_basis$'('set_of_vector$'(A__questionmark_v0))
     => 'linear$'('vector_scalar_mult$','vector_scalar_mult$','coord$'(A__questionmark_v0)) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ (vec_nth$(fun_app$f(interchange_rows$(?v0, ?v1), ?v2)) = fun_app$z(interchange_rows_row$(?v0, ?v1), ?v2))
tff(axiom661,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] : 'vec_nth$'('fun_app$f'('interchange_rows$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2)) = 'fun_app$z'('interchange_rows_row$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:A_n_vec_n_vec$ (vector_matrix_mult$d(fun_app$a(vec_nth$(?v0), ?v1), ?v2) = fun_app$a(vec_nth$(matrix_matrix_mult$(?v0, ?v2)), ?v1))
tff(axiom662,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'A_n_vec_n_vec$'] : 'vector_matrix_mult$d'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v1),A__questionmark_v2) = 'fun_app$a'('vec_nth$'('matrix_matrix_mult$'(A__questionmark_v0,A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:N$ ?v1:A_n_vec$ ?v2:A_n_vec_n_vec$ (fun_app$w(det$, vec_lambda$a(vbj$(?v0, ?v1, ?v2))) = fun_app$k(fun_app$l(times$, fun_app$d(vec_nth$a(?v1), ?v0)), fun_app$w(det$, ?v2)))
tff(axiom663,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'A_n_vec_n_vec$'] : 'fun_app$w'('det$','vec_lambda$a'('vbj$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2))) = 'fun_app$k'('fun_app$l'('times$','fun_app$d'('vec_nth$a'(A__questionmark_v1),A__questionmark_v0)),'fun_app$w'('det$',A__questionmark_v2)) ).

%% ∀ ?v0:N$ ?v1:A_n_vec_n_vec$ (row$(?v0, ?v1) = vec_lambda$(vec_nth$a(fun_app$a(vec_nth$(?v1), ?v0))))
tff(axiom664,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'A_n_vec_n_vec$'] : 'row$'(A__questionmark_v0,A__questionmark_v1) = 'vec_lambda$'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v0))) ).

%% ∀ ?v0:A_n_vec_a_n_vec_fun$ (linear$(vector_scalar_mult$, vector_scalar_mult$, ?v0) ⇒ (matrix_vector_mult$(matrix$a(?v0)) = ?v0))
tff(axiom665,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_n_vec_fun$'] :
      ( 'linear$'('vector_scalar_mult$','vector_scalar_mult$',A__questionmark_v0)
     => ( 'matrix_vector_mult$'('matrix$a'(A__questionmark_v0)) = A__questionmark_v0 ) ) ).

%% ∀ ?v0:A_n_vec_a_n_vec_fun$ ?v1:A_n_vec_a_n_vec_fun$ ((linear$(vector_scalar_mult$, vector_scalar_mult$, ?v0) ∧ linear$(vector_scalar_mult$, vector_scalar_mult$, ?v1)) ⇒ (matrix$a(comp$a(?v1, ?v0)) = matrix_matrix_mult$(matrix$a(?v1), matrix$a(?v0))))
tff(axiom666,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_n_vec_fun$',A__questionmark_v1: 'A_n_vec_a_n_vec_fun$'] :
      ( ( 'linear$'('vector_scalar_mult$','vector_scalar_mult$',A__questionmark_v0)
        & 'linear$'('vector_scalar_mult$','vector_scalar_mult$',A__questionmark_v1) )
     => ( 'matrix$a'('comp$a'(A__questionmark_v1,A__questionmark_v0)) = 'matrix_matrix_mult$'('matrix$a'(A__questionmark_v1),'matrix$a'(A__questionmark_v0)) ) ) ).

%% ∀ ?v0:A$ ?v1:A_n_vec_n_vec$ (matrix_scalar_mult$(?v0, ?v1) = vec_lambda$a(vbl$(?v0, ?v1)))
tff(axiom667,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A_n_vec_n_vec$'] : 'matrix_scalar_mult$'(A__questionmark_v0,A__questionmark_v1) = 'vec_lambda$a'('vbl$'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:N_set$ ?v1:N_n_a_n_vec_fun_fun$ (finite$(?v0) ⇒ (fun_app$w(det$, vec_lambda$a(vbm$(?v0, ?v1))) = sum$c(vbo$(?v1), collect$f(vbp$(?v0)))))
tff(axiom668,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_n_a_n_vec_fun_fun$'] :
      ( 'finite$'(A__questionmark_v0)
     => ( 'fun_app$w'('det$','vec_lambda$a'('vbm$'(A__questionmark_v0,A__questionmark_v1))) = 'sum$c'('vbo$'(A__questionmark_v1),'collect$f'('vbp$'(A__questionmark_v0))) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ finite$a(set_of_vector$(?v0))
tff(axiom669,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$'] : 'finite$a'('set_of_vector$'(A__questionmark_v0)) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_set$ ((finite$b(?v0) ∧ finite$b(?v1)) ⇒ finite$b(times$k(?v0, ?v1)))
tff(axiom670,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_set$'] :
      ( ( 'finite$b'(A__questionmark_v0)
        & 'finite$b'(A__questionmark_v1) )
     => 'finite$b'('times$k'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:A_n_vec_set$ (is_basis$(?v0) ⇒ finite$a(?v0))
tff(axiom671,axiom,
    ! [A__questionmark_v0: 'A_n_vec_set$'] :
      ( 'is_basis$'(A__questionmark_v0)
     => 'finite$a'(A__questionmark_v0) ) ).

%% ∀ ?v0:Nat_set$ ?v1:N_set$ ?v2:Nat_n_a_n_vec_fun_fun$ ?v3:Nat_n_bool_fun_fun$ ((finite$b(?v0) ∧ finite$(?v1)) ⇒ (sum$g(vbr$(?v1, ?v2, ?v3), ?v0) = sum$(vbu$(?v0, ?v2, ?v3), ?v1)))
tff(axiom672,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'Nat_n_a_n_vec_fun_fun$',A__questionmark_v3: 'Nat_n_bool_fun_fun$'] :
      ( ( 'finite$b'(A__questionmark_v0)
        & 'finite$'(A__questionmark_v1) )
     => ( 'sum$g'('vbr$'(A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v0) = 'sum$'('vbu$'(A__questionmark_v0,A__questionmark_v2,A__questionmark_v3),A__questionmark_v1) ) ) ).

%% ∀ ?v0:Nat_set$ ?v1:N_set$ ?v2:Nat_n_a_fun_fun$ ?v3:Nat_n_bool_fun_fun$ ((finite$b(?v0) ∧ finite$(?v1)) ⇒ (sum$d(vbv$(?v1, ?v2, ?v3), ?v0) = sum$a(vbw$(?v0, ?v2, ?v3), ?v1)))
tff(axiom673,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'Nat_n_a_fun_fun$',A__questionmark_v3: 'Nat_n_bool_fun_fun$'] :
      ( ( 'finite$b'(A__questionmark_v0)
        & 'finite$'(A__questionmark_v1) )
     => ( 'sum$d'('vbv$'(A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v0) = 'sum$a'('vbw$'(A__questionmark_v0,A__questionmark_v2,A__questionmark_v3),A__questionmark_v1) ) ) ).

%% ∀ ?v0:N_set$ ?v1:Nat_set$ ?v2:N_nat_a_n_vec_fun_fun$ ?v3:N_nat_bool_fun_fun$ ((finite$(?v0) ∧ finite$b(?v1)) ⇒ (sum$(vby$(?v1, ?v2, ?v3), ?v0) = sum$g(vcb$(?v0, ?v2, ?v3), ?v1)))
tff(axiom674,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'N_nat_a_n_vec_fun_fun$',A__questionmark_v3: 'N_nat_bool_fun_fun$'] :
      ( ( 'finite$'(A__questionmark_v0)
        & 'finite$b'(A__questionmark_v1) )
     => ( 'sum$'('vby$'(A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v0) = 'sum$g'('vcb$'(A__questionmark_v0,A__questionmark_v2,A__questionmark_v3),A__questionmark_v1) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_set$ ?v2:N_n_a_n_vec_fun_fun$ ?v3:N_n_bool_fun_fun$ ((finite$(?v0) ∧ finite$(?v1)) ⇒ (sum$(vcd$(?v1, ?v2, ?v3), ?v0) = sum$(vcf$(?v0, ?v2, ?v3), ?v1)))
tff(axiom675,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_n_a_n_vec_fun_fun$',A__questionmark_v3: 'N_n_bool_fun_fun$'] :
      ( ( 'finite$'(A__questionmark_v0)
        & 'finite$'(A__questionmark_v1) )
     => ( 'sum$'('vcd$'(A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v0) = 'sum$'('vcf$'(A__questionmark_v0,A__questionmark_v2,A__questionmark_v3),A__questionmark_v1) ) ) ).

%% ∀ ?v0:N_set$ ?v1:Nat_set$ ?v2:N_nat_a_fun_fun$ ?v3:N_nat_bool_fun_fun$ ((finite$(?v0) ∧ finite$b(?v1)) ⇒ (sum$a(vcg$(?v1, ?v2, ?v3), ?v0) = sum$d(vch$(?v0, ?v2, ?v3), ?v1)))
tff(axiom676,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'N_nat_a_fun_fun$',A__questionmark_v3: 'N_nat_bool_fun_fun$'] :
      ( ( 'finite$'(A__questionmark_v0)
        & 'finite$b'(A__questionmark_v1) )
     => ( 'sum$a'('vcg$'(A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v0) = 'sum$d'('vch$'(A__questionmark_v0,A__questionmark_v2,A__questionmark_v3),A__questionmark_v1) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_set$ ?v2:N_n_a_fun_fun$ ?v3:N_n_bool_fun_fun$ ((finite$(?v0) ∧ finite$(?v1)) ⇒ (sum$a(vci$(?v1, ?v2, ?v3), ?v0) = sum$a(vcj$(?v0, ?v2, ?v3), ?v1)))
tff(axiom677,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_n_a_fun_fun$',A__questionmark_v3: 'N_n_bool_fun_fun$'] :
      ( ( 'finite$'(A__questionmark_v0)
        & 'finite$'(A__questionmark_v1) )
     => ( 'sum$a'('vci$'(A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v0) = 'sum$a'('vcj$'(A__questionmark_v0,A__questionmark_v2,A__questionmark_v3),A__questionmark_v1) ) ) ).

%% ∀ ?v0:A_n_vec_a_n_vec_fun$ ?v1:A_n_vec$ (linear$(vector_scalar_mult$, vector_scalar_mult$, ?v0) ⇒ (fun_app$b(matrix_vector_mult$(matrix$a(?v0)), ?v1) = fun_app$b(?v0, ?v1)))
tff(axiom678,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_n_vec_fun$',A__questionmark_v1: 'A_n_vec$'] :
      ( 'linear$'('vector_scalar_mult$','vector_scalar_mult$',A__questionmark_v0)
     => ( 'fun_app$b'('matrix_vector_mult$'('matrix$a'(A__questionmark_v0)),A__questionmark_v1) = 'fun_app$b'(A__questionmark_v0,A__questionmark_v1) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N$ ?v2:N_n_a_n_vec_fun_fun$ ?v3:N_a_n_vec_fun$ (finite$(?v0) ⇒ (fun_app$w(det$, vec_lambda$a(vck$(?v0, ?v1, ?v2, ?v3))) = sum$a(vcm$(?v1, ?v2, ?v3), ?v0)))
tff(axiom679,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N_n_a_n_vec_fun_fun$',A__questionmark_v3: 'N_a_n_vec_fun$'] :
      ( 'finite$'(A__questionmark_v0)
     => ( 'fun_app$w'('det$','vec_lambda$a'('vck$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3))) = 'sum$a'('vcm$'(A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v0) ) ) ).

%% ∀ ?v0:Nat_bool_fun$ ?v1:Nat_nat_bool_fun_fun$ (finite$b(collect$a(?v0)) ⇒ (finite$b(collect$a(vcn$(?v0, ?v1))) = ∀ ?v2:Nat$ (fun_app$m(?v0, ?v2) ⇒ finite$b(collect$a(fun_app$n(vco$(?v1), ?v2))))))
tff(axiom680,axiom,
    ! [A__questionmark_v0: 'Nat_bool_fun$',A__questionmark_v1: 'Nat_nat_bool_fun_fun$'] :
      ( 'finite$b'('collect$a'(A__questionmark_v0))
     => ( 'finite$b'('collect$a'('vcn$'(A__questionmark_v0,A__questionmark_v1)))
      <=> ! [A__questionmark_v2: 'Nat$'] :
            ( 'fun_app$m'(A__questionmark_v0,A__questionmark_v2)
           => 'finite$b'('collect$a'('fun_app$n'('vco$'(A__questionmark_v1),A__questionmark_v2))) ) ) ) ).

%% ∀ ?v0:Nat_bool_fun$ (finite$b(collect$a(?v0)) ⇒ (finite$b(collect$a(vcp$(?v0))) = finite$b(top$e)))
tff(axiom681,axiom,
    ! [A__questionmark_v0: 'Nat_bool_fun$'] :
      ( 'finite$b'('collect$a'(A__questionmark_v0))
     => ( 'finite$b'('collect$a'('vcp$'(A__questionmark_v0)))
      <=> 'finite$b'('top$e') ) ) ).

%% ∀ ?v0:N_bool_fun$ (finite$(collect$(?v0)) ⇒ (finite$(collect$(vcq$(?v0))) = finite$(top$)))
tff(axiom682,axiom,
    ! [A__questionmark_v0: 'N_bool_fun$'] :
      ( 'finite$'('collect$'(A__questionmark_v0))
     => ( 'finite$'('collect$'('vcq$'(A__questionmark_v0)))
      <=> 'finite$'('top$') ) ) ).

%% (finite$c(top$s) = (finite$b(top$e) ∧ finite$b(top$e)))
tff(axiom683,axiom,
    ( 'finite$c'('top$s')
  <=> ( 'finite$b'('top$e')
      & 'finite$b'('top$e') ) ) ).

%% (finite$d(top$t) = (finite$b(top$e) ∧ finite$(top$)))
tff(axiom684,axiom,
    ( 'finite$d'('top$t')
  <=> ( 'finite$b'('top$e')
      & 'finite$'('top$') ) ) ).

%% (finite$e(top$u) = (finite$(top$) ∧ finite$b(top$e)))
tff(axiom685,axiom,
    ( 'finite$e'('top$u')
  <=> ( 'finite$'('top$')
      & 'finite$b'('top$e') ) ) ).

%% (finite$f(top$v) = (finite$(top$) ∧ finite$(top$)))
tff(axiom686,axiom,
    ( 'finite$f'('top$v')
  <=> ( 'finite$'('top$')
      & 'finite$'('top$') ) ) ).

%% (finite$g(top$w) = finite$b(top$e))
tff(axiom687,axiom,
    ( 'finite$g'('top$w')
  <=> 'finite$b'('top$e') ) ).

%% (finite$h(top$x) = finite$(top$))
tff(axiom688,axiom,
    ( 'finite$h'('top$x')
  <=> 'finite$'('top$') ) ).

%% ∀ ?v0:Nat_bool_fun$ ?v1:Nat_bool_fun$ ((finite$b(collect$a(?v0)) ∨ finite$b(collect$a(?v1))) ⇒ finite$b(collect$a(vcr$(?v0, ?v1))))
tff(axiom689,axiom,
    ! [A__questionmark_v0: 'Nat_bool_fun$',A__questionmark_v1: 'Nat_bool_fun$'] :
      ( ( 'finite$b'('collect$a'(A__questionmark_v0))
        | 'finite$b'('collect$a'(A__questionmark_v1)) )
     => 'finite$b'('collect$a'('vcr$'(A__questionmark_v0,A__questionmark_v1))) ) ).

%% ∀ ?v0:Nat_bool_fun$ ?v1:Nat_bool_fun$ (finite$b(collect$a(vcs$(?v0, ?v1))) = (finite$b(collect$a(?v0)) ∧ finite$b(collect$a(?v1))))
tff(axiom690,axiom,
    ! [A__questionmark_v0: 'Nat_bool_fun$',A__questionmark_v1: 'Nat_bool_fun$'] :
      ( 'finite$b'('collect$a'('vcs$'(A__questionmark_v0,A__questionmark_v1)))
    <=> ( 'finite$b'('collect$a'(A__questionmark_v0))
        & 'finite$b'('collect$a'(A__questionmark_v1)) ) ) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_set$ ?v2:Nat_nat_bool_fun_fun$ ((¬finite$b(?v0) ∧ (finite$b(?v1) ∧ ∀ ?v3:Nat$ (member$a(?v3, ?v0) ⇒ ∃ ?v4:Nat$ (member$a(?v4, ?v1) ∧ fun_app$m(fun_app$n(?v2, ?v3), ?v4))))) ⇒ ∃ ?v3:Nat$ (member$a(?v3, ?v1) ∧ ¬finite$b(collect$a(fun_app$n(vct$(?v0, ?v2), ?v3)))))
tff(axiom691,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'Nat_nat_bool_fun_fun$'] :
      ( ( ~ 'finite$b'(A__questionmark_v0)
        & 'finite$b'(A__questionmark_v1)
        & ! [A__questionmark_v3: 'Nat$'] :
            ( 'member$a'(A__questionmark_v3,A__questionmark_v0)
           => ? [A__questionmark_v4: 'Nat$'] :
                ( 'member$a'(A__questionmark_v4,A__questionmark_v1)
                & 'fun_app$m'('fun_app$n'(A__questionmark_v2,A__questionmark_v3),A__questionmark_v4) ) ) )
     => ? [A__questionmark_v3: 'Nat$'] :
          ( 'member$a'(A__questionmark_v3,A__questionmark_v1)
          & ~ 'finite$b'('collect$a'('fun_app$n'('vct$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v3))) ) ) ).

%% ∀ ?v0:Nat_bool_fun$ (¬finite$b(collect$a(?v0)) ⇒ ∃ ?v1:Nat$ fun_app$m(?v0, ?v1))
tff(axiom692,axiom,
    ! [A__questionmark_v0: 'Nat_bool_fun$'] :
      ( ~ 'finite$b'('collect$a'(A__questionmark_v0))
     => ? [A__questionmark_v1: 'Nat$'] : 'fun_app$m'(A__questionmark_v0,A__questionmark_v1) ) ).

%% (finite$i(top$y) = finite$b(top$e))
tff(axiom693,axiom,
    ( 'finite$i'('top$y')
  <=> 'finite$b'('top$e') ) ).

%% (finite$j(top$z) = finite$(top$))
tff(axiom694,axiom,
    ( 'finite$j'('top$z')
  <=> 'finite$'('top$') ) ).

%% (finite$k(top$aa) = (finite$b(top$e) ∧ finite$b(top$e)))
tff(axiom695,axiom,
    ( 'finite$k'('top$aa')
  <=> ( 'finite$b'('top$e')
      & 'finite$b'('top$e') ) ) ).

%% (finite$l(top$ab) = (finite$b(top$e) ∧ finite$(top$)))
tff(axiom696,axiom,
    ( 'finite$l'('top$ab')
  <=> ( 'finite$b'('top$e')
      & 'finite$'('top$') ) ) ).

%% (finite$m(top$ac) = (finite$(top$) ∧ finite$b(top$e)))
tff(axiom697,axiom,
    ( 'finite$m'('top$ac')
  <=> ( 'finite$'('top$')
      & 'finite$b'('top$e') ) ) ).

%% (finite$n(top$ad) = (finite$(top$) ∧ finite$(top$)))
tff(axiom698,axiom,
    ( 'finite$n'('top$ad')
  <=> ( 'finite$'('top$')
      & 'finite$'('top$') ) ) ).

%% ((finite$b(top$e) ∧ finite$b(top$e)) ⇒ finite$k(top$aa))
tff(axiom699,axiom,
    ( ( 'finite$b'('top$e')
      & 'finite$b'('top$e') )
   => 'finite$k'('top$aa') ) ).

%% ((finite$b(top$e) ∧ finite$(top$)) ⇒ finite$l(top$ab))
tff(axiom700,axiom,
    ( ( 'finite$b'('top$e')
      & 'finite$'('top$') )
   => 'finite$l'('top$ab') ) ).

%% ((finite$(top$) ∧ finite$b(top$e)) ⇒ finite$m(top$ac))
tff(axiom701,axiom,
    ( ( 'finite$'('top$')
      & 'finite$b'('top$e') )
   => 'finite$m'('top$ac') ) ).

%% ((finite$(top$) ∧ finite$(top$)) ⇒ finite$n(top$ad))
tff(axiom702,axiom,
    ( ( 'finite$'('top$')
      & 'finite$'('top$') )
   => 'finite$n'('top$ad') ) ).

%% ¬finite$b(top$e)
tff(axiom703,axiom,
    ~ 'finite$b'('top$e') ).

%% ∀ ?v0:Nat_set$ ((¬finite$b(top$e) ∧ finite$b(?v0)) ⇒ ∃ ?v1:Nat$ ¬member$a(?v1, ?v0))
tff(axiom704,axiom,
    ! [A__questionmark_v0: 'Nat_set$'] :
      ( ( ~ 'finite$b'('top$e')
        & 'finite$b'(A__questionmark_v0) )
     => ? [A__questionmark_v1: 'Nat$'] : ~ 'member$a'(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:N_set$ ((¬finite$(top$) ∧ finite$(?v0)) ⇒ ∃ ?v1:N$ ¬member$f(?v1, ?v0))
tff(axiom705,axiom,
    ! [A__questionmark_v0: 'N_set$'] :
      ( ( ~ 'finite$'('top$')
        & 'finite$'(A__questionmark_v0) )
     => ? [A__questionmark_v1: 'N$'] : ~ 'member$f'(A__questionmark_v1,A__questionmark_v0) ) ).

%% finite$(top$)
tff(axiom706,axiom,
    'finite$'('top$') ).

%% ∀ ?v0:Nat_bool_fun$ ?v1:Nat_nat_fun$ (finite$b(collect$a(?v0)) ⇒ finite$b(collect$a(vcu$(?v0, ?v1))))
tff(axiom707,axiom,
    ! [A__questionmark_v0: 'Nat_bool_fun$',A__questionmark_v1: 'Nat_nat_fun$'] :
      ( 'finite$b'('collect$a'(A__questionmark_v0))
     => 'finite$b'('collect$a'('vcu$'(A__questionmark_v0,A__questionmark_v1))) ) ).

%% ∀ ?v0:Nat_bool_fun$ ?v1:Nat_bool_fun$ ?v2:Nat_nat_nat_fun_fun$ ((finite$b(collect$a(?v0)) ∧ finite$b(collect$a(?v1))) ⇒ finite$b(collect$a(vcv$(?v0, ?v1, ?v2))))
tff(axiom708,axiom,
    ! [A__questionmark_v0: 'Nat_bool_fun$',A__questionmark_v1: 'Nat_bool_fun$',A__questionmark_v2: 'Nat_nat_nat_fun_fun$'] :
      ( ( 'finite$b'('collect$a'(A__questionmark_v0))
        & 'finite$b'('collect$a'(A__questionmark_v1)) )
     => 'finite$b'('collect$a'('vcv$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2))) ) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_set$ ?v2:Nat$ ((finite$b(?v0) ∧ finite$b(?v1)) ⇒ finite$o(collect$g(vcw$(?v0, ?v1, ?v2))))
tff(axiom709,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_set$',A__questionmark_v2: 'Nat$'] :
      ( ( 'finite$b'(A__questionmark_v0)
        & 'finite$b'(A__questionmark_v1) )
     => 'finite$o'('collect$g'('vcw$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2))) ) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_ennreal_fun$ (finite$b(?v0) ⇒ ((sum$p(?v1, ?v0) = top$ae) = ∃ ?v2:Nat$ (member$a(?v2, ?v0) ∧ (fun_app$bi(?v1, ?v2) = top$ae))))
tff(axiom710,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_ennreal_fun$'] :
      ( 'finite$b'(A__questionmark_v0)
     => ( ( 'sum$p'(A__questionmark_v1,A__questionmark_v0) = 'top$ae' )
      <=> ? [A__questionmark_v2: 'Nat$'] :
            ( 'member$a'(A__questionmark_v2,A__questionmark_v0)
            & ( 'fun_app$bi'(A__questionmark_v1,A__questionmark_v2) = 'top$ae' ) ) ) ) ).

%% ∀ ?v0:N_nat_fun$ finite$b(collect$a(vcx$(?v0)))
tff(axiom711,axiom,
    ! [A__questionmark_v0: 'N_nat_fun$'] : 'finite$b'('collect$a'('vcx$'(A__questionmark_v0))) ).

%% ∀ ?v0:N_set$ ?v1:N_set$ ?v2:N_n_a_n_vec_fun_fun$ ?v3:N_a_n_vec_fun$ ((finite$(?v0) ∧ finite$(?v1)) ⇒ (fun_app$w(det$, vec_lambda$a(vcy$(?v0, ?v1, ?v2, ?v3))) = sum$c(vda$(?v1, ?v2, ?v3), collect$f(vdb$(?v0, ?v1)))))
tff(axiom712,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_n_a_n_vec_fun_fun$',A__questionmark_v3: 'N_a_n_vec_fun$'] :
      ( ( 'finite$'(A__questionmark_v0)
        & 'finite$'(A__questionmark_v1) )
     => ( 'fun_app$w'('det$','vec_lambda$a'('vcy$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3))) = 'sum$c'('vda$'(A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),'collect$f'('vdb$'(A__questionmark_v0,A__questionmark_v1))) ) ) ).

%% ∀ ?v0:N_bool_fun$ (∀ ?v1:N$ (member$f(?v1, top$) ⇒ fun_app$t(?v0, ?v1)) = ∀ ?v1:N$ fun_app$t(?v0, ?v1))
tff(axiom713,axiom,
    ! [A__questionmark_v0: 'N_bool_fun$'] :
      ( ! [A__questionmark_v1: 'N$'] :
          ( 'member$f'(A__questionmark_v1,'top$')
         => 'fun_app$t'(A__questionmark_v0,A__questionmark_v1) )
    <=> ! [A__questionmark_v1: 'N$'] : 'fun_app$t'(A__questionmark_v0,A__questionmark_v1) ) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_nat_set_fun$ (finite$b(?v0) ⇒ (sum$q(?v1, ?v0) = collect$a(vdc$(?v0, ?v1))))
tff(axiom714,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_nat_set_fun$'] :
      ( 'finite$b'(A__questionmark_v0)
     => ( 'sum$q'(A__questionmark_v1,A__questionmark_v0) = 'collect$a'('vdc$'(A__questionmark_v0,A__questionmark_v1)) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_a_n_vec_set_fun$ (finite$(?v0) ⇒ (sum$j(?v1, ?v0) = collect$d(vdd$(?v0, ?v1))))
tff(axiom715,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_a_n_vec_set_fun$'] :
      ( 'finite$'(A__questionmark_v0)
     => ( 'sum$j'(A__questionmark_v1,A__questionmark_v0) = 'collect$d'('vdd$'(A__questionmark_v0,A__questionmark_v1)) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_a_set_fun$ (finite$(?v0) ⇒ (sum$e(?v1, ?v0) = collect$e(vde$(?v0, ?v1))))
tff(axiom716,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_a_set_fun$'] :
      ( 'finite$'(A__questionmark_v0)
     => ( 'sum$e'(A__questionmark_v1,A__questionmark_v0) = 'collect$e'('vde$'(A__questionmark_v0,A__questionmark_v1)) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_a_fun$ (finite$(?v0) ⇒ (fun_app$o(vec$a, sum$a(?v1, ?v0)) = sum$(comp$b(vec$a, ?v1), ?v0)))
tff(axiom717,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_a_fun$'] :
      ( 'finite$'(A__questionmark_v0)
     => ( 'fun_app$o'('vec$a','sum$a'(A__questionmark_v1,A__questionmark_v0)) = 'sum$'('comp$b'('vec$a',A__questionmark_v1),A__questionmark_v0) ) ) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_a_n_vec_fun$ (fun_app$w(det$, vec_lambda$a(vdf$(?v0, ?v1))) = fun_app$k(fun_app$l(times$, prod$(?v0, top$)), fun_app$w(det$, vec_lambda$a(?v1))))
tff(axiom718,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_a_n_vec_fun$'] : 'fun_app$w'('det$','vec_lambda$a'('vdf$'(A__questionmark_v0,A__questionmark_v1))) = 'fun_app$k'('fun_app$l'('times$','prod$'(A__questionmark_v0,'top$')),'fun_app$w'('det$','vec_lambda$a'(A__questionmark_v1))) ).

%% ∀ ?v0:A_n_vec$ ?v1:N$ (fun_app$a(vec_nth$(vec$b(?v0)), ?v1) = ?v0)
tff(axiom719,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'N$'] : 'fun_app$a'('vec_nth$'('vec$b'(A__questionmark_v0)),A__questionmark_v1) = A__questionmark_v0 ).

%% ∀ ?v0:A$ ?v1:N$ (fun_app$d(vec_nth$a(fun_app$o(vec$a, ?v0)), ?v1) = ?v0)
tff(axiom720,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'N$'] : 'fun_app$d'('vec_nth$a'('fun_app$o'('vec$a',A__questionmark_v0)),A__questionmark_v1) = A__questionmark_v0 ).

%% ∀ ?v0:A$ ?v1:A$ (fun_app$o(vec$a, fun_app$k(fun_app$l(times$, ?v0), ?v1)) = fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), fun_app$o(vec$a, ?v1)))
tff(axiom721,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$'] : 'fun_app$o'('vec$a','fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1)) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),'fun_app$o'('vec$a',A__questionmark_v1)) ).

%% linear$c(times$, vector_scalar_mult$, vec$a)
tff(axiom722,axiom,
    'linear$c'('times$','vector_scalar_mult$','vec$a') ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_nat_set_fun$ ((finite$b(?v0) ∧ ∀ ?v2:Nat$ (member$a(?v2, ?v0) ⇒ finite$b(fun_app$at(?v1, ?v2)))) ⇒ finite$b(sum$q(?v1, ?v0)))
tff(axiom723,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_nat_set_fun$'] :
      ( ( 'finite$b'(A__questionmark_v0)
        & ! [A__questionmark_v2: 'Nat$'] :
            ( 'member$a'(A__questionmark_v2,A__questionmark_v0)
           => 'finite$b'('fun_app$at'(A__questionmark_v1,A__questionmark_v2)) ) )
     => 'finite$b'('sum$q'(A__questionmark_v1,A__questionmark_v0)) ) ).

%% ∀ ?v0:A_n_vec_n_vec_n_vec$ (∀ ?v1:N$ ?v2:N$ (¬(?v1 = ?v2) ⇒ (fun_app$a(vec_nth$(fun_app$f(vec_nth$b(?v0), ?v1)), ?v2) = zero$)) ⇒ (det$a(?v0) = prod$a(uve$(?v0), top$)))
tff(axiom724,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec_n_vec$'] :
      ( ! [A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] :
          ( ( A__questionmark_v1 != A__questionmark_v2 )
         => ( 'fun_app$a'('vec_nth$'('fun_app$f'('vec_nth$b'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'zero$' ) )
     => ( 'det$a'(A__questionmark_v0) = 'prod$a'('uve$'(A__questionmark_v0),'top$') ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ (∀ ?v1:N$ ?v2:N$ (¬(?v1 = ?v2) ⇒ (fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v1)), ?v2) = zero$a)) ⇒ (fun_app$w(det$, ?v0) = prod$(uvf$(?v0), top$)))
tff(axiom725,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$'] :
      ( ! [A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] :
          ( ( A__questionmark_v1 != A__questionmark_v2 )
         => ( 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'zero$a' ) )
     => ( 'fun_app$w'('det$',A__questionmark_v0) = 'prod$'('uvf$'(A__questionmark_v0),'top$') ) ) ).

%% ∀ ?v0:N$ ?v1:N$ ?v2:A_n_vec_n_vec$ ?v3:A$ (¬(?v0 = ?v1) ⇒ (fun_app$w(det$, vec_lambda$a(vdg$(?v0, ?v1, ?v2, ?v3))) = fun_app$w(det$, ?v2)))
tff(axiom726,axiom,
    ! [A__questionmark_v0: 'N$',A__questionmark_v1: 'N$',A__questionmark_v2: 'A_n_vec_n_vec$',A__questionmark_v3: 'A$'] :
      ( ( A__questionmark_v0 != A__questionmark_v1 )
     => ( 'fun_app$w'('det$','vec_lambda$a'('vdg$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3))) = 'fun_app$w'('det$',A__questionmark_v2) ) ) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_ennreal_fun$ (finite$b(?v0) ⇒ (less$(sum$p(?v1, ?v0), top$ae) = ∀ ?v2:Nat$ (member$a(?v2, ?v0) ⇒ less$(fun_app$bi(?v1, ?v2), top$ae))))
tff(axiom727,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_ennreal_fun$'] :
      ( 'finite$b'(A__questionmark_v0)
     => ( 'less$'('sum$p'(A__questionmark_v1,A__questionmark_v0),'top$ae')
      <=> ! [A__questionmark_v2: 'Nat$'] :
            ( 'member$a'(A__questionmark_v2,A__questionmark_v0)
           => 'less$'('fun_app$bi'(A__questionmark_v1,A__questionmark_v2),'top$ae') ) ) ) ).

%% ∀ ?v0:A$ (fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), zero$) = zero$)
tff(axiom728,axiom,
    ! [A__questionmark_v0: 'A$'] : 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),'zero$') = 'zero$' ).

%% ∀ ?v0:A$ ?v1:A_n_vec$ ?v2:A$ ((fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), ?v1) = fun_app$b(fun_app$c(vector_scalar_mult$, ?v2), ?v1)) = ((?v0 = ?v2) ∨ (?v1 = zero$)))
tff(axiom729,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'A$'] :
      ( ( 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),A__questionmark_v1) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v2),A__questionmark_v1) )
    <=> ( ( A__questionmark_v0 = A__questionmark_v2 )
        | ( A__questionmark_v1 = 'zero$' ) ) ) ).

%% ∀ ?v0:A$ (fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), zero$) = zero$)
tff(axiom730,axiom,
    ! [A__questionmark_v0: 'A$'] : 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),'zero$') = 'zero$' ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ ((fun_app$k(fun_app$l(times$, ?v0), ?v1) = fun_app$k(fun_app$l(times$, ?v2), ?v1)) = ((?v0 = ?v2) ∨ (?v1 = zero$a)))
tff(axiom731,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1) = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v2),A__questionmark_v1) )
    <=> ( ( A__questionmark_v0 = A__questionmark_v2 )
        | ( A__questionmark_v1 = 'zero$a' ) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ ((fun_app$k(fun_app$l(times$, ?v0), ?v1) = fun_app$k(fun_app$l(times$, ?v0), ?v2)) = ((?v1 = ?v2) ∨ (?v0 = zero$a)))
tff(axiom732,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1) = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2) )
    <=> ( ( A__questionmark_v1 = A__questionmark_v2 )
        | ( A__questionmark_v0 = 'zero$a' ) ) ) ).

%% ∀ ?v0:A$ (fun_app$k(fun_app$l(times$, ?v0), zero$a) = zero$a)
tff(axiom733,axiom,
    ! [A__questionmark_v0: 'A$'] : 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),'zero$a') = 'zero$a' ).

%% ∀ ?v0:A$ (fun_app$k(fun_app$l(times$, zero$a), ?v0) = zero$a)
tff(axiom734,axiom,
    ! [A__questionmark_v0: 'A$'] : 'fun_app$k'('fun_app$l'('times$','zero$a'),A__questionmark_v0) = 'zero$a' ).

%% ∀ ?v0:A$ ?v1:A$ ((fun_app$k(fun_app$l(times$, ?v0), ?v1) = zero$a) = ((?v0 = zero$a) ∨ (?v1 = zero$a)))
tff(axiom735,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$'] :
      ( ( 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1) = 'zero$a' )
    <=> ( ( A__questionmark_v0 = 'zero$a' )
        | ( A__questionmark_v1 = 'zero$a' ) ) ) ).

%% ∀ ?v0:A_n_vec$ (fun_app$b(fun_app$c(vector_scalar_mult$, zero$a), ?v0) = zero$)
tff(axiom736,axiom,
    ! [A__questionmark_v0: 'A_n_vec$'] : 'fun_app$b'('fun_app$c'('vector_scalar_mult$','zero$a'),A__questionmark_v0) = 'zero$' ).

%% ∀ ?v0:A$ ?v1:A_n_vec$ ((fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), ?v1) = zero$) = ((?v0 = zero$a) ∨ (?v1 = zero$)))
tff(axiom737,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A_n_vec$'] :
      ( ( 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),A__questionmark_v1) = 'zero$' )
    <=> ( ( A__questionmark_v0 = 'zero$a' )
        | ( A__questionmark_v1 = 'zero$' ) ) ) ).

%% ∀ ?v0:A_n_vec$ (fun_app$b(fun_app$c(vector_scalar_mult$, zero$a), ?v0) = zero$)
tff(axiom738,axiom,
    ! [A__questionmark_v0: 'A_n_vec$'] : 'fun_app$b'('fun_app$c'('vector_scalar_mult$','zero$a'),A__questionmark_v0) = 'zero$' ).

%% ∀ ?v0:A$ ?v1:A_n_vec$ ((fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), ?v1) = zero$) = ((?v0 = zero$a) ∨ (?v1 = zero$)))
tff(axiom739,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A_n_vec$'] :
      ( ( 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),A__questionmark_v1) = 'zero$' )
    <=> ( ( A__questionmark_v0 = 'zero$a' )
        | ( A__questionmark_v1 = 'zero$' ) ) ) ).

%% ∀ ?v0:A$ ?v1:A_n_vec$ ?v2:A_n_vec$ ((fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), ?v1) = fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), ?v2)) = ((?v0 = zero$a) ∨ (?v1 = ?v2)))
tff(axiom740,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'A_n_vec$'] :
      ( ( 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),A__questionmark_v1) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),A__questionmark_v2) )
    <=> ( ( A__questionmark_v0 = 'zero$a' )
        | ( A__questionmark_v1 = A__questionmark_v2 ) ) ) ).

%% ∀ ?v0:A$ ?v1:A_n_vec$ ?v2:A_n_vec$ ((fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), ?v1) = fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), ?v2)) = ((?v1 = ?v2) ∨ (?v0 = zero$a)))
tff(axiom741,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'A_n_vec$'] :
      ( ( 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),A__questionmark_v1) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),A__questionmark_v2) )
    <=> ( ( A__questionmark_v1 = A__questionmark_v2 )
        | ( A__questionmark_v0 = 'zero$a' ) ) ) ).

%% ∀ ?v0:N$ (fun_app$a(vec_nth$(zero$b), ?v0) = zero$)
tff(axiom742,axiom,
    ! [A__questionmark_v0: 'N$'] : 'fun_app$a'('vec_nth$'('zero$b'),A__questionmark_v0) = 'zero$' ).

%% ∀ ?v0:N$ (fun_app$d(vec_nth$a(zero$), ?v0) = zero$a)
tff(axiom743,axiom,
    ! [A__questionmark_v0: 'N$'] : 'fun_app$d'('vec_nth$a'('zero$'),A__questionmark_v0) = 'zero$a' ).

%% ∀ ?v0:A$ ?v1:A_n_vec$ ?v2:A_n_vec$ (fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), fun_app$b(plus$(?v1), ?v2)) = fun_app$b(plus$(fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), ?v1)), fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), ?v2)))
tff(axiom744,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'A_n_vec$'] : 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),'fun_app$b'('plus$'(A__questionmark_v1),A__questionmark_v2)) = 'fun_app$b'('plus$'('fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),A__questionmark_v1)),'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),A__questionmark_v2)) ).

%% ∀ ?v0:N_set$ (sum$(vdh$, ?v0) = zero$)
tff(axiom745,axiom,
    ! [A__questionmark_v0: 'N_set$'] : 'sum$'('vdh$',A__questionmark_v0) = 'zero$' ).

%% ∀ ?v0:N_set$ (sum$a(vdi$, ?v0) = zero$a)
tff(axiom746,axiom,
    ! [A__questionmark_v0: 'N_set$'] : 'sum$a'('vdi$',A__questionmark_v0) = 'zero$a' ).

%% ∀ ?v0:N_set$ ?v1:N_a_n_vec_fun$ (¬finite$(?v0) ⇒ (sum$(?v1, ?v0) = zero$))
tff(axiom747,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_a_n_vec_fun$'] :
      ( ~ 'finite$'(A__questionmark_v0)
     => ( 'sum$'(A__questionmark_v1,A__questionmark_v0) = 'zero$' ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_a_fun$ (¬finite$(?v0) ⇒ (sum$a(?v1, ?v0) = zero$a))
tff(axiom748,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_a_fun$'] :
      ( ~ 'finite$'(A__questionmark_v0)
     => ( 'sum$a'(A__questionmark_v1,A__questionmark_v0) = 'zero$a' ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A_n_vec$ (fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$k(plus$a(?v0), ?v1)), ?v2) = fun_app$b(plus$(fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), ?v2)), fun_app$b(fun_app$c(vector_scalar_mult$, ?v1), ?v2)))
tff(axiom749,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A_n_vec$'] : 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$k'('plus$a'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$b'('plus$'('fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),A__questionmark_v2)),'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ (fun_app$a(vec_nth$(plus$b(?v0, ?v1)), ?v2) = fun_app$b(plus$(fun_app$a(vec_nth$(?v0), ?v2)), fun_app$a(vec_nth$(?v1), ?v2)))
tff(axiom750,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$a'('vec_nth$'('plus$b'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'fun_app$b'('plus$'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v2)),'fun_app$a'('vec_nth$'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec$ ?v2:N$ (fun_app$d(vec_nth$a(fun_app$b(plus$(?v0), ?v1)), ?v2) = fun_app$k(plus$a(fun_app$d(vec_nth$a(?v0), ?v2)), fun_app$d(vec_nth$a(?v1), ?v2)))
tff(axiom751,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'N$'] : 'fun_app$d'('vec_nth$a'('fun_app$b'('plus$'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$k'('plus$a'('fun_app$d'('vec_nth$a'(A__questionmark_v0),A__questionmark_v2)),'fun_app$d'('vec_nth$a'(A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:N_set$ ?v1:N$ ?v2:N_a_n_vec_fun$ (finite$(?v0) ⇒ (sum$(vdj$(?v1, ?v2), ?v0) = (if member$f(?v1, ?v0) fun_app$a(?v2, ?v1) else zero$)))
tff(axiom752,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N_a_n_vec_fun$'] :
      ( 'finite$'(A__questionmark_v0)
     => ( ( 'member$f'(A__questionmark_v1,A__questionmark_v0)
         => ( 'sum$'('vdj$'(A__questionmark_v1,A__questionmark_v2),A__questionmark_v0) = 'fun_app$a'(A__questionmark_v2,A__questionmark_v1) ) )
        & ( ~ 'member$f'(A__questionmark_v1,A__questionmark_v0)
         => ( 'sum$'('vdj$'(A__questionmark_v1,A__questionmark_v2),A__questionmark_v0) = 'zero$' ) ) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N$ ?v2:N_a_fun$ (finite$(?v0) ⇒ (sum$a(vdk$(?v1, ?v2), ?v0) = (if member$f(?v1, ?v0) fun_app$d(?v2, ?v1) else zero$a)))
tff(axiom753,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N_a_fun$'] :
      ( 'finite$'(A__questionmark_v0)
     => ( ( 'member$f'(A__questionmark_v1,A__questionmark_v0)
         => ( 'sum$a'('vdk$'(A__questionmark_v1,A__questionmark_v2),A__questionmark_v0) = 'fun_app$d'(A__questionmark_v2,A__questionmark_v1) ) )
        & ( ~ 'member$f'(A__questionmark_v1,A__questionmark_v0)
         => ( 'sum$a'('vdk$'(A__questionmark_v1,A__questionmark_v2),A__questionmark_v0) = 'zero$a' ) ) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N$ ?v2:N_a_n_vec_fun$ (finite$(?v0) ⇒ (sum$(vdl$(?v1, ?v2), ?v0) = (if member$f(?v1, ?v0) fun_app$a(?v2, ?v1) else zero$)))
tff(axiom754,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N_a_n_vec_fun$'] :
      ( 'finite$'(A__questionmark_v0)
     => ( ( 'member$f'(A__questionmark_v1,A__questionmark_v0)
         => ( 'sum$'('vdl$'(A__questionmark_v1,A__questionmark_v2),A__questionmark_v0) = 'fun_app$a'(A__questionmark_v2,A__questionmark_v1) ) )
        & ( ~ 'member$f'(A__questionmark_v1,A__questionmark_v0)
         => ( 'sum$'('vdl$'(A__questionmark_v1,A__questionmark_v2),A__questionmark_v0) = 'zero$' ) ) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N$ ?v2:N_a_fun$ (finite$(?v0) ⇒ (sum$a(vdm$(?v1, ?v2), ?v0) = (if member$f(?v1, ?v0) fun_app$d(?v2, ?v1) else zero$a)))
tff(axiom755,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N_a_fun$'] :
      ( 'finite$'(A__questionmark_v0)
     => ( ( 'member$f'(A__questionmark_v1,A__questionmark_v0)
         => ( 'sum$a'('vdm$'(A__questionmark_v1,A__questionmark_v2),A__questionmark_v0) = 'fun_app$d'(A__questionmark_v2,A__questionmark_v1) ) )
        & ( ~ 'member$f'(A__questionmark_v1,A__questionmark_v0)
         => ( 'sum$a'('vdm$'(A__questionmark_v1,A__questionmark_v2),A__questionmark_v0) = 'zero$a' ) ) ) ) ).

%% ∀ ?v0:A_n_vec_a_n_vec_fun$ ?v1:N_a_n_vec_fun$ ?v2:N_set$ (((fun_app$b(?v0, zero$) = zero$) ∧ ∀ ?v3:A_n_vec$ ?v4:A_n_vec$ (fun_app$b(?v0, fun_app$b(plus$(?v3), ?v4)) = fun_app$b(plus$(fun_app$b(?v0, ?v3)), fun_app$b(?v0, ?v4)))) ⇒ (sum$(comp$d(?v0, ?v1), ?v2) = fun_app$b(?v0, sum$(?v1, ?v2))))
tff(axiom756,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_n_vec_fun$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N_set$'] :
      ( ( ( 'fun_app$b'(A__questionmark_v0,'zero$') = 'zero$' )
        & ! [A__questionmark_v3: 'A_n_vec$',A__questionmark_v4: 'A_n_vec$'] : 'fun_app$b'(A__questionmark_v0,'fun_app$b'('plus$'(A__questionmark_v3),A__questionmark_v4)) = 'fun_app$b'('plus$'('fun_app$b'(A__questionmark_v0,A__questionmark_v3)),'fun_app$b'(A__questionmark_v0,A__questionmark_v4)) )
     => ( 'sum$'('comp$d'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'(A__questionmark_v0,'sum$'(A__questionmark_v1,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:A_a_n_vec_fun$ ?v1:N_a_fun$ ?v2:N_set$ (((fun_app$o(?v0, zero$a) = zero$) ∧ ∀ ?v3:A$ ?v4:A$ (fun_app$o(?v0, fun_app$k(plus$a(?v3), ?v4)) = fun_app$b(plus$(fun_app$o(?v0, ?v3)), fun_app$o(?v0, ?v4)))) ⇒ (sum$(comp$b(?v0, ?v1), ?v2) = fun_app$o(?v0, sum$a(?v1, ?v2))))
tff(axiom757,axiom,
    ! [A__questionmark_v0: 'A_a_n_vec_fun$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N_set$'] :
      ( ( ( 'fun_app$o'(A__questionmark_v0,'zero$a') = 'zero$' )
        & ! [A__questionmark_v3: 'A$',A__questionmark_v4: 'A$'] : 'fun_app$o'(A__questionmark_v0,'fun_app$k'('plus$a'(A__questionmark_v3),A__questionmark_v4)) = 'fun_app$b'('plus$'('fun_app$o'(A__questionmark_v0,A__questionmark_v3)),'fun_app$o'(A__questionmark_v0,A__questionmark_v4)) )
     => ( 'sum$'('comp$b'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$o'(A__questionmark_v0,'sum$a'(A__questionmark_v1,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:A_n_vec_a_fun$ ?v1:N_a_n_vec_fun$ ?v2:N_set$ (((fun_app$j(?v0, zero$) = zero$a) ∧ ∀ ?v3:A_n_vec$ ?v4:A_n_vec$ (fun_app$j(?v0, fun_app$b(plus$(?v3), ?v4)) = fun_app$k(plus$a(fun_app$j(?v0, ?v3)), fun_app$j(?v0, ?v4)))) ⇒ (sum$a(comp$(?v0, ?v1), ?v2) = fun_app$j(?v0, sum$(?v1, ?v2))))
tff(axiom758,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_fun$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N_set$'] :
      ( ( ( 'fun_app$j'(A__questionmark_v0,'zero$') = 'zero$a' )
        & ! [A__questionmark_v3: 'A_n_vec$',A__questionmark_v4: 'A_n_vec$'] : 'fun_app$j'(A__questionmark_v0,'fun_app$b'('plus$'(A__questionmark_v3),A__questionmark_v4)) = 'fun_app$k'('plus$a'('fun_app$j'(A__questionmark_v0,A__questionmark_v3)),'fun_app$j'(A__questionmark_v0,A__questionmark_v4)) )
     => ( 'sum$a'('comp$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$j'(A__questionmark_v0,'sum$'(A__questionmark_v1,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:A_a_fun$ ?v1:N_a_fun$ ?v2:N_set$ (((fun_app$k(?v0, zero$a) = zero$a) ∧ ∀ ?v3:A$ ?v4:A$ (fun_app$k(?v0, fun_app$k(plus$a(?v3), ?v4)) = fun_app$k(plus$a(fun_app$k(?v0, ?v3)), fun_app$k(?v0, ?v4)))) ⇒ (sum$a(comp$c(?v0, ?v1), ?v2) = fun_app$k(?v0, sum$a(?v1, ?v2))))
tff(axiom759,axiom,
    ! [A__questionmark_v0: 'A_a_fun$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N_set$'] :
      ( ( ( 'fun_app$k'(A__questionmark_v0,'zero$a') = 'zero$a' )
        & ! [A__questionmark_v3: 'A$',A__questionmark_v4: 'A$'] : 'fun_app$k'(A__questionmark_v0,'fun_app$k'('plus$a'(A__questionmark_v3),A__questionmark_v4)) = 'fun_app$k'('plus$a'('fun_app$k'(A__questionmark_v0,A__questionmark_v3)),'fun_app$k'(A__questionmark_v0,A__questionmark_v4)) )
     => ( 'sum$a'('comp$c'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$k'(A__questionmark_v0,'sum$a'(A__questionmark_v1,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:A_n_vec_a_n_vec_bool_fun_fun$ ?v1:N_set$ ?v2:N_a_n_vec_fun$ ?v3:N_a_n_vec_fun$ ((fun_app$p(fun_app$bj(?v0, zero$), zero$) ∧ (∀ ?v4:A_n_vec$ ?v5:A_n_vec$ ?v6:A_n_vec$ ?v7:A_n_vec$ ((fun_app$p(fun_app$bj(?v0, ?v4), ?v6) ∧ fun_app$p(fun_app$bj(?v0, ?v5), ?v7)) ⇒ fun_app$p(fun_app$bj(?v0, fun_app$b(plus$(?v4), ?v5)), fun_app$b(plus$(?v6), ?v7))) ∧ (finite$(?v1) ∧ ∀ ?v4:N$ (member$f(?v4, ?v1) ⇒ fun_app$p(fun_app$bj(?v0, fun_app$a(?v2, ?v4)), fun_app$a(?v3, ?v4)))))) ⇒ fun_app$p(fun_app$bj(?v0, sum$(?v2, ?v1)), sum$(?v3, ?v1)))
tff(axiom760,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_n_vec_bool_fun_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_a_n_vec_fun$',A__questionmark_v3: 'N_a_n_vec_fun$'] :
      ( ( 'fun_app$p'('fun_app$bj'(A__questionmark_v0,'zero$'),'zero$')
        & ! [A__questionmark_v4: 'A_n_vec$',A__questionmark_v5: 'A_n_vec$',A__questionmark_v6: 'A_n_vec$',A__questionmark_v7: 'A_n_vec$'] :
            ( ( 'fun_app$p'('fun_app$bj'(A__questionmark_v0,A__questionmark_v4),A__questionmark_v6)
              & 'fun_app$p'('fun_app$bj'(A__questionmark_v0,A__questionmark_v5),A__questionmark_v7) )
           => 'fun_app$p'('fun_app$bj'(A__questionmark_v0,'fun_app$b'('plus$'(A__questionmark_v4),A__questionmark_v5)),'fun_app$b'('plus$'(A__questionmark_v6),A__questionmark_v7)) )
        & 'finite$'(A__questionmark_v1)
        & ! [A__questionmark_v4: 'N$'] :
            ( 'member$f'(A__questionmark_v4,A__questionmark_v1)
           => 'fun_app$p'('fun_app$bj'(A__questionmark_v0,'fun_app$a'(A__questionmark_v2,A__questionmark_v4)),'fun_app$a'(A__questionmark_v3,A__questionmark_v4)) ) )
     => 'fun_app$p'('fun_app$bj'(A__questionmark_v0,'sum$'(A__questionmark_v2,A__questionmark_v1)),'sum$'(A__questionmark_v3,A__questionmark_v1)) ) ).

%% ∀ ?v0:A_a_bool_fun_fun$ ?v1:N_set$ ?v2:N_a_fun$ ?v3:N_a_fun$ ((fun_app$u(fun_app$bk(?v0, zero$a), zero$a) ∧ (∀ ?v4:A$ ?v5:A$ ?v6:A$ ?v7:A$ ((fun_app$u(fun_app$bk(?v0, ?v4), ?v6) ∧ fun_app$u(fun_app$bk(?v0, ?v5), ?v7)) ⇒ fun_app$u(fun_app$bk(?v0, fun_app$k(plus$a(?v4), ?v5)), fun_app$k(plus$a(?v6), ?v7))) ∧ (finite$(?v1) ∧ ∀ ?v4:N$ (member$f(?v4, ?v1) ⇒ fun_app$u(fun_app$bk(?v0, fun_app$d(?v2, ?v4)), fun_app$d(?v3, ?v4)))))) ⇒ fun_app$u(fun_app$bk(?v0, sum$a(?v2, ?v1)), sum$a(?v3, ?v1)))
tff(axiom761,axiom,
    ! [A__questionmark_v0: 'A_a_bool_fun_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'N_a_fun$',A__questionmark_v3: 'N_a_fun$'] :
      ( ( 'fun_app$u'('fun_app$bk'(A__questionmark_v0,'zero$a'),'zero$a')
        & ! [A__questionmark_v4: 'A$',A__questionmark_v5: 'A$',A__questionmark_v6: 'A$',A__questionmark_v7: 'A$'] :
            ( ( 'fun_app$u'('fun_app$bk'(A__questionmark_v0,A__questionmark_v4),A__questionmark_v6)
              & 'fun_app$u'('fun_app$bk'(A__questionmark_v0,A__questionmark_v5),A__questionmark_v7) )
           => 'fun_app$u'('fun_app$bk'(A__questionmark_v0,'fun_app$k'('plus$a'(A__questionmark_v4),A__questionmark_v5)),'fun_app$k'('plus$a'(A__questionmark_v6),A__questionmark_v7)) )
        & 'finite$'(A__questionmark_v1)
        & ! [A__questionmark_v4: 'N$'] :
            ( 'member$f'(A__questionmark_v4,A__questionmark_v1)
           => 'fun_app$u'('fun_app$bk'(A__questionmark_v0,'fun_app$d'(A__questionmark_v2,A__questionmark_v4)),'fun_app$d'(A__questionmark_v3,A__questionmark_v4)) ) )
     => 'fun_app$u'('fun_app$bk'(A__questionmark_v0,'sum$a'(A__questionmark_v2,A__questionmark_v1)),'sum$a'(A__questionmark_v3,A__questionmark_v1)) ) ).

%% ∀ ?v0:N_set$ ?v1:N_a_n_vec_fun$ (∀ ?v2:N$ (member$f(?v2, ?v0) ⇒ (fun_app$a(?v1, ?v2) = zero$)) ⇒ (sum$(?v1, ?v0) = zero$))
tff(axiom762,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_a_n_vec_fun$'] :
      ( ! [A__questionmark_v2: 'N$'] :
          ( 'member$f'(A__questionmark_v2,A__questionmark_v0)
         => ( 'fun_app$a'(A__questionmark_v1,A__questionmark_v2) = 'zero$' ) )
     => ( 'sum$'(A__questionmark_v1,A__questionmark_v0) = 'zero$' ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_a_fun$ (∀ ?v2:N$ (member$f(?v2, ?v0) ⇒ (fun_app$d(?v1, ?v2) = zero$a)) ⇒ (sum$a(?v1, ?v0) = zero$a))
tff(axiom763,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_a_fun$'] :
      ( ! [A__questionmark_v2: 'N$'] :
          ( 'member$f'(A__questionmark_v2,A__questionmark_v0)
         => ( 'fun_app$d'(A__questionmark_v1,A__questionmark_v2) = 'zero$a' ) )
     => ( 'sum$a'(A__questionmark_v1,A__questionmark_v0) = 'zero$a' ) ) ).

%% ∀ ?v0:N_a_n_vec_fun$ ?v1:N_set$ ((¬(sum$(?v0, ?v1) = zero$) ∧ ∀ ?v2:N$ ((member$f(?v2, ?v1) ∧ ¬(fun_app$a(?v0, ?v2) = zero$)) ⇒ false)) ⇒ false)
tff(axiom764,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$',A__questionmark_v1: 'N_set$'] :
      ( ( ( 'sum$'(A__questionmark_v0,A__questionmark_v1) != 'zero$' )
        & ! [A__questionmark_v2: 'N$'] :
            ( ( 'member$f'(A__questionmark_v2,A__questionmark_v1)
              & ( 'fun_app$a'(A__questionmark_v0,A__questionmark_v2) != 'zero$' ) )
           => $false ) )
     => $false ) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_set$ ((¬(sum$a(?v0, ?v1) = zero$a) ∧ ∀ ?v2:N$ ((member$f(?v2, ?v1) ∧ ¬(fun_app$d(?v0, ?v2) = zero$a)) ⇒ false)) ⇒ false)
tff(axiom765,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_set$'] :
      ( ( ( 'sum$a'(A__questionmark_v0,A__questionmark_v1) != 'zero$a' )
        & ! [A__questionmark_v2: 'N$'] :
            ( ( 'member$f'(A__questionmark_v2,A__questionmark_v1)
              & ( 'fun_app$d'(A__questionmark_v0,A__questionmark_v2) != 'zero$a' ) )
           => $false ) )
     => $false ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec_n_vec$ (plus$b(?v0, ?v1) = vec_lambda$a(vdn$(?v0, ?v1)))
tff(axiom766,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$'] : 'plus$b'(A__questionmark_v0,A__questionmark_v1) = 'vec_lambda$a'('vdn$'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec$ (fun_app$b(plus$(?v0), ?v1) = vec_lambda$(vdo$(?v0, ?v1)))
tff(axiom767,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec$'] : 'fun_app$b'('plus$'(A__questionmark_v0),A__questionmark_v1) = 'vec_lambda$'('vdo$'(A__questionmark_v0,A__questionmark_v1)) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ ((¬(?v0 = zero$a) ∧ (fun_app$k(fun_app$l(times$, ?v0), ?v1) = fun_app$k(fun_app$l(times$, ?v0), ?v2))) ⇒ (?v1 = ?v2))
tff(axiom768,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( ( A__questionmark_v0 != 'zero$a' )
        & ( 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1) = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2) ) )
     => ( A__questionmark_v1 = A__questionmark_v2 ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ ((¬(?v0 = zero$a) ∧ (fun_app$k(fun_app$l(times$, ?v1), ?v0) = fun_app$k(fun_app$l(times$, ?v2), ?v0))) ⇒ (?v1 = ?v2))
tff(axiom769,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( ( A__questionmark_v0 != 'zero$a' )
        & ( 'fun_app$k'('fun_app$l'('times$',A__questionmark_v1),A__questionmark_v0) = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v2),A__questionmark_v0) ) )
     => ( A__questionmark_v1 = A__questionmark_v2 ) ) ).

%% ∀ ?v0:A$ ?v1:A_n_vec$ ?v2:A_n_vec$ ((¬(?v0 = zero$a) ∧ (fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), ?v1) = fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), ?v2))) ⇒ (?v1 = ?v2))
tff(axiom770,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'A_n_vec$'] :
      ( ( ( A__questionmark_v0 != 'zero$a' )
        & ( 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),A__questionmark_v1) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),A__questionmark_v2) ) )
     => ( A__questionmark_v1 = A__questionmark_v2 ) ) ).

%% ∀ ?v0:A_n_vec$ ?v1:A$ ?v2:A$ ((¬(?v0 = zero$) ∧ (fun_app$b(fun_app$c(vector_scalar_mult$, ?v1), ?v0) = fun_app$b(fun_app$c(vector_scalar_mult$, ?v2), ?v0))) ⇒ (?v1 = ?v2))
tff(axiom771,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( ( A__questionmark_v0 != 'zero$' )
        & ( 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v1),A__questionmark_v0) = 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v2),A__questionmark_v0) ) )
     => ( A__questionmark_v1 = A__questionmark_v2 ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (fun_app$k(fun_app$l(times$, fun_app$k(plus$a(?v0), ?v1)), ?v2) = fun_app$k(plus$a(fun_app$k(fun_app$l(times$, ?v0), ?v2)), fun_app$k(fun_app$l(times$, ?v1), ?v2)))
tff(axiom772,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] : 'fun_app$k'('fun_app$l'('times$','fun_app$k'('plus$a'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$k'('plus$a'('fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2)),'fun_app$k'('fun_app$l'('times$',A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (fun_app$k(fun_app$l(times$, ?v0), fun_app$k(plus$a(?v1), ?v2)) = fun_app$k(plus$a(fun_app$k(fun_app$l(times$, ?v0), ?v1)), fun_app$k(fun_app$l(times$, ?v0), ?v2)))
tff(axiom773,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] : 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),'fun_app$k'('plus$a'(A__questionmark_v1),A__questionmark_v2)) = 'fun_app$k'('plus$a'('fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1)),'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2)) ).

%% ∀ ?v0:Int ?v1:Int ((?v0 < ?v1) ⇒ (¬(?v1 < ?v0) = true))
tff(axiom774,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( $less(A__questionmark_v0,A__questionmark_v1)
     => ( ~ $less(A__questionmark_v1,A__questionmark_v0)
      <=> $true ) ) ).

%% ∀ ?v0:Int ?v1:Int ((?v0 < ?v1) ⇒ ((?v1 = ?v0) = false))
tff(axiom775,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( $less(A__questionmark_v0,A__questionmark_v1)
     => ( ( A__questionmark_v1 = A__questionmark_v0 )
      <=> $false ) ) ).

%% ∀ ?v0:Int ?v1:Int ((?v0 < ?v1) ⇒ ((?v0 = ?v1) = false))
tff(axiom776,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( $less(A__questionmark_v0,A__questionmark_v1)
     => ( ( A__questionmark_v0 = A__questionmark_v1 )
      <=> $false ) ) ).

%% ∀ ?v0:Int ?v1:Int ((?v0 < ?v1) ∨ ((?v0 = ?v1) ∨ (?v1 < ?v0)))
tff(axiom777,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( $less(A__questionmark_v0,A__questionmark_v1)
      | ( A__questionmark_v0 = A__questionmark_v1 )
      | $less(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:Int ?v1:Int ?v2:Bool ((?v0 < ?v1) ⇒ (((?v1 < ?v0) ⇒ ?v2) = true))
tff(axiom778,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int,A__questionmark_v2: tlbool] :
      ( $less(A__questionmark_v0,A__questionmark_v1)
     => ( ( $less(A__questionmark_v1,A__questionmark_v0)
         => ( A__questionmark_v2 = tltrue ) )
      <=> $true ) ) ).

%% ∀ ?v0:Int ?v1:Int ((?v0 < ?v1) ⇒ ¬(?v1 < ?v0))
tff(axiom779,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( $less(A__questionmark_v0,A__questionmark_v1)
     => ~ $less(A__questionmark_v1,A__questionmark_v0) ) ).

%% ∀ ?v0:Int ?v1:Int ?v2:Int_int_fun$ ?v3:Int (((?v0 < ?v1) ∧ ((fun_app$aq(?v2, ?v1) < ?v3) ∧ ∀ ?v4:Int ?v5:Int ((?v4 < ?v5) ⇒ (fun_app$aq(?v2, ?v4) < fun_app$aq(?v2, ?v5))))) ⇒ (fun_app$aq(?v2, ?v0) < ?v3))
tff(axiom780,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int,A__questionmark_v2: 'Int_int_fun$',A__questionmark_v3: $int] :
      ( ( $less(A__questionmark_v0,A__questionmark_v1)
        & $less('fun_app$aq'(A__questionmark_v2,A__questionmark_v1),A__questionmark_v3)
        & ! [A__questionmark_v4: $int,A__questionmark_v5: $int] :
            ( $less(A__questionmark_v4,A__questionmark_v5)
           => $less('fun_app$aq'(A__questionmark_v2,A__questionmark_v4),'fun_app$aq'(A__questionmark_v2,A__questionmark_v5)) ) )
     => $less('fun_app$aq'(A__questionmark_v2,A__questionmark_v0),A__questionmark_v3) ) ).

%% ∀ ?v0:Int ?v1:Int_int_fun$ ?v2:Int ?v3:Int (((?v0 < fun_app$aq(?v1, ?v2)) ∧ ((?v2 < ?v3) ∧ ∀ ?v4:Int ?v5:Int ((?v4 < ?v5) ⇒ (fun_app$aq(?v1, ?v4) < fun_app$aq(?v1, ?v5))))) ⇒ (?v0 < fun_app$aq(?v1, ?v3)))
tff(axiom781,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: 'Int_int_fun$',A__questionmark_v2: $int,A__questionmark_v3: $int] :
      ( ( $less(A__questionmark_v0,'fun_app$aq'(A__questionmark_v1,A__questionmark_v2))
        & $less(A__questionmark_v2,A__questionmark_v3)
        & ! [A__questionmark_v4: $int,A__questionmark_v5: $int] :
            ( $less(A__questionmark_v4,A__questionmark_v5)
           => $less('fun_app$aq'(A__questionmark_v1,A__questionmark_v4),'fun_app$aq'(A__questionmark_v1,A__questionmark_v5)) ) )
     => $less(A__questionmark_v0,'fun_app$aq'(A__questionmark_v1,A__questionmark_v3)) ) ).

%% ∀ ?v0:Int ¬(?v0 < ?v0)
tff(axiom782,axiom,
    ! [A__questionmark_v0: $int] : ~ $less(A__questionmark_v0,A__questionmark_v0) ).

%% ∀ ?v0:Int ?v1:Int ?v2:Int_int_fun$ ?v3:Int (((?v0 < ?v1) ∧ ((fun_app$aq(?v2, ?v1) = ?v3) ∧ ∀ ?v4:Int ?v5:Int ((?v4 < ?v5) ⇒ (fun_app$aq(?v2, ?v4) < fun_app$aq(?v2, ?v5))))) ⇒ (fun_app$aq(?v2, ?v0) < ?v3))
tff(axiom783,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int,A__questionmark_v2: 'Int_int_fun$',A__questionmark_v3: $int] :
      ( ( $less(A__questionmark_v0,A__questionmark_v1)
        & ( 'fun_app$aq'(A__questionmark_v2,A__questionmark_v1) = A__questionmark_v3 )
        & ! [A__questionmark_v4: $int,A__questionmark_v5: $int] :
            ( $less(A__questionmark_v4,A__questionmark_v5)
           => $less('fun_app$aq'(A__questionmark_v2,A__questionmark_v4),'fun_app$aq'(A__questionmark_v2,A__questionmark_v5)) ) )
     => $less('fun_app$aq'(A__questionmark_v2,A__questionmark_v0),A__questionmark_v3) ) ).

%% ∀ ?v0:Int ?v1:Int_int_fun$ ?v2:Int ?v3:Int (((?v0 = fun_app$aq(?v1, ?v2)) ∧ ((?v2 < ?v3) ∧ ∀ ?v4:Int ?v5:Int ((?v4 < ?v5) ⇒ (fun_app$aq(?v1, ?v4) < fun_app$aq(?v1, ?v5))))) ⇒ (?v0 < fun_app$aq(?v1, ?v3)))
tff(axiom784,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: 'Int_int_fun$',A__questionmark_v2: $int,A__questionmark_v3: $int] :
      ( ( ( A__questionmark_v0 = 'fun_app$aq'(A__questionmark_v1,A__questionmark_v2) )
        & $less(A__questionmark_v2,A__questionmark_v3)
        & ! [A__questionmark_v4: $int,A__questionmark_v5: $int] :
            ( $less(A__questionmark_v4,A__questionmark_v5)
           => $less('fun_app$aq'(A__questionmark_v1,A__questionmark_v4),'fun_app$aq'(A__questionmark_v1,A__questionmark_v5)) ) )
     => $less(A__questionmark_v0,'fun_app$aq'(A__questionmark_v1,A__questionmark_v3)) ) ).

%% ∀ ?v0:Int ?v1:Int ?v2:Int (((?v0 < ?v1) ∧ (?v1 < ?v2)) ⇒ (?v0 < ?v2))
tff(axiom785,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int,A__questionmark_v2: $int] :
      ( ( $less(A__questionmark_v0,A__questionmark_v1)
        & $less(A__questionmark_v1,A__questionmark_v2) )
     => $less(A__questionmark_v0,A__questionmark_v2) ) ).

%% ∀ ?v0:Int ?v1:Int (((?v0 < ?v1) ∧ (?v1 < ?v0)) ⇒ false)
tff(axiom786,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( ( $less(A__questionmark_v0,A__questionmark_v1)
        & $less(A__questionmark_v1,A__questionmark_v0) )
     => $false ) ).

%% ∀ ?v0:Int ?v1:Int (¬(?v0 = ?v1) = ((?v0 < ?v1) ∨ (?v1 < ?v0)))
tff(axiom787,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( ( A__questionmark_v0 != A__questionmark_v1 )
    <=> ( $less(A__questionmark_v0,A__questionmark_v1)
        | $less(A__questionmark_v1,A__questionmark_v0) ) ) ).

%% ∀ ?v0:Int ?v1:Int (((?v0 < ?v1) ∧ (¬false ⇒ (?v1 < ?v0))) ⇒ false)
tff(axiom788,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( ( $less(A__questionmark_v0,A__questionmark_v1)
        & $less(A__questionmark_v1,A__questionmark_v0) )
     => $false ) ).

%% ∀ ?v0:Int ?v1:Int ((¬(?v0 = ?v1) ∧ (((?v0 < ?v1) ⇒ false) ∧ ((?v1 < ?v0) ⇒ false))) ⇒ false)
tff(axiom789,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( ( ( A__questionmark_v0 != A__questionmark_v1 )
        & ( $less(A__questionmark_v0,A__questionmark_v1)
         => $false )
        & ( $less(A__questionmark_v1,A__questionmark_v0)
         => $false ) )
     => $false ) ).

%% ∀ ?v0:Int ?v1:Int ((?v0 < ?v1) ⇒ ¬(?v1 = ?v0))
tff(axiom790,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( $less(A__questionmark_v0,A__questionmark_v1)
     => ( A__questionmark_v1 != A__questionmark_v0 ) ) ).

%% ∀ ?v0:Int ?v1:Int ((?v0 < ?v1) ⇒ ¬(?v0 = ?v1))
tff(axiom791,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( $less(A__questionmark_v0,A__questionmark_v1)
     => ( A__questionmark_v0 != A__questionmark_v1 ) ) ).

%% ∀ ?v0:Int ?v1:Int ?v2:Int (((?v0 < ?v1) ∧ (?v2 < ?v0)) ⇒ (?v2 < ?v1))
tff(axiom792,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int,A__questionmark_v2: $int] :
      ( ( $less(A__questionmark_v0,A__questionmark_v1)
        & $less(A__questionmark_v2,A__questionmark_v0) )
     => $less(A__questionmark_v2,A__questionmark_v1) ) ).

%% ∀ ?v0:Int ?v1:Int (¬(?v0 < ?v1) = ((?v1 < ?v0) ∨ (?v0 = ?v1)))
tff(axiom793,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( ~ $less(A__questionmark_v0,A__questionmark_v1)
    <=> ( $less(A__questionmark_v1,A__questionmark_v0)
        | ( A__questionmark_v0 = A__questionmark_v1 ) ) ) ).

%% ∀ ?v0:Int ?v1:Int ?v2:Int (((?v0 < ?v1) ∧ (?v1 < ?v2)) ⇒ (?v0 < ?v2))
tff(axiom794,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int,A__questionmark_v2: $int] :
      ( ( $less(A__questionmark_v0,A__questionmark_v1)
        & $less(A__questionmark_v1,A__questionmark_v2) )
     => $less(A__questionmark_v0,A__questionmark_v2) ) ).

%% ∀ ?v0:Int_int_bool_fun_fun$ ?v1:Int ?v2:Int ((∀ ?v3:Int ?v4:Int ((?v3 < ?v4) ⇒ fun_app$bl(fun_app$bm(?v0, ?v3), ?v4)) ∧ (∀ ?v3:Int fun_app$bl(fun_app$bm(?v0, ?v3), ?v3) ∧ ∀ ?v3:Int ?v4:Int (fun_app$bl(fun_app$bm(?v0, ?v4), ?v3) ⇒ fun_app$bl(fun_app$bm(?v0, ?v3), ?v4)))) ⇒ fun_app$bl(fun_app$bm(?v0, ?v1), ?v2))
tff(axiom795,axiom,
    ! [A__questionmark_v0: 'Int_int_bool_fun_fun$',A__questionmark_v1: $int,A__questionmark_v2: $int] :
      ( ( ! [A__questionmark_v3: $int,A__questionmark_v4: $int] :
            ( $less(A__questionmark_v3,A__questionmark_v4)
           => 'fun_app$bl'('fun_app$bm'(A__questionmark_v0,A__questionmark_v3),A__questionmark_v4) )
        & ! [A__questionmark_v3: $int] : 'fun_app$bl'('fun_app$bm'(A__questionmark_v0,A__questionmark_v3),A__questionmark_v3)
        & ! [A__questionmark_v3: $int,A__questionmark_v4: $int] :
            ( 'fun_app$bl'('fun_app$bm'(A__questionmark_v0,A__questionmark_v4),A__questionmark_v3)
           => 'fun_app$bl'('fun_app$bm'(A__questionmark_v0,A__questionmark_v3),A__questionmark_v4) ) )
     => 'fun_app$bl'('fun_app$bm'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) ) ).

%% ∀ ?v0:Int ¬(?v0 < ?v0)
tff(axiom796,axiom,
    ! [A__questionmark_v0: $int] : ~ $less(A__questionmark_v0,A__questionmark_v0) ).

%% ∀ ?v0:Int ?v1:Int (((?v0 < ?v1) ∧ (?v1 < ?v0)) ⇒ false)
tff(axiom797,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( ( $less(A__questionmark_v0,A__questionmark_v1)
        & $less(A__questionmark_v1,A__questionmark_v0) )
     => $false ) ).

%% ∀ ?v0:Int ?v1:Int ((((?v0 < ?v1) ⇒ false) ∧ (((?v0 = ?v1) ⇒ false) ∧ ((?v1 < ?v0) ⇒ false))) ⇒ false)
tff(axiom798,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( ( ( $less(A__questionmark_v0,A__questionmark_v1)
         => $false )
        & ( ( A__questionmark_v0 = A__questionmark_v1 )
         => $false )
        & ( $less(A__questionmark_v1,A__questionmark_v0)
         => $false ) )
     => $false ) ).

%% ∀ ?v0:Int ?v1:Int (¬(?v0 < ?v1) ⇒ (¬(?v1 < ?v0) = (?v1 = ?v0)))
tff(axiom799,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( ~ $less(A__questionmark_v0,A__questionmark_v1)
     => ( ~ $less(A__questionmark_v1,A__questionmark_v0)
      <=> ( A__questionmark_v1 = A__questionmark_v0 ) ) ) ).

%% ∀ ?v0:Int ?v1:Int ?v2:Int (((?v0 < ?v1) ∧ (?v1 = ?v2)) ⇒ (?v0 < ?v2))
tff(axiom800,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int,A__questionmark_v2: $int] :
      ( ( $less(A__questionmark_v0,A__questionmark_v1)
        & ( A__questionmark_v1 = A__questionmark_v2 ) )
     => $less(A__questionmark_v0,A__questionmark_v2) ) ).

%% ∀ ?v0:Int ?v1:Int ?v2:Int (((?v0 = ?v1) ∧ (?v1 < ?v2)) ⇒ (?v0 < ?v2))
tff(axiom801,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int,A__questionmark_v2: $int] :
      ( ( ( A__questionmark_v0 = A__questionmark_v1 )
        & $less(A__questionmark_v1,A__questionmark_v2) )
     => $less(A__questionmark_v0,A__questionmark_v2) ) ).

%% ∀ ?v0:Int ?v1:Int (((?v0 < ?v1) ∧ (?v1 < ?v0)) ⇒ false)
tff(axiom802,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( ( $less(A__questionmark_v0,A__questionmark_v1)
        & $less(A__questionmark_v1,A__questionmark_v0) )
     => $false ) ).

%% ∀ ?v0:Int ?v1:Int ((?v0 < ?v1) ⇒ ¬(?v0 = ?v1))
tff(axiom803,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( $less(A__questionmark_v0,A__questionmark_v1)
     => ( A__questionmark_v0 != A__questionmark_v1 ) ) ).

%% ∀ ?v0:Int ∃ ?v1:Int (?v0 < ?v1)
tff(axiom804,axiom,
    ! [A__questionmark_v0: $int] :
    ? [A__questionmark_v1: $int] : $less(A__questionmark_v0,A__questionmark_v1) ).

%% ∀ ?v0:Int ∃ ?v1:Int (?v1 < ?v0)
tff(axiom805,axiom,
    ! [A__questionmark_v0: $int] :
    ? [A__questionmark_v1: $int] : $less(A__questionmark_v1,A__questionmark_v0) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A_n_vec$ (fun_app$b(fun_app$c(vector_scalar_mult$, fun_app$k(plus$a(?v0), ?v1)), ?v2) = fun_app$b(plus$(fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), ?v2)), fun_app$b(fun_app$c(vector_scalar_mult$, ?v1), ?v2)))
tff(axiom806,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A_n_vec$'] : 'fun_app$b'('fun_app$c'('vector_scalar_mult$','fun_app$k'('plus$a'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$b'('plus$'('fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),A__questionmark_v2)),'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A$ ?v1:A_n_vec$ ?v2:A_n_vec$ (fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), fun_app$b(plus$(?v1), ?v2)) = fun_app$b(plus$(fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), ?v1)), fun_app$b(fun_app$c(vector_scalar_mult$, ?v0), ?v2)))
tff(axiom807,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'A_n_vec$'] : 'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),'fun_app$b'('plus$'(A__questionmark_v1),A__questionmark_v2)) = 'fun_app$b'('plus$'('fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),A__questionmark_v1)),'fun_app$b'('fun_app$c'('vector_scalar_mult$',A__questionmark_v0),A__questionmark_v2)) ).

%% ∀ ?v0:N_set$ ¬less$a(top$, ?v0)
tff(axiom808,axiom,
    ! [A__questionmark_v0: 'N_set$'] : ~ 'less$a'('top$',A__questionmark_v0) ).

%% ∀ ?v0:N_set$ (¬(?v0 = top$) = less$a(?v0, top$))
tff(axiom809,axiom,
    ! [A__questionmark_v0: 'N_set$'] :
      ( ( A__questionmark_v0 != 'top$' )
    <=> 'less$a'(A__questionmark_v0,'top$') ) ).

%% ∀ ?v0:N_a_n_vec_fun$ ?v1:N_a_n_vec_fun$ ?v2:N_set$ (sum$(vdp$(?v0, ?v1), ?v2) = fun_app$b(plus$(sum$(?v0, ?v2)), sum$(?v1, ?v2)))
tff(axiom810,axiom,
    ! [A__questionmark_v0: 'N_a_n_vec_fun$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N_set$'] : 'sum$'('vdp$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$b'('plus$'('sum$'(A__questionmark_v0,A__questionmark_v2)),'sum$'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_a_fun$ ?v2:N_set$ (sum$a(vdq$(?v0, ?v1), ?v2) = fun_app$k(plus$a(sum$a(?v0, ?v2)), sum$a(?v1, ?v2)))
tff(axiom811,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N_set$'] : 'sum$a'('vdq$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$k'('plus$a'('sum$a'(A__questionmark_v0,A__questionmark_v2)),'sum$a'(A__questionmark_v1,A__questionmark_v2)) ).

%% ∀ ?v0:A_n_vec_a_n_vec_fun$ ?v1:A_n_vec$ ?v2:A_n_vec$ (linear$(vector_scalar_mult$, vector_scalar_mult$, ?v0) ⇒ (fun_app$b(?v0, fun_app$b(plus$(?v1), ?v2)) = fun_app$b(plus$(fun_app$b(?v0, ?v1)), fun_app$b(?v0, ?v2))))
tff(axiom812,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_n_vec_fun$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'A_n_vec$'] :
      ( 'linear$'('vector_scalar_mult$','vector_scalar_mult$',A__questionmark_v0)
     => ( 'fun_app$b'(A__questionmark_v0,'fun_app$b'('plus$'(A__questionmark_v1),A__questionmark_v2)) = 'fun_app$b'('plus$'('fun_app$b'(A__questionmark_v0,A__questionmark_v1)),'fun_app$b'(A__questionmark_v0,A__questionmark_v2)) ) ) ).

%% ∀ ?v0:A_n_vec_a_n_vec_fun$ (linear$(vector_scalar_mult$, vector_scalar_mult$, ?v0) ⇒ (fun_app$b(?v0, zero$) = zero$))
tff(axiom813,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_n_vec_fun$'] :
      ( 'linear$'('vector_scalar_mult$','vector_scalar_mult$',A__questionmark_v0)
     => ( 'fun_app$b'(A__questionmark_v0,'zero$') = 'zero$' ) ) ).

%% ∀ ?v0:A_n_vec_a_n_vec_fun$ ?v1:A_n_vec_a_n_vec_fun$ ((linear$(vector_scalar_mult$, vector_scalar_mult$, ?v0) ∧ linear$(vector_scalar_mult$, vector_scalar_mult$, ?v1)) ⇒ linear$(vector_scalar_mult$, vector_scalar_mult$, vdr$(?v0, ?v1)))
tff(axiom814,axiom,
    ! [A__questionmark_v0: 'A_n_vec_a_n_vec_fun$',A__questionmark_v1: 'A_n_vec_a_n_vec_fun$'] :
      ( ( 'linear$'('vector_scalar_mult$','vector_scalar_mult$',A__questionmark_v0)
        & 'linear$'('vector_scalar_mult$','vector_scalar_mult$',A__questionmark_v1) )
     => 'linear$'('vector_scalar_mult$','vector_scalar_mult$','vdr$'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:N_set$ ?v1:N_a_n_vec_fun$ ?v2:N_bool_fun$ (finite$(?v0) ⇒ (sum$(?v1, collect$(vds$(?v0, ?v2))) = sum$(vdt$(?v1, ?v2), ?v0)))
tff(axiom815,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_a_n_vec_fun$',A__questionmark_v2: 'N_bool_fun$'] :
      ( 'finite$'(A__questionmark_v0)
     => ( 'sum$'(A__questionmark_v1,'collect$'('vds$'(A__questionmark_v0,A__questionmark_v2))) = 'sum$'('vdt$'(A__questionmark_v1,A__questionmark_v2),A__questionmark_v0) ) ) ).

%% ∀ ?v0:N_set$ ?v1:N_a_fun$ ?v2:N_bool_fun$ (finite$(?v0) ⇒ (sum$a(?v1, collect$(vds$(?v0, ?v2))) = sum$a(vdu$(?v1, ?v2), ?v0)))
tff(axiom816,axiom,
    ! [A__questionmark_v0: 'N_set$',A__questionmark_v1: 'N_a_fun$',A__questionmark_v2: 'N_bool_fun$'] :
      ( 'finite$'(A__questionmark_v0)
     => ( 'sum$a'(A__questionmark_v1,'collect$'('vds$'(A__questionmark_v0,A__questionmark_v2))) = 'sum$a'('vdu$'(A__questionmark_v1,A__questionmark_v2),A__questionmark_v0) ) ) ).

%% ∀ ?v0:Nat_ennreal_fun$ ?v1:Nat_set$ ((prod$b(?v0, ?v1) = top$ae) = (finite$b(?v1) ∧ (∀ ?v2:Nat$ (member$a(?v2, ?v1) ⇒ ¬(fun_app$bi(?v0, ?v2) = zero$c)) ∧ ∃ ?v2:Nat$ (member$a(?v2, ?v1) ∧ (fun_app$bi(?v0, ?v2) = top$ae)))))
tff(axiom817,axiom,
    ! [A__questionmark_v0: 'Nat_ennreal_fun$',A__questionmark_v1: 'Nat_set$'] :
      ( ( 'prod$b'(A__questionmark_v0,A__questionmark_v1) = 'top$ae' )
    <=> ( 'finite$b'(A__questionmark_v1)
        & ! [A__questionmark_v2: 'Nat$'] :
            ( 'member$a'(A__questionmark_v2,A__questionmark_v1)
           => ( 'fun_app$bi'(A__questionmark_v0,A__questionmark_v2) != 'zero$c' ) )
        & ? [A__questionmark_v2: 'Nat$'] :
            ( 'member$a'(A__questionmark_v2,A__questionmark_v1)
            & ( 'fun_app$bi'(A__questionmark_v0,A__questionmark_v2) = 'top$ae' ) ) ) ) ).

%% linear$(vector_scalar_mult$, vector_scalar_mult$, vdv$)
tff(axiom818,axiom,
    'linear$'('vector_scalar_mult$','vector_scalar_mult$','vdv$') ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N_a_fun$ ((is_basis$(set_of_vector$(?v0)) ∧ (sum$(uvw$(?v0, ?v1), top$) = zero$)) ⇒ ∀ ?v2:N$ (member$f(?v2, top$) ⇒ (fun_app$d(?v1, ?v2) = zero$a)))
tff(axiom819,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N_a_fun$'] :
      ( ( 'is_basis$'('set_of_vector$'(A__questionmark_v0))
        & ( 'sum$'('uvw$'(A__questionmark_v0,A__questionmark_v1),'top$') = 'zero$' ) )
     => ! [A__questionmark_v2: 'N$'] :
          ( 'member$f'(A__questionmark_v2,'top$')
         => ( 'fun_app$d'(A__questionmark_v1,A__questionmark_v2) = 'zero$a' ) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ ?v3:A$ ?v4:N$ (fun_app$a(column_add_row$(?v0, ?v1, ?v2, ?v3), ?v4) = vec_lambda$(fun_app$e(vdw$(?v0, ?v1, ?v2, ?v3), ?v4)))
tff(axiom820,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$',A__questionmark_v3: 'A$',A__questionmark_v4: 'N$'] : 'fun_app$a'('column_add_row$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4) = 'vec_lambda$'('fun_app$e'('vdw$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ ?v3:A$ ?v4:N$ (fun_app$a(row_add_row$(?v0, ?v1, ?v2, ?v3), ?v4) = vec_lambda$(fun_app$e(vdx$(?v0, ?v1, ?v2, ?v3), ?v4)))
tff(axiom821,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$',A__questionmark_v3: 'A$',A__questionmark_v4: 'N$'] : 'fun_app$a'('row_add_row$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4) = 'vec_lambda$'('fun_app$e'('vdx$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ ((fun_app$k(fun_app$l(times$, ?v0), ?v1) = fun_app$k(fun_app$l(times$, ?v2), ?v1)) = ((?v1 = zero$a) ∨ (?v0 = ?v2)))
tff(axiom822,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1) = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v2),A__questionmark_v1) )
    <=> ( ( A__questionmark_v1 = 'zero$a' )
        | ( A__questionmark_v0 = A__questionmark_v2 ) ) ) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_nat_fun$ (finite$b(?v0) ⇒ ((0 < of_nat$(prod$c(?v1, ?v0))) = ∀ ?v2:Nat$ (member$a(?v2, ?v0) ⇒ (0 < of_nat$(fun_app$v(?v1, ?v2))))))
tff(axiom823,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_nat_fun$'] :
      ( 'finite$b'(A__questionmark_v0)
     => ( $less(0,'of_nat$'('prod$c'(A__questionmark_v1,A__questionmark_v0)))
      <=> ! [A__questionmark_v2: 'Nat$'] :
            ( 'member$a'(A__questionmark_v2,A__questionmark_v0)
           => $less(0,'of_nat$'('fun_app$v'(A__questionmark_v1,A__questionmark_v2))) ) ) ) ).

%% ∀ ?v0:A$ (fun_app$k(fun_app$l(times$, zero$a), ?v0) = zero$a)
tff(axiom824,axiom,
    ! [A__questionmark_v0: 'A$'] : 'fun_app$k'('fun_app$l'('times$','zero$a'),A__questionmark_v0) = 'zero$a' ).

%% ∀ ?v0:A$ (fun_app$k(fun_app$l(times$, ?v0), zero$a) = zero$a)
tff(axiom825,axiom,
    ! [A__questionmark_v0: 'A$'] : 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),'zero$a') = 'zero$a' ).

%% ∀ ?v0:A$ ?v1:A$ ((fun_app$k(fun_app$l(times$, ?v0), ?v1) = zero$a) = ((?v0 = zero$a) ∨ (?v1 = zero$a)))
tff(axiom826,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$'] :
      ( ( 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1) = 'zero$a' )
    <=> ( ( A__questionmark_v0 = 'zero$a' )
        | ( A__questionmark_v1 = 'zero$a' ) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ ((fun_app$k(fun_app$l(times$, ?v0), ?v1) = fun_app$k(fun_app$l(times$, ?v0), ?v2)) = ((?v0 = zero$a) ∨ (?v1 = ?v2)))
tff(axiom827,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1) = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2) )
    <=> ( ( A__questionmark_v0 = 'zero$a' )
        | ( A__questionmark_v1 = A__questionmark_v2 ) ) ) ).

%% ∀ ?v0:Nat_set$ ?v1:Nat_set$ ((finite$b(?v0) ∧ finite$b(?v1)) ⇒ finite$b(plus$c(?v0, ?v1)))
tff(axiom828,axiom,
    ! [A__questionmark_v0: 'Nat_set$',A__questionmark_v1: 'Nat_set$'] :
      ( ( 'finite$b'(A__questionmark_v0)
        & 'finite$b'(A__questionmark_v1) )
     => 'finite$b'('plus$c'(A__questionmark_v0,A__questionmark_v1)) ) ).

%% ∀ ?v0:A$ ?v1:A$ (¬(fun_app$k(fun_app$l(times$, ?v0), ?v1) = zero$a) ⇒ (¬(?v0 = zero$a) ∧ ¬(?v1 = zero$a)))
tff(axiom829,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$'] :
      ( ( 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1) != 'zero$a' )
     => ( ( A__questionmark_v0 != 'zero$a' )
        & ( A__questionmark_v1 != 'zero$a' ) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ((fun_app$k(fun_app$l(times$, ?v0), ?v1) = zero$a) ⇒ ((?v0 = zero$a) ∨ (?v1 = zero$a)))
tff(axiom830,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$'] :
      ( ( 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1) = 'zero$a' )
     => ( ( A__questionmark_v0 = 'zero$a' )
        | ( A__questionmark_v1 = 'zero$a' ) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ((¬(?v0 = zero$a) ∧ ¬(?v1 = zero$a)) ⇒ ¬(fun_app$k(fun_app$l(times$, ?v0), ?v1) = zero$a))
tff(axiom831,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$'] :
      ( ( ( A__questionmark_v0 != 'zero$a' )
        & ( A__questionmark_v1 != 'zero$a' ) )
     => ( 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1) != 'zero$a' ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (¬(?v0 = zero$a) ⇒ ((fun_app$k(fun_app$l(times$, ?v0), ?v1) = fun_app$k(fun_app$l(times$, ?v0), ?v2)) = (?v1 = ?v2)))
tff(axiom832,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( A__questionmark_v0 != 'zero$a' )
     => ( ( 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1) = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2) )
      <=> ( A__questionmark_v1 = A__questionmark_v2 ) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (¬(?v0 = zero$a) ⇒ ((fun_app$k(fun_app$l(times$, ?v1), ?v0) = fun_app$k(fun_app$l(times$, ?v2), ?v0)) = (?v1 = ?v2)))
tff(axiom833,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( A__questionmark_v0 != 'zero$a' )
     => ( ( 'fun_app$k'('fun_app$l'('times$',A__questionmark_v1),A__questionmark_v0) = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v2),A__questionmark_v0) )
      <=> ( A__questionmark_v1 = A__questionmark_v2 ) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (fun_app$k(fun_app$l(times$, fun_app$k(plus$a(?v0), ?v1)), ?v2) = fun_app$k(plus$a(fun_app$k(fun_app$l(times$, ?v0), ?v2)), fun_app$k(fun_app$l(times$, ?v1), ?v2)))
tff(axiom834,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] : 'fun_app$k'('fun_app$l'('times$','fun_app$k'('plus$a'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$k'('plus$a'('fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2)),'fun_app$k'('fun_app$l'('times$',A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (fun_app$k(fun_app$l(times$, ?v0), fun_app$k(plus$a(?v1), ?v2)) = fun_app$k(plus$a(fun_app$k(fun_app$l(times$, ?v0), ?v1)), fun_app$k(fun_app$l(times$, ?v0), ?v2)))
tff(axiom835,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] : 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),'fun_app$k'('plus$a'(A__questionmark_v1),A__questionmark_v2)) = 'fun_app$k'('plus$a'('fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1)),'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2)) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (fun_app$k(fun_app$l(times$, fun_app$k(plus$a(?v0), ?v1)), ?v2) = fun_app$k(plus$a(fun_app$k(fun_app$l(times$, ?v0), ?v2)), fun_app$k(fun_app$l(times$, ?v1), ?v2)))
tff(axiom836,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] : 'fun_app$k'('fun_app$l'('times$','fun_app$k'('plus$a'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$k'('plus$a'('fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2)),'fun_app$k'('fun_app$l'('times$',A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (fun_app$k(fun_app$l(times$, ?v0), fun_app$k(plus$a(?v1), ?v2)) = fun_app$k(plus$a(fun_app$k(fun_app$l(times$, ?v0), ?v1)), fun_app$k(fun_app$l(times$, ?v0), ?v2)))
tff(axiom837,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] : 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),'fun_app$k'('plus$a'(A__questionmark_v1),A__questionmark_v2)) = 'fun_app$k'('plus$a'('fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1)),'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2)) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (fun_app$k(fun_app$l(times$, fun_app$k(plus$a(?v0), ?v1)), ?v2) = fun_app$k(plus$a(fun_app$k(fun_app$l(times$, ?v0), ?v2)), fun_app$k(fun_app$l(times$, ?v1), ?v2)))
tff(axiom838,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] : 'fun_app$k'('fun_app$l'('times$','fun_app$k'('plus$a'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$k'('plus$a'('fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2)),'fun_app$k'('fun_app$l'('times$',A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ ?v3:A$ (fun_app$k(plus$a(fun_app$k(fun_app$l(times$, ?v0), ?v1)), fun_app$k(plus$a(fun_app$k(fun_app$l(times$, ?v2), ?v1)), ?v3)) = fun_app$k(plus$a(fun_app$k(fun_app$l(times$, fun_app$k(plus$a(?v0), ?v2)), ?v1)), ?v3))
tff(axiom839,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$',A__questionmark_v3: 'A$'] : 'fun_app$k'('plus$a'('fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1)),'fun_app$k'('plus$a'('fun_app$k'('fun_app$l'('times$',A__questionmark_v2),A__questionmark_v1)),A__questionmark_v3)) = 'fun_app$k'('plus$a'('fun_app$k'('fun_app$l'('times$','fun_app$k'('plus$a'(A__questionmark_v0),A__questionmark_v2)),A__questionmark_v1)),A__questionmark_v3) ).

%% (vdy$ = fun_app$l(times$, zero$a))
tff(axiom840,axiom,
    'vdy$' = 'fun_app$l'('times$','zero$a') ).

%% ∀ ?v0:Int ?v1:Int ?v2:Int (((?v0 < ?v1) ∧ (0 < ?v2)) ⇒ (fun_app$aq(times$d(?v2), ?v0) < fun_app$aq(times$d(?v2), ?v1)))
tff(axiom841,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int,A__questionmark_v2: $int] :
      ( ( $less(A__questionmark_v0,A__questionmark_v1)
        & $less(0,A__questionmark_v2) )
     => $less('fun_app$aq'('times$d'(A__questionmark_v2),A__questionmark_v0),'fun_app$aq'('times$d'(A__questionmark_v2),A__questionmark_v1)) ) ).

%% ∀ ?v0:Int ?v1:Int ?v2:Int ((fun_app$aq(times$d(?v0), ?v1) < fun_app$aq(times$d(?v2), ?v1)) = (((0 < ?v1) ∧ (?v0 < ?v2)) ∨ ((?v1 < 0) ∧ (?v2 < ?v0))))
tff(axiom842,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int,A__questionmark_v2: $int] :
      ( $less('fun_app$aq'('times$d'(A__questionmark_v0),A__questionmark_v1),'fun_app$aq'('times$d'(A__questionmark_v2),A__questionmark_v1))
    <=> ( ( $less(0,A__questionmark_v1)
          & $less(A__questionmark_v0,A__questionmark_v2) )
        | ( $less(A__questionmark_v1,0)
          & $less(A__questionmark_v2,A__questionmark_v0) ) ) ) ).

%% ∀ ?v0:Int ?v1:Int ?v2:Int (((?v0 < ?v1) ∧ (0 < ?v2)) ⇒ (fun_app$aq(times$d(?v0), ?v2) < fun_app$aq(times$d(?v1), ?v2)))
tff(axiom843,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int,A__questionmark_v2: $int] :
      ( ( $less(A__questionmark_v0,A__questionmark_v1)
        & $less(0,A__questionmark_v2) )
     => $less('fun_app$aq'('times$d'(A__questionmark_v0),A__questionmark_v2),'fun_app$aq'('times$d'(A__questionmark_v1),A__questionmark_v2)) ) ).

%% ∀ ?v0:Int ?v1:Int ?v2:Int (((?v0 < ?v1) ∧ (?v2 < 0)) ⇒ (fun_app$aq(times$d(?v1), ?v2) < fun_app$aq(times$d(?v0), ?v2)))
tff(axiom844,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int,A__questionmark_v2: $int] :
      ( ( $less(A__questionmark_v0,A__questionmark_v1)
        & $less(A__questionmark_v2,0) )
     => $less('fun_app$aq'('times$d'(A__questionmark_v1),A__questionmark_v2),'fun_app$aq'('times$d'(A__questionmark_v0),A__questionmark_v2)) ) ).

%% ∀ ?v0:Int ?v1:Int ?v2:Int ((fun_app$aq(times$d(?v0), ?v1) < fun_app$aq(times$d(?v0), ?v2)) = (((0 < ?v0) ∧ (?v1 < ?v2)) ∨ ((?v0 < 0) ∧ (?v2 < ?v1))))
tff(axiom845,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int,A__questionmark_v2: $int] :
      ( $less('fun_app$aq'('times$d'(A__questionmark_v0),A__questionmark_v1),'fun_app$aq'('times$d'(A__questionmark_v0),A__questionmark_v2))
    <=> ( ( $less(0,A__questionmark_v0)
          & $less(A__questionmark_v1,A__questionmark_v2) )
        | ( $less(A__questionmark_v0,0)
          & $less(A__questionmark_v2,A__questionmark_v1) ) ) ) ).

%% ∀ ?v0:Int ?v1:Int ?v2:Int (((?v0 < ?v1) ∧ (0 < ?v2)) ⇒ (fun_app$aq(times$d(?v2), ?v0) < fun_app$aq(times$d(?v2), ?v1)))
tff(axiom846,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int,A__questionmark_v2: $int] :
      ( ( $less(A__questionmark_v0,A__questionmark_v1)
        & $less(0,A__questionmark_v2) )
     => $less('fun_app$aq'('times$d'(A__questionmark_v2),A__questionmark_v0),'fun_app$aq'('times$d'(A__questionmark_v2),A__questionmark_v1)) ) ).

%% ∀ ?v0:Int ?v1:Int ?v2:Int (((?v0 < ?v1) ∧ (?v2 < 0)) ⇒ (fun_app$aq(times$d(?v2), ?v1) < fun_app$aq(times$d(?v2), ?v0)))
tff(axiom847,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int,A__questionmark_v2: $int] :
      ( ( $less(A__questionmark_v0,A__questionmark_v1)
        & $less(A__questionmark_v2,0) )
     => $less('fun_app$aq'('times$d'(A__questionmark_v2),A__questionmark_v1),'fun_app$aq'('times$d'(A__questionmark_v2),A__questionmark_v0)) ) ).

%% ∀ ?v0:Int ?v1:Int ?v2:Int ((0 < ?v0) ⇒ ((fun_app$aq(times$d(?v0), ?v1) < fun_app$aq(times$d(?v0), ?v2)) = (?v1 < ?v2)))
tff(axiom848,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int,A__questionmark_v2: $int] :
      ( $less(0,A__questionmark_v0)
     => ( $less('fun_app$aq'('times$d'(A__questionmark_v0),A__questionmark_v1),'fun_app$aq'('times$d'(A__questionmark_v0),A__questionmark_v2))
      <=> $less(A__questionmark_v1,A__questionmark_v2) ) ) ).

%% ∀ ?v0:Int ?v1:Int ?v2:Int ((?v0 < 0) ⇒ ((fun_app$aq(times$d(?v0), ?v1) < fun_app$aq(times$d(?v0), ?v2)) = (?v2 < ?v1)))
tff(axiom849,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int,A__questionmark_v2: $int] :
      ( $less(A__questionmark_v0,0)
     => ( $less('fun_app$aq'('times$d'(A__questionmark_v0),A__questionmark_v1),'fun_app$aq'('times$d'(A__questionmark_v0),A__questionmark_v2))
      <=> $less(A__questionmark_v2,A__questionmark_v1) ) ) ).

%% ∀ ?v0:Int ?v1:Int (((0 < fun_app$aq(times$d(?v0), ?v1)) ∧ (0 < ?v1)) ⇒ (0 < ?v0))
tff(axiom850,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( ( $less(0,'fun_app$aq'('times$d'(A__questionmark_v0),A__questionmark_v1))
        & $less(0,A__questionmark_v1) )
     => $less(0,A__questionmark_v0) ) ).

%% ∀ ?v0:Int ?v1:Int (((0 < fun_app$aq(times$d(?v0), ?v1)) ∧ (0 < ?v0)) ⇒ (0 < ?v1))
tff(axiom851,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( ( $less(0,'fun_app$aq'('times$d'(A__questionmark_v0),A__questionmark_v1))
        & $less(0,A__questionmark_v0) )
     => $less(0,A__questionmark_v1) ) ).

%% ∀ ?v0:Int ?v1:Int ((0 < fun_app$aq(times$d(?v0), ?v1)) = (((0 < ?v0) ∧ (0 < ?v1)) ∨ ((?v0 < 0) ∧ (?v1 < 0))))
tff(axiom852,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( $less(0,'fun_app$aq'('times$d'(A__questionmark_v0),A__questionmark_v1))
    <=> ( ( $less(0,A__questionmark_v0)
          & $less(0,A__questionmark_v1) )
        | ( $less(A__questionmark_v0,0)
          & $less(A__questionmark_v1,0) ) ) ) ).

%% ∀ ?v0:Int ?v1:Int (((0 < ?v0) ∧ (?v1 < 0)) ⇒ (fun_app$aq(times$d(?v1), ?v0) < 0))
tff(axiom853,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( ( $less(0,A__questionmark_v0)
        & $less(A__questionmark_v1,0) )
     => $less('fun_app$aq'('times$d'(A__questionmark_v1),A__questionmark_v0),0) ) ).

%% ∀ ?v0:Int ?v1:Int (((0 < ?v0) ∧ (0 < ?v1)) ⇒ (0 < fun_app$aq(times$d(?v0), ?v1)))
tff(axiom854,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( ( $less(0,A__questionmark_v0)
        & $less(0,A__questionmark_v1) )
     => $less(0,'fun_app$aq'('times$d'(A__questionmark_v0),A__questionmark_v1)) ) ).

%% ∀ ?v0:Int ?v1:Int (((0 < ?v0) ∧ (?v1 < 0)) ⇒ (fun_app$aq(times$d(?v0), ?v1) < 0))
tff(axiom855,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( ( $less(0,A__questionmark_v0)
        & $less(A__questionmark_v1,0) )
     => $less('fun_app$aq'('times$d'(A__questionmark_v0),A__questionmark_v1),0) ) ).

%% ∀ ?v0:Int ?v1:Int (((?v0 < 0) ∧ (0 < ?v1)) ⇒ (fun_app$aq(times$d(?v0), ?v1) < 0))
tff(axiom856,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( ( $less(A__questionmark_v0,0)
        & $less(0,A__questionmark_v1) )
     => $less('fun_app$aq'('times$d'(A__questionmark_v0),A__questionmark_v1),0) ) ).

%% ∀ ?v0:Int ?v1:Int ((fun_app$aq(times$d(?v0), ?v1) < 0) = (((0 < ?v0) ∧ (?v1 < 0)) ∨ ((?v0 < 0) ∧ (0 < ?v1))))
tff(axiom857,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( $less('fun_app$aq'('times$d'(A__questionmark_v0),A__questionmark_v1),0)
    <=> ( ( $less(0,A__questionmark_v0)
          & $less(A__questionmark_v1,0) )
        | ( $less(A__questionmark_v0,0)
          & $less(0,A__questionmark_v1) ) ) ) ).

%% ∀ ?v0:Int ¬(fun_app$aq(times$d(?v0), ?v0) < 0)
tff(axiom858,axiom,
    ! [A__questionmark_v0: $int] : ~ $less('fun_app$aq'('times$d'(A__questionmark_v0),A__questionmark_v0),0) ).

%% ∀ ?v0:Int ?v1:Int (((?v0 < 0) ∧ (?v1 < 0)) ⇒ (0 < fun_app$aq(times$d(?v0), ?v1)))
tff(axiom859,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( ( $less(A__questionmark_v0,0)
        & $less(A__questionmark_v1,0) )
     => $less(0,'fun_app$aq'('times$d'(A__questionmark_v0),A__questionmark_v1)) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ ?v3:A$ ?v4:N$ ?v5:N$ (fun_app$d(vec_nth$a(fun_app$a(row_add_row$(?v0, ?v1, ?v2, ?v3), ?v4)), ?v5) = (if (?v4 = ?v1) fun_app$k(plus$a(fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v1)), ?v5)), fun_app$k(fun_app$l(times$, ?v3), fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v2)), ?v5))) else fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v4)), ?v5)))
tff(axiom860,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$',A__questionmark_v3: 'A$',A__questionmark_v4: 'N$',A__questionmark_v5: 'N$'] :
      ( ( ( A__questionmark_v4 = A__questionmark_v1 )
       => ( 'fun_app$d'('vec_nth$a'('fun_app$a'('row_add_row$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)),A__questionmark_v5) = 'fun_app$k'('plus$a'('fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v5)),'fun_app$k'('fun_app$l'('times$',A__questionmark_v3),'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v2)),A__questionmark_v5))) ) )
      & ( ( A__questionmark_v4 != A__questionmark_v1 )
       => ( 'fun_app$d'('vec_nth$a'('fun_app$a'('row_add_row$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)),A__questionmark_v5) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v4)),A__questionmark_v5) ) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ ?v3:A$ ?v4:N$ ?v5:N$ (fun_app$d(vec_nth$a(fun_app$a(column_add_row$(?v0, ?v1, ?v2, ?v3), ?v4)), ?v5) = (if (?v5 = ?v1) fun_app$k(plus$a(fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v4)), ?v1)), fun_app$k(fun_app$l(times$, fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v4)), ?v2)), ?v3)) else fun_app$d(vec_nth$a(fun_app$a(vec_nth$(?v0), ?v4)), ?v5)))
tff(axiom861,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$',A__questionmark_v3: 'A$',A__questionmark_v4: 'N$',A__questionmark_v5: 'N$'] :
      ( ( ( A__questionmark_v5 = A__questionmark_v1 )
       => ( 'fun_app$d'('vec_nth$a'('fun_app$a'('column_add_row$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)),A__questionmark_v5) = 'fun_app$k'('plus$a'('fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v4)),A__questionmark_v1)),'fun_app$k'('fun_app$l'('times$','fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v4)),A__questionmark_v2)),A__questionmark_v3)) ) )
      & ( ( A__questionmark_v5 != A__questionmark_v1 )
       => ( 'fun_app$d'('vec_nth$a'('fun_app$a'('column_add_row$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3),A__questionmark_v4)),A__questionmark_v5) = 'fun_app$d'('vec_nth$a'('fun_app$a'('vec_nth$'(A__questionmark_v0),A__questionmark_v4)),A__questionmark_v5) ) ) ) ).

%% ∀ ?v0:Int ?v1:Int ((0 < (fun_app$aq(times$d(?v0), ?v0) + fun_app$aq(times$d(?v1), ?v1))) = (¬(?v0 = 0) ∨ ¬(?v1 = 0)))
tff(axiom862,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] :
      ( $less(0,$sum('fun_app$aq'('times$d'(A__questionmark_v0),A__questionmark_v0),'fun_app$aq'('times$d'(A__questionmark_v1),A__questionmark_v1)))
    <=> ( ( A__questionmark_v0 != 0 )
        | ( A__questionmark_v1 != 0 ) ) ) ).

%% ∀ ?v0:Int ?v1:Int ¬((fun_app$aq(times$d(?v0), ?v0) + fun_app$aq(times$d(?v1), ?v1)) < 0)
tff(axiom863,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int] : ~ $less($sum('fun_app$aq'('times$d'(A__questionmark_v0),A__questionmark_v0),'fun_app$aq'('times$d'(A__questionmark_v1),A__questionmark_v1)),0) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ ?v3:A$ (fun_app$be(column_add$(?v0, ?v1, ?v2), ?v3) = vec_lambda$a(vdz$(?v0, ?v1, ?v2, ?v3)))
tff(axiom864,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$',A__questionmark_v3: 'A$'] : 'fun_app$be'('column_add$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'vec_lambda$a'('vdz$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3)) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ ?v3:A$ (fun_app$be(row_add$(?v0, ?v1, ?v2), ?v3) = vec_lambda$a(vea$(?v0, ?v1, ?v2, ?v3)))
tff(axiom865,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$',A__questionmark_v3: 'A$'] : 'fun_app$be'('row_add$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3) = 'vec_lambda$a'('vea$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3)) ).

%% ∀ ?v0:Nat$ finite$b(collect$a(fun_app$n(veb$, ?v0)))
tff(axiom866,axiom,
    ! [A__questionmark_v0: 'Nat$'] : 'finite$b'('collect$a'('fun_app$n'('veb$',A__questionmark_v0))) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ ?v3:A$ (vec_nth$(fun_app$be(row_add$(?v0, ?v1, ?v2), ?v3)) = row_add_row$(?v0, ?v1, ?v2, ?v3))
tff(axiom867,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$',A__questionmark_v3: 'A$'] : 'vec_nth$'('fun_app$be'('row_add$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3)) = 'row_add_row$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:N$ ?v2:N$ ?v3:A$ (vec_nth$(fun_app$be(column_add$(?v0, ?v1, ?v2), ?v3)) = column_add_row$(?v0, ?v1, ?v2, ?v3))
tff(axiom868,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$',A__questionmark_v3: 'A$'] : 'vec_nth$'('fun_app$be'('column_add$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2),A__questionmark_v3)) = 'column_add_row$'(A__questionmark_v0,A__questionmark_v1,A__questionmark_v2,A__questionmark_v3) ).

%% ∀ ?v0:Nat_nat_fun$ ?v1:Nat_bool_fun$ (finite$b(collect$a(vec$(?v0))) ⇒ finite$b(collect$a(ved$(?v0, ?v1))))
tff(axiom869,axiom,
    ! [A__questionmark_v0: 'Nat_nat_fun$',A__questionmark_v1: 'Nat_bool_fun$'] :
      ( 'finite$b'('collect$a'('vec$'(A__questionmark_v0)))
     => 'finite$b'('collect$a'('ved$'(A__questionmark_v0,A__questionmark_v1))) ) ).

%% ∀ ?v0:A_n_vec$ ?v1:N$ ?v2:N$ (fun_app$a(vec_nth$(fun_app$f(mat_row$(?v0), ?v1)), ?v2) = (if (?v1 = ?v2) ?v0 else zero$))
tff(axiom870,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] :
      ( ( ( A__questionmark_v1 = A__questionmark_v2 )
       => ( 'fun_app$a'('vec_nth$'('fun_app$f'('mat_row$'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = A__questionmark_v0 ) )
      & ( ( A__questionmark_v1 != A__questionmark_v2 )
       => ( 'fun_app$a'('vec_nth$'('fun_app$f'('mat_row$'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'zero$' ) ) ) ).

%% ∀ ?v0:A$ ?v1:N$ ?v2:N$ (fun_app$d(vec_nth$a(fun_app$a(mat_row$a(?v0), ?v1)), ?v2) = (if (?v1 = ?v2) ?v0 else zero$a))
tff(axiom871,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'N$',A__questionmark_v2: 'N$'] :
      ( ( ( A__questionmark_v1 = A__questionmark_v2 )
       => ( 'fun_app$d'('vec_nth$a'('fun_app$a'('mat_row$a'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = A__questionmark_v0 ) )
      & ( ( A__questionmark_v1 != A__questionmark_v2 )
       => ( 'fun_app$d'('vec_nth$a'('fun_app$a'('mat_row$a'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'zero$a' ) ) ) ).

%% ∀ ?v0:Int ?v1:Int ?v2:Int ((0 < ?v0) ⇒ ((fun_app$aq(times$d(?v1), ?v0) < fun_app$aq(times$d(?v2), ?v0)) = (?v1 < ?v2)))
tff(axiom872,axiom,
    ! [A__questionmark_v0: $int,A__questionmark_v1: $int,A__questionmark_v2: $int] :
      ( $less(0,A__questionmark_v0)
     => ( $less('fun_app$aq'('times$d'(A__questionmark_v1),A__questionmark_v0),'fun_app$aq'('times$d'(A__questionmark_v2),A__questionmark_v0))
      <=> $less(A__questionmark_v1,A__questionmark_v2) ) ) ).

%% ∀ ?v0:A_n_vec_n_vec$ ?v1:A_n_vec$ ?v2:A_n_vec$ (¬(fun_app$w(det$, ?v0) = zero$a) ⇒ ((fun_app$b(matrix_vector_mult$(?v0), ?v1) = ?v2) = (?v1 = vec_lambda$(veg$(?v0, ?v2)))))
tff(axiom873,axiom,
    ! [A__questionmark_v0: 'A_n_vec_n_vec$',A__questionmark_v1: 'A_n_vec$',A__questionmark_v2: 'A_n_vec$'] :
      ( ( 'fun_app$w'('det$',A__questionmark_v0) != 'zero$a' )
     => ( ( 'fun_app$b'('matrix_vector_mult$'(A__questionmark_v0),A__questionmark_v1) = A__questionmark_v2 )
      <=> ( A__questionmark_v1 = 'vec_lambda$'('veg$'(A__questionmark_v0,A__questionmark_v2)) ) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ (¬(?v0 = zero$a) ⇒ (fun_app$k(divide$(fun_app$k(fun_app$l(times$, ?v0), ?v1)), ?v0) = ?v1))
tff(axiom874,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$'] :
      ( ( A__questionmark_v0 != 'zero$a' )
     => ( 'fun_app$k'('divide$'('fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1)),A__questionmark_v0) = A__questionmark_v1 ) ) ).

%% ∀ ?v0:A$ ?v1:A$ (¬(?v0 = zero$a) ⇒ (fun_app$k(divide$(fun_app$k(fun_app$l(times$, ?v1), ?v0)), ?v0) = ?v1))
tff(axiom875,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$'] :
      ( ( A__questionmark_v0 != 'zero$a' )
     => ( 'fun_app$k'('divide$'('fun_app$k'('fun_app$l'('times$',A__questionmark_v1),A__questionmark_v0)),A__questionmark_v0) = A__questionmark_v1 ) ) ).

%% ∀ ?v0:N_a_fun$ ?v1:N_set$ ?v2:A$ (fun_app$k(divide$(sum$a(?v0, ?v1)), ?v2) = sum$a(veh$(?v0, ?v2), ?v1))
tff(axiom876,axiom,
    ! [A__questionmark_v0: 'N_a_fun$',A__questionmark_v1: 'N_set$',A__questionmark_v2: 'A$'] : 'fun_app$k'('divide$'('sum$a'(A__questionmark_v0,A__questionmark_v1)),A__questionmark_v2) = 'sum$a'('veh$'(A__questionmark_v0,A__questionmark_v2),A__questionmark_v1) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (¬(?v0 = zero$a) ⇒ (fun_app$k(divide$(fun_app$k(fun_app$l(times$, ?v1), ?v0)), fun_app$k(fun_app$l(times$, ?v0), ?v2)) = fun_app$k(divide$(?v1), ?v2)))
tff(axiom877,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( A__questionmark_v0 != 'zero$a' )
     => ( 'fun_app$k'('divide$'('fun_app$k'('fun_app$l'('times$',A__questionmark_v1),A__questionmark_v0)),'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2)) = 'fun_app$k'('divide$'(A__questionmark_v1),A__questionmark_v2) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (¬(?v0 = zero$a) ⇒ (fun_app$k(divide$(fun_app$k(fun_app$l(times$, ?v1), ?v0)), fun_app$k(fun_app$l(times$, ?v2), ?v0)) = fun_app$k(divide$(?v1), ?v2)))
tff(axiom878,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( A__questionmark_v0 != 'zero$a' )
     => ( 'fun_app$k'('divide$'('fun_app$k'('fun_app$l'('times$',A__questionmark_v1),A__questionmark_v0)),'fun_app$k'('fun_app$l'('times$',A__questionmark_v2),A__questionmark_v0)) = 'fun_app$k'('divide$'(A__questionmark_v1),A__questionmark_v2) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (fun_app$k(fun_app$l(times$, fun_app$k(divide$(?v0), ?v1)), ?v2) = fun_app$k(divide$(fun_app$k(fun_app$l(times$, ?v0), ?v2)), ?v1))
tff(axiom879,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] : 'fun_app$k'('fun_app$l'('times$','fun_app$k'('divide$'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$k'('divide$'('fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (fun_app$k(divide$(fun_app$k(divide$(?v0), ?v1)), ?v2) = fun_app$k(divide$(?v0), fun_app$k(fun_app$l(times$, ?v1), ?v2)))
tff(axiom880,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] : 'fun_app$k'('divide$'('fun_app$k'('divide$'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$k'('divide$'(A__questionmark_v0),'fun_app$k'('fun_app$l'('times$',A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (fun_app$k(divide$(?v0), fun_app$k(divide$(?v1), ?v2)) = fun_app$k(divide$(fun_app$k(fun_app$l(times$, ?v0), ?v2)), ?v1))
tff(axiom881,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] : 'fun_app$k'('divide$'(A__questionmark_v0),'fun_app$k'('divide$'(A__questionmark_v1),A__questionmark_v2)) = 'fun_app$k'('divide$'('fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2)),A__questionmark_v1) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (fun_app$k(fun_app$l(times$, ?v0), fun_app$k(divide$(?v1), ?v2)) = fun_app$k(divide$(fun_app$k(fun_app$l(times$, ?v0), ?v1)), ?v2))
tff(axiom882,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] : 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),'fun_app$k'('divide$'(A__questionmark_v1),A__questionmark_v2)) = 'fun_app$k'('divide$'('fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (fun_app$k(divide$(fun_app$k(fun_app$l(times$, ?v0), ?v1)), fun_app$k(fun_app$l(times$, ?v0), ?v2)) = (if (?v0 = zero$a) zero$a else fun_app$k(divide$(?v1), ?v2)))
tff(axiom883,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( ( A__questionmark_v0 = 'zero$a' )
       => ( 'fun_app$k'('divide$'('fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1)),'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2)) = 'zero$a' ) )
      & ( ( A__questionmark_v0 != 'zero$a' )
       => ( 'fun_app$k'('divide$'('fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1)),'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2)) = 'fun_app$k'('divide$'(A__questionmark_v1),A__questionmark_v2) ) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (¬(?v0 = zero$a) ⇒ (fun_app$k(divide$(fun_app$k(fun_app$l(times$, ?v0), ?v1)), fun_app$k(fun_app$l(times$, ?v0), ?v2)) = fun_app$k(divide$(?v1), ?v2)))
tff(axiom884,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( A__questionmark_v0 != 'zero$a' )
     => ( 'fun_app$k'('divide$'('fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1)),'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2)) = 'fun_app$k'('divide$'(A__questionmark_v1),A__questionmark_v2) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (¬(?v0 = zero$a) ⇒ (fun_app$k(divide$(fun_app$k(fun_app$l(times$, ?v0), ?v1)), fun_app$k(fun_app$l(times$, ?v2), ?v0)) = fun_app$k(divide$(?v1), ?v2)))
tff(axiom885,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( A__questionmark_v0 != 'zero$a' )
     => ( 'fun_app$k'('divide$'('fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1)),'fun_app$k'('fun_app$l'('times$',A__questionmark_v2),A__questionmark_v0)) = 'fun_app$k'('divide$'(A__questionmark_v1),A__questionmark_v2) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ ?v3:A$ (fun_app$k(fun_app$l(times$, fun_app$k(divide$(?v0), ?v1)), fun_app$k(divide$(?v2), ?v3)) = fun_app$k(divide$(fun_app$k(fun_app$l(times$, ?v0), ?v2)), fun_app$k(fun_app$l(times$, ?v1), ?v3)))
tff(axiom886,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$',A__questionmark_v3: 'A$'] : 'fun_app$k'('fun_app$l'('times$','fun_app$k'('divide$'(A__questionmark_v0),A__questionmark_v1)),'fun_app$k'('divide$'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$k'('divide$'('fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2)),'fun_app$k'('fun_app$l'('times$',A__questionmark_v1),A__questionmark_v3)) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ ?v3:A$ (fun_app$k(divide$(fun_app$k(divide$(?v0), ?v1)), fun_app$k(divide$(?v2), ?v3)) = fun_app$k(divide$(fun_app$k(fun_app$l(times$, ?v0), ?v3)), fun_app$k(fun_app$l(times$, ?v1), ?v2)))
tff(axiom887,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$',A__questionmark_v3: 'A$'] : 'fun_app$k'('divide$'('fun_app$k'('divide$'(A__questionmark_v0),A__questionmark_v1)),'fun_app$k'('divide$'(A__questionmark_v2),A__questionmark_v3)) = 'fun_app$k'('divide$'('fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v3)),'fun_app$k'('fun_app$l'('times$',A__questionmark_v1),A__questionmark_v2)) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (fun_app$k(divide$(fun_app$k(divide$(?v0), ?v1)), ?v2) = fun_app$k(divide$(?v0), fun_app$k(fun_app$l(times$, ?v2), ?v1)))
tff(axiom888,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] : 'fun_app$k'('divide$'('fun_app$k'('divide$'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$k'('divide$'(A__questionmark_v0),'fun_app$k'('fun_app$l'('times$',A__questionmark_v2),A__questionmark_v1)) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ ?v3:A$ ((¬(?v0 = zero$a) ∧ ¬(?v1 = zero$a)) ⇒ ((fun_app$k(divide$(?v2), ?v0) = fun_app$k(divide$(?v3), ?v1)) = (fun_app$k(fun_app$l(times$, ?v2), ?v1) = fun_app$k(fun_app$l(times$, ?v3), ?v0))))
tff(axiom889,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$',A__questionmark_v3: 'A$'] :
      ( ( ( A__questionmark_v0 != 'zero$a' )
        & ( A__questionmark_v1 != 'zero$a' ) )
     => ( ( 'fun_app$k'('divide$'(A__questionmark_v2),A__questionmark_v0) = 'fun_app$k'('divide$'(A__questionmark_v3),A__questionmark_v1) )
      <=> ( 'fun_app$k'('fun_app$l'('times$',A__questionmark_v2),A__questionmark_v1) = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v3),A__questionmark_v0) ) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ ((fun_app$k(divide$(?v0), ?v1) = ?v2) = (if ¬(?v1 = zero$a) (?v0 = fun_app$k(fun_app$l(times$, ?v2), ?v1)) else (?v2 = zero$a)))
tff(axiom890,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( 'fun_app$k'('divide$'(A__questionmark_v0),A__questionmark_v1) = A__questionmark_v2 )
    <=> ( ( ( A__questionmark_v1 != 'zero$a' )
         => ( A__questionmark_v0 = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v2),A__questionmark_v1) ) )
        & ( ~ ( ( A__questionmark_v1 != 'zero$a' ) )
         => ( A__questionmark_v2 = 'zero$a' ) ) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ ((?v0 = fun_app$k(divide$(?v1), ?v2)) = (if ¬(?v2 = zero$a) (fun_app$k(fun_app$l(times$, ?v0), ?v2) = ?v1) else (?v0 = zero$a)))
tff(axiom891,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( A__questionmark_v0 = 'fun_app$k'('divide$'(A__questionmark_v1),A__questionmark_v2) )
    <=> ( ( ( A__questionmark_v2 != 'zero$a' )
         => ( 'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2) = A__questionmark_v1 ) )
        & ( ~ ( ( A__questionmark_v2 != 'zero$a' ) )
         => ( A__questionmark_v0 = 'zero$a' ) ) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ ((¬(?v0 = zero$a) ∧ (?v1 = fun_app$k(fun_app$l(times$, ?v2), ?v0))) ⇒ (fun_app$k(divide$(?v1), ?v0) = ?v2))
tff(axiom892,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( ( A__questionmark_v0 != 'zero$a' )
        & ( A__questionmark_v1 = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v2),A__questionmark_v0) ) )
     => ( 'fun_app$k'('divide$'(A__questionmark_v1),A__questionmark_v0) = A__questionmark_v2 ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ ((¬(?v0 = zero$a) ∧ (fun_app$k(fun_app$l(times$, ?v1), ?v0) = ?v2)) ⇒ (?v1 = fun_app$k(divide$(?v2), ?v0)))
tff(axiom893,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( ( A__questionmark_v0 != 'zero$a' )
        & ( 'fun_app$k'('fun_app$l'('times$',A__questionmark_v1),A__questionmark_v0) = A__questionmark_v2 ) )
     => ( A__questionmark_v1 = 'fun_app$k'('divide$'(A__questionmark_v2),A__questionmark_v0) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (¬(?v0 = zero$a) ⇒ ((fun_app$k(divide$(?v1), ?v0) = ?v2) = (?v1 = fun_app$k(fun_app$l(times$, ?v2), ?v0))))
tff(axiom894,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( A__questionmark_v0 != 'zero$a' )
     => ( ( 'fun_app$k'('divide$'(A__questionmark_v1),A__questionmark_v0) = A__questionmark_v2 )
      <=> ( A__questionmark_v1 = 'fun_app$k'('fun_app$l'('times$',A__questionmark_v2),A__questionmark_v0) ) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (¬(?v0 = zero$a) ⇒ ((?v1 = fun_app$k(divide$(?v2), ?v0)) = (fun_app$k(fun_app$l(times$, ?v1), ?v0) = ?v2)))
tff(axiom895,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( A__questionmark_v0 != 'zero$a' )
     => ( ( A__questionmark_v1 = 'fun_app$k'('divide$'(A__questionmark_v2),A__questionmark_v0) )
      <=> ( 'fun_app$k'('fun_app$l'('times$',A__questionmark_v1),A__questionmark_v0) = A__questionmark_v2 ) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (¬(?v0 = zero$a) ⇒ (fun_app$k(plus$a(fun_app$k(divide$(?v1), ?v0)), ?v2) = fun_app$k(divide$(fun_app$k(plus$a(?v1), fun_app$k(fun_app$l(times$, ?v2), ?v0))), ?v0)))
tff(axiom896,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( A__questionmark_v0 != 'zero$a' )
     => ( 'fun_app$k'('plus$a'('fun_app$k'('divide$'(A__questionmark_v1),A__questionmark_v0)),A__questionmark_v2) = 'fun_app$k'('divide$'('fun_app$k'('plus$a'(A__questionmark_v1),'fun_app$k'('fun_app$l'('times$',A__questionmark_v2),A__questionmark_v0))),A__questionmark_v0) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (¬(?v0 = zero$a) ⇒ (fun_app$k(plus$a(?v1), fun_app$k(divide$(?v2), ?v0)) = fun_app$k(divide$(fun_app$k(plus$a(fun_app$k(fun_app$l(times$, ?v1), ?v0)), ?v2)), ?v0)))
tff(axiom897,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( A__questionmark_v0 != 'zero$a' )
     => ( 'fun_app$k'('plus$a'(A__questionmark_v1),'fun_app$k'('divide$'(A__questionmark_v2),A__questionmark_v0)) = 'fun_app$k'('divide$'('fun_app$k'('plus$a'('fun_app$k'('fun_app$l'('times$',A__questionmark_v1),A__questionmark_v0)),A__questionmark_v2)),A__questionmark_v0) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (¬(?v0 = zero$a) ⇒ (fun_app$k(plus$a(?v1), fun_app$k(divide$(?v2), ?v0)) = fun_app$k(divide$(fun_app$k(plus$a(?v2), fun_app$k(fun_app$l(times$, ?v1), ?v0))), ?v0)))
tff(axiom898,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( A__questionmark_v0 != 'zero$a' )
     => ( 'fun_app$k'('plus$a'(A__questionmark_v1),'fun_app$k'('divide$'(A__questionmark_v2),A__questionmark_v0)) = 'fun_app$k'('divide$'('fun_app$k'('plus$a'(A__questionmark_v2),'fun_app$k'('fun_app$l'('times$',A__questionmark_v1),A__questionmark_v0))),A__questionmark_v0) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (¬(?v0 = zero$a) ⇒ (fun_app$k(plus$a(fun_app$k(divide$(?v1), ?v0)), ?v2) = fun_app$k(divide$(fun_app$k(plus$a(?v1), fun_app$k(fun_app$l(times$, ?v2), ?v0))), ?v0)))
tff(axiom899,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( A__questionmark_v0 != 'zero$a' )
     => ( 'fun_app$k'('plus$a'('fun_app$k'('divide$'(A__questionmark_v1),A__questionmark_v0)),A__questionmark_v2) = 'fun_app$k'('divide$'('fun_app$k'('plus$a'(A__questionmark_v1),'fun_app$k'('fun_app$l'('times$',A__questionmark_v2),A__questionmark_v0))),A__questionmark_v0) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ ?v3:A$ ((¬(?v0 = zero$a) ∧ ¬(?v1 = zero$a)) ⇒ (fun_app$k(plus$a(fun_app$k(divide$(?v2), ?v0)), fun_app$k(divide$(?v3), ?v1)) = fun_app$k(divide$(fun_app$k(plus$a(fun_app$k(fun_app$l(times$, ?v2), ?v1)), fun_app$k(fun_app$l(times$, ?v3), ?v0))), fun_app$k(fun_app$l(times$, ?v0), ?v1))))
tff(axiom900,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$',A__questionmark_v3: 'A$'] :
      ( ( ( A__questionmark_v0 != 'zero$a' )
        & ( A__questionmark_v1 != 'zero$a' ) )
     => ( 'fun_app$k'('plus$a'('fun_app$k'('divide$'(A__questionmark_v2),A__questionmark_v0)),'fun_app$k'('divide$'(A__questionmark_v3),A__questionmark_v1)) = 'fun_app$k'('divide$'('fun_app$k'('plus$a'('fun_app$k'('fun_app$l'('times$',A__questionmark_v2),A__questionmark_v1)),'fun_app$k'('fun_app$l'('times$',A__questionmark_v3),A__questionmark_v0))),'fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v1)) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (fun_app$k(plus$a(?v0), fun_app$k(divide$(?v1), ?v2)) = (if (?v2 = zero$a) ?v0 else fun_app$k(divide$(fun_app$k(plus$a(fun_app$k(fun_app$l(times$, ?v0), ?v2)), ?v1)), ?v2)))
tff(axiom901,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( ( A__questionmark_v2 = 'zero$a' )
       => ( 'fun_app$k'('plus$a'(A__questionmark_v0),'fun_app$k'('divide$'(A__questionmark_v1),A__questionmark_v2)) = A__questionmark_v0 ) )
      & ( ( A__questionmark_v2 != 'zero$a' )
       => ( 'fun_app$k'('plus$a'(A__questionmark_v0),'fun_app$k'('divide$'(A__questionmark_v1),A__questionmark_v2)) = 'fun_app$k'('divide$'('fun_app$k'('plus$a'('fun_app$k'('fun_app$l'('times$',A__questionmark_v0),A__questionmark_v2)),A__questionmark_v1)),A__questionmark_v2) ) ) ) ).

%% ∀ ?v0:A$ ?v1:A$ ?v2:A$ (fun_app$k(plus$a(fun_app$k(divide$(?v0), ?v1)), ?v2) = (if (?v1 = zero$a) ?v2 else fun_app$k(divide$(fun_app$k(plus$a(?v0), fun_app$k(fun_app$l(times$, ?v2), ?v1))), ?v1)))
tff(axiom902,axiom,
    ! [A__questionmark_v0: 'A$',A__questionmark_v1: 'A$',A__questionmark_v2: 'A$'] :
      ( ( ( A__questionmark_v1 = 'zero$a' )
       => ( 'fun_app$k'('plus$a'('fun_app$k'('divide$'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = A__questionmark_v2 ) )
      & ( ( A__questionmark_v1 != 'zero$a' )
       => ( 'fun_app$k'('plus$a'('fun_app$k'('divide$'(A__questionmark_v0),A__questionmark_v1)),A__questionmark_v2) = 'fun_app$k'('divide$'('fun_app$k'('plus$a'(A__questionmark_v0),'fun_app$k'('fun_app$l'('times$',A__questionmark_v2),A__questionmark_v1))),A__questionmark_v1) ) ) ) ).

%% ∀ ?v0:Nat_a_fun$ ?v1:Nat_a_fun$ ?v2:Nat_set$ (sum$d(vei$(?v0, ?v1), ?v2) = (if (finite$b(?v2) ∧ member$a(nat$(0), ?v2)) fun_app$k(divide$(fun_app$aa(?v0, nat$(0))), fun_app$aa(?v1, nat$(0))) else zero$a))
tff(axiom903,axiom,
    ! [A__questionmark_v0: 'Nat_a_fun$',A__questionmark_v1: 'Nat_a_fun$',A__questionmark_v2: 'Nat_set$'] :
      ( ( ( 'finite$b'(A__questionmark_v2)
          & 'member$a'('nat$'(0),A__questionmark_v2) )
       => ( 'sum$d'('vei$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'fun_app$k'('divide$'('fun_app$aa'(A__questionmark_v0,'nat$'(0))),'fun_app$aa'(A__questionmark_v1,'nat$'(0))) ) )
      & ( ~ ( 'finite$b'(A__questionmark_v2)
            & 'member$a'('nat$'(0),A__questionmark_v2) )
       => ( 'sum$d'('vei$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2) = 'zero$a' ) ) ) ).

%% ∀ ?v0:A_n_vec$ ?v1:A_n_vec_n_vec$ ?v2:N$ (member$(?v0, span$(vector_scalar_mult$, collect$d(fun_app$as(vej$(?v1), ?v2)))) ⇒ (fun_app$w(det$, vec_lambda$a(fun_app$z(vek$(?v0, ?v1), ?v2))) = fun_app$w(det$, ?v1)))
tff(axiom904,axiom,
    ! [A__questionmark_v0: 'A_n_vec$',A__questionmark_v1: 'A_n_vec_n_vec$',A__questionmark_v2: 'N$'] :
      ( 'member$'(A__questionmark_v0,'span$'('vector_scalar_mult$','collect$d'('fun_app$as'('vej$'(A__questionmark_v1),A__questionmark_v2))))
     => ( 'fun_app$w'('det$','vec_lambda$a'('fun_app$z'('vek$'(A__questionmark_v0,A__questionmark_v1),A__questionmark_v2))) = 'fun_app$w'('det$',A__questionmark_v1) ) ) ).

%% (span$a(times$, top$f) = top$f)
tff(axiom905,axiom,
    'span$a'('times$','top$f') = 'top$f' ).

%% (span$(vector_scalar_mult$, top$k) = top$k)
tff(axiom906,axiom,
    'span$'('vector_scalar_mult$','top$k') = 'top$k' ).

%% ∀ ?v0:Nat$ (0 ≤ of_nat$(?v0))
tff(axiom907,axiom,
    ! [A__questionmark_v0: 'Nat$'] : $lesseq(0,'of_nat$'(A__questionmark_v0)) ).

%% ∀ ?v0:Nat$ (nat$(of_nat$(?v0)) = ?v0)
tff(axiom908,axiom,
    ! [A__questionmark_v0: 'Nat$'] : 'nat$'('of_nat$'(A__questionmark_v0)) = A__questionmark_v0 ).

%% ∀ ?v0:Int (of_nat$(nat$(?v0)) = (if (0 ≤ ?v0) ?v0 else 0))
tff(axiom909,axiom,
    ! [A__questionmark_v0: $int] :
      ( ( $lesseq(0,A__questionmark_v0)
       => ( 'of_nat$'('nat$'(A__questionmark_v0)) = A__questionmark_v0 ) )
      & ( ~ $lesseq(0,A__questionmark_v0)
       => ( 'of_nat$'('nat$'(A__questionmark_v0)) = 0 ) ) ) ).

%% ∀ b:tlbool ((b = tltrue) ∨ (b = tlfalse))
tff(formula_911,axiom,
    ! [B: tlbool] :
      ( ( B = tltrue )
      | ( B = tlfalse ) ) ).

%% ¬(tltrue = tlfalse)
tff(formula_912,axiom,
    tltrue != tlfalse ).

%------------------------------------------------------------------------------