SET007 Axioms: SET007+244.ax
%------------------------------------------------------------------------------
% File : SET007+244 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Basis of Real Linear Space
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : rlvect_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 49 ( 7 unt; 0 def)
% Number of atoms : 466 ( 42 equ)
% Maximal formula atoms : 19 ( 9 avg)
% Number of connectives : 483 ( 66 ~; 2 |; 283 &)
% ( 8 <=>; 124 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 1 prp; 0-3 aty)
% Number of functors : 35 ( 35 usr; 3 con; 0-4 aty)
% Number of variables : 118 ( 114 !; 4 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_rlvect_3(B,A) ) ) ).
fof(t1_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> ! [C] :
( m1_rlvect_2(C,A)
=> k13_rlvect_2(A,k14_rlvect_2(A,B,C)) = k4_rlvect_1(A,k13_rlvect_2(A,B),k13_rlvect_2(A,C)) ) ) ) ).
fof(t2_rlvect_3,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B) )
=> ! [C] :
( m1_rlvect_2(C,B)
=> k13_rlvect_2(B,k15_rlvect_2(B,A,C)) = k3_rlvect_1(B,k13_rlvect_2(B,C),A) ) ) ) ).
fof(t3_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> k13_rlvect_2(A,k16_rlvect_2(A,B)) = k5_rlvect_1(A,k13_rlvect_2(A,B)) ) ) ).
fof(t4_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_2(B,A)
=> ! [C] :
( m1_rlvect_2(C,A)
=> k13_rlvect_2(A,k17_rlvect_2(A,B,C)) = k6_rlvect_1(A,k13_rlvect_2(A,B),k13_rlvect_2(A,C)) ) ) ) ).
fof(d1_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_rlvect_3(B,A)
<=> ! [C] :
( m2_rlvect_2(C,A,B)
=> ( k13_rlvect_2(A,C) = k1_rlvect_1(A)
=> k10_rlvect_2(A,C) = k1_xboole_0 ) ) ) ) ) ).
fof(t5_rlvect_3,axiom,
$true ).
fof(t6_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r1_tarski(B,C)
& v1_rlvect_3(C,A) )
=> v1_rlvect_3(B,A) ) ) ) ) ).
fof(t7_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v1_rlvect_3(B,A)
& r2_hidden(k1_rlvect_1(A),B) ) ) ) ).
fof(t8_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> v1_rlvect_3(k1_subset_1(u1_struct_0(A)),A) ) ).
fof(t9_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v1_rlvect_3(k7_rlvect_2(A,B),A)
<=> B != k1_rlvect_1(A) ) ) ) ).
fof(t10_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ~ v1_rlvect_3(k7_rlvect_2(A,k1_rlvect_1(A)),A) ) ).
fof(t11_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( v1_rlvect_3(k8_rlvect_2(A,B,C),A)
=> ( B != k1_rlvect_1(A)
& C != k1_rlvect_1(A) ) ) ) ) ) ).
fof(t12_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ~ v1_rlvect_3(k8_rlvect_2(A,B,k1_rlvect_1(A)),A)
& ~ v1_rlvect_3(k8_rlvect_2(A,k1_rlvect_1(A),B),A) ) ) ) ).
fof(t13_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( v1_rlvect_3(k8_rlvect_2(A,B,C),A)
=> ( B = C
| ( C != k1_rlvect_1(A)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> B != k3_rlvect_1(A,C,D) ) ) ) )
& ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> B != k3_rlvect_1(A,C,D) )
=> ( C = k1_rlvect_1(A)
| ( B != C
& v1_rlvect_3(k8_rlvect_2(A,B,C),A) ) ) ) ) ) ) ) ).
fof(t14_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( B != C
& v1_rlvect_3(k8_rlvect_2(A,B,C),A) )
<=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( k4_rlvect_1(A,k3_rlvect_1(A,B,D),k3_rlvect_1(A,C,E)) = k1_rlvect_1(A)
=> ( D = np__0
& E = np__0 ) ) ) ) ) ) ) ) ).
fof(t15_rlvect_3,axiom,
$true ).
fof(t16_rlvect_3,axiom,
$true ).
fof(t17_rlvect_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( r1_rlvect_1(k1_rlvect_3(B,C),A)
<=> ? [D] :
( m2_rlvect_2(D,B,C)
& A = k13_rlvect_2(B,D) ) ) ) ) ).
fof(t18_rlvect_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( r2_hidden(A,C)
=> r1_rlvect_1(k1_rlvect_3(B,C),A) ) ) ) ).
fof(t19_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> k1_rlvect_3(A,k1_subset_1(u1_struct_0(A))) = k1_rlsub_1(A) ) ).
fof(t20_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( k1_rlvect_3(A,B) = k1_rlsub_1(A)
& B != k1_xboole_0
& B != k7_rlvect_2(A,k1_rlvect_1(A)) ) ) ) ).
fof(t21_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( v2_rlvect_1(C)
& m1_rlsub_1(C,A) )
=> ( B = u1_struct_0(C)
=> k1_rlvect_3(A,B) = C ) ) ) ) ).
fof(t22_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_rlvect_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( B = u1_struct_0(A)
=> k1_rlvect_3(A,B) = A ) ) ) ).
fof(t23_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(B,C)
=> m1_rlsub_1(k1_rlvect_3(A,B),k1_rlvect_3(A,C)) ) ) ) ) ).
fof(t24_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_rlvect_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( k1_rlvect_3(A,B) = A
& r1_tarski(B,C) )
=> k1_rlvect_3(A,C) = A ) ) ) ) ).
fof(t25_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> k1_rlvect_3(A,k4_subset_1(u1_struct_0(A),B,C)) = k1_rlsub_2(A,k1_rlvect_3(A,B),k1_rlvect_3(A,C)) ) ) ) ).
fof(t26_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> m1_rlsub_1(k1_rlvect_3(A,k5_subset_1(u1_struct_0(A),B,C)),k2_rlsub_2(A,k1_rlvect_3(A,B),k1_rlvect_3(A,C))) ) ) ) ).
fof(t27_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v1_rlvect_3(B,A)
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r1_tarski(B,C)
& v1_rlvect_3(C,A)
& k1_rlvect_3(A,C) = g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) ) ) ) ) ) ).
fof(t28_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( k1_rlvect_3(A,B) = A
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r1_tarski(C,B)
& v1_rlvect_3(C,A)
& k1_rlvect_3(A,C) = A ) ) ) ) ) ).
fof(d3_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( m1_rlvect_3(B,A)
<=> ( v1_rlvect_3(B,A)
& k1_rlvect_3(A,B) = g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) ) ) ) ) ).
fof(t29_rlvect_3,axiom,
$true ).
fof(t30_rlvect_3,axiom,
$true ).
fof(t31_rlvect_3,axiom,
$true ).
fof(t32_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_rlvect_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( v1_rlvect_3(B,A)
& ! [C] :
( m1_rlvect_3(C,A)
=> ~ r1_tarski(B,C) ) ) ) ) ).
fof(t33_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( k1_rlvect_3(A,B) = A
& ! [C] :
( m1_rlvect_3(C,A)
=> ~ r1_tarski(C,B) ) ) ) ) ).
fof(t34_rlvect_3,axiom,
$true ).
fof(t35_rlvect_3,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_orders_1(B,A)
=> ( ~ r2_hidden(k1_xboole_0,A)
=> ( k1_relat_1(B) = A
& r1_tarski(k2_relat_1(B),k3_tarski(A)) ) ) ) ) ).
fof(t36_rlvect_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B) )
=> ( r1_rlvect_1(k1_rlsub_1(B),A)
<=> A = k1_rlvect_1(B) ) ) ).
fof(t37_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlsub_1(B,A)
=> ! [C] :
( m1_rlsub_1(C,A)
=> ! [D] :
( m1_rlsub_1(D,A)
=> ( m1_rlsub_1(B,C)
=> m1_rlsub_1(k2_rlsub_2(A,B,D),C) ) ) ) ) ) ).
fof(t38_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlsub_1(B,A)
=> ! [C] :
( m1_rlsub_1(C,A)
=> ! [D] :
( m1_rlsub_1(D,A)
=> ( ( m1_rlsub_1(B,C)
& m1_rlsub_1(B,D) )
=> m1_rlsub_1(B,k2_rlsub_2(A,C,D)) ) ) ) ) ) ).
fof(t39_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlsub_1(B,A)
=> ! [C] :
( m1_rlsub_1(C,A)
=> ! [D] :
( m1_rlsub_1(D,A)
=> ( ( m1_rlsub_1(B,C)
& m1_rlsub_1(D,C) )
=> m1_rlsub_1(k1_rlsub_2(A,B,D),C) ) ) ) ) ) ).
fof(t40_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlsub_1(B,A)
=> ! [C] :
( m1_rlsub_1(C,A)
=> ! [D] :
( m1_rlsub_1(D,A)
=> ( m1_rlsub_1(B,C)
=> m1_rlsub_1(B,k1_rlsub_2(A,C,D)) ) ) ) ) ) ).
fof(t41_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),k1_numbers)
& m2_relset_1(D,u1_struct_0(A),k1_numbers) )
=> k12_rlvect_2(A,k8_finseq_1(u1_struct_0(A),B,C),D) = k8_finseq_1(u1_struct_0(A),k12_rlvect_2(A,B,D),k12_rlvect_2(A,C,D)) ) ) ) ) ).
fof(dt_m1_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlvect_3(B,A)
=> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(existence_m1_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ? [B] : m1_rlvect_3(B,A) ) ).
fof(dt_k1_rlvect_3,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v2_rlvect_1(k1_rlvect_3(A,B))
& m1_rlsub_1(k1_rlvect_3(A,B),A) ) ) ).
fof(d2_rlvect_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( v2_rlvect_1(C)
& m1_rlsub_1(C,A) )
=> ( C = k1_rlvect_3(A,B)
<=> u1_struct_0(C) = a_2_0_rlvect_3(A,B) ) ) ) ) ).
fof(fraenkel_a_2_0_rlvect_3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& l2_rlvect_1(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_2_0_rlvect_3(B,C))
<=> ? [D] :
( m2_rlvect_2(D,B,C)
& A = k13_rlvect_2(B,D) ) ) ) ).
%------------------------------------------------------------------------------