SET007 Axioms: SET007+518.ax
%------------------------------------------------------------------------------
% File : SET007+518 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Steinitz Theorem and the Dimension of a 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_5 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 52 ( 2 unt; 0 def)
% Number of atoms : 605 ( 47 equ)
% Maximal formula atoms : 19 ( 11 avg)
% Number of connectives : 624 ( 71 ~; 0 |; 389 &)
% ( 11 <=>; 153 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 10 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 1 prp; 0-3 aty)
% Number of functors : 40 ( 40 usr; 6 con; 0-4 aty)
% Number of variables : 146 ( 131 !; 15 ?)
% 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_5,axiom,
? [A] :
( l2_rlvect_1(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)
& v1_rlvect_5(A) ) ).
fof(rc2_rlvect_5,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)
& ~ v3_struct_0(B)
& v2_rlvect_1(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v1_rlvect_5(B) ) ) ).
fof(cc1_rlvect_5,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)
& v1_rlvect_5(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlsub_1(B,A)
=> v1_rlvect_5(B) ) ) ).
fof(rc3_rlvect_5,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)
& v1_rlvect_5(A)
& l2_rlvect_1(A) )
=> ? [B] :
( m1_rlsub_1(B,A)
& ~ v3_struct_0(B)
& v2_rlvect_1(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v1_rlvect_5(B) ) ) ).
fof(t1_rlvect_5,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)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v1_rlvect_3(D,A)
& r1_tarski(k10_rlvect_2(A,B),D)
& r1_tarski(k10_rlvect_2(A,C),D)
& k13_rlvect_2(A,B) = k13_rlvect_2(A,C) )
=> r1_rlvect_2(A,B,C) ) ) ) ) ) ).
fof(t2_rlvect_5,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_rlvect_3(C,A)
=> ~ r1_tarski(B,C) ) ) ) ) ).
fof(t3_rlvect_5,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_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(C,k10_rlvect_2(A,B))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& C = D
& k8_funct_2(u1_struct_0(A),k1_numbers,B,D) != np__0 ) ) ) ) ) ).
fof(t4_rlvect_5,axiom,
$true ).
fof(t5_rlvect_5,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] :
( m2_finseq_1(C,u1_struct_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k4_finseq_1(C),k4_finseq_1(C))
& v3_funct_2(E,k4_finseq_1(C),k4_finseq_1(C))
& m2_relset_1(E,k4_finseq_1(C),k4_finseq_1(C)) )
=> ( D = k5_relat_1(E,C)
=> k9_rlvect_1(A,k12_rlvect_2(A,C,B)) = k9_rlvect_1(A,k12_rlvect_2(A,D,B)) ) ) ) ) ) ) ).
fof(t6_rlvect_5,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] :
( m2_finseq_1(C,u1_struct_0(A))
=> ( r1_xboole_0(k10_rlvect_2(A,B),k2_relat_1(C))
=> k9_rlvect_1(A,k12_rlvect_2(A,C,B)) = k1_rlvect_1(A) ) ) ) ) ).
fof(t7_rlvect_5,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))
=> ( v2_funct_1(B)
=> ! [C] :
( m1_rlvect_2(C,A)
=> ( r1_tarski(k10_rlvect_2(A,C),k2_relat_1(B))
=> k9_rlvect_1(A,k12_rlvect_2(A,B,C)) = k13_rlvect_2(A,C) ) ) ) ) ) ).
fof(t8_rlvect_5,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] :
( m2_finseq_1(C,u1_struct_0(A))
=> ? [D] :
( m1_rlvect_2(D,A)
& k10_rlvect_2(A,D) = k3_xboole_0(k2_relat_1(C),k10_rlvect_2(A,B))
& k12_rlvect_2(A,C,B) = k12_rlvect_2(A,C,D) ) ) ) ) ).
fof(t9_rlvect_5,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_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(A))
=> ~ ( r1_tarski(k2_relat_1(D),u1_struct_0(k1_rlvect_3(A,C)))
& ! [E] :
( m2_rlvect_2(E,A,C)
=> k9_rlvect_1(A,k12_rlvect_2(A,D,B)) != k13_rlvect_2(A,E) ) ) ) ) ) ) ).
fof(t10_rlvect_5,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_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r1_tarski(k10_rlvect_2(A,B),u1_struct_0(k1_rlvect_3(A,C)))
& ! [D] :
( m2_rlvect_2(D,A,C)
=> k13_rlvect_2(A,B) != k13_rlvect_2(A,D) ) ) ) ) ) ).
fof(t11_rlvect_5,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_rlvect_2(C,A)
=> ( r1_tarski(k10_rlvect_2(A,C),u1_struct_0(B))
=> ! [D] :
( m1_rlvect_2(D,B)
=> ( D = k7_relat_1(C,u1_struct_0(B))
=> ( k10_rlvect_2(A,C) = k10_rlvect_2(B,D)
& k13_rlvect_2(A,C) = k13_rlvect_2(B,D) ) ) ) ) ) ) ) ).
fof(t12_rlvect_5,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_rlvect_2(C,B)
=> ? [D] :
( m1_rlvect_2(D,A)
& k10_rlvect_2(B,C) = k10_rlvect_2(A,D)
& k13_rlvect_2(B,C) = k13_rlvect_2(A,D) ) ) ) ) ).
fof(t13_rlvect_5,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_rlvect_2(C,A)
=> ~ ( r1_tarski(k10_rlvect_2(A,C),u1_struct_0(B))
& ! [D] :
( m1_rlvect_2(D,B)
=> ~ ( k10_rlvect_2(B,D) = k10_rlvect_2(A,C)
& k13_rlvect_2(B,D) = k13_rlvect_2(A,C) ) ) ) ) ) ) ).
fof(t14_rlvect_5,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)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_rlvect_1(k1_rlvect_3(A,B),C) ) ) ) ).
fof(t15_rlvect_5,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_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( v1_rlvect_3(C,B)
=> ( v1_rlvect_3(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) ).
fof(t16_rlvect_5,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_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v1_rlvect_3(C,A)
& r1_tarski(C,u1_struct_0(B)) )
=> ( v1_rlvect_3(C,B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) ) ).
fof(t17_rlvect_5,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_rlvect_3(C,B)
=> ? [D] :
( m1_rlvect_3(D,A)
& r1_tarski(C,D) ) ) ) ) ).
fof(t18_rlvect_5,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,u1_struct_0(A))
=> ( r2_hidden(C,B)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( D = k6_subset_1(u1_struct_0(A),B,k7_rlvect_2(A,C))
& r1_rlvect_1(k1_rlvect_3(A,D),C) ) ) ) ) ) ) ) ).
fof(t19_rlvect_5,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)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r1_xboole_0(C,B)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( D = k4_subset_1(u1_struct_0(A),B,C)
& v1_rlvect_3(D,A) ) ) ) ) ) ) ).
fof(t20_rlvect_5,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_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_tarski(C,u1_struct_0(B))
=> m1_rlsub_1(k1_rlvect_3(A,C),B) ) ) ) ) ).
fof(t21_rlvect_5,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_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( C = D
=> k1_rlvect_3(A,C) = k1_rlvect_3(B,D) ) ) ) ) ) ).
fof(t22_rlvect_5,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] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r1_rlvect_1(k1_rlvect_3(A,k2_rlvect_2(A,B,C)),D)
& ~ r1_rlvect_1(k1_rlvect_3(A,C),D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(E,B)
& r1_rlvect_1(k1_rlvect_3(A,k2_rlvect_2(A,k4_rlvect_2(A,k2_rlvect_2(A,B,C),k7_rlvect_2(A,E)),k7_rlvect_2(A,D))),E) ) ) ) ) ) ) ) ).
fof(t23_rlvect_5,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] :
( ( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ( g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) = k1_rlvect_3(A,B)
& v1_rlvect_3(C,A) )
=> ( r1_xreal_0(k4_card_1(C),k4_card_1(B))
& ? [D] :
( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
& r1_tarski(D,B)
& k4_card_1(D) = k5_real_1(k4_card_1(B),k4_card_1(C))
& g2_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A)) = k1_rlvect_3(A,k2_rlvect_2(A,C,D)) ) ) ) ) ) ) ).
fof(d1_rlvect_5,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_5(A)
<=> ? [B] :
( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_rlvect_3(B,A) ) ) ) ).
fof(d2_rlvect_5,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_5(A)
<=> ? [B] :
( v1_finset_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& m1_rlvect_3(B,A) ) ) ) ).
fof(t24_rlvect_5,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_5(A)
=> ! [B] :
( m1_rlvect_3(B,A)
=> v1_finset_1(B) ) ) ) ).
fof(t25_rlvect_5,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_5(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_rlvect_3(B,A)
=> v1_finset_1(B) ) ) ) ) ).
fof(t26_rlvect_5,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_5(A)
=> ! [B] :
( m1_rlvect_3(B,A)
=> ! [C] :
( m1_rlvect_3(C,A)
=> k1_card_1(B) = k1_card_1(C) ) ) ) ) ).
fof(t27_rlvect_5,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_5(k1_rlsub_1(A)) ) ).
fof(t28_rlvect_5,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)
=> ( v1_rlvect_5(A)
=> v1_rlvect_5(B) ) ) ) ).
fof(d3_rlvect_5,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_5(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( B = k1_rlvect_5(A)
<=> ! [C] :
( m1_rlvect_3(C,A)
=> B = k1_card_1(C) ) ) ) ) ) ).
fof(t29_rlvect_5,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)
& v1_rlvect_5(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlsub_1(B,A)
=> r1_xreal_0(k1_rlvect_5(B),k1_rlvect_5(A)) ) ) ).
fof(t30_rlvect_5,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)
& v1_rlvect_5(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_rlvect_3(B,A)
=> k1_card_1(B) = k1_rlvect_5(k1_rlvect_3(A,B)) ) ) ) ).
fof(t31_rlvect_5,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)
& v1_rlvect_5(A)
& l2_rlvect_1(A) )
=> k1_rlvect_5(A) = k1_rlvect_5(k2_rlsub_1(A)) ) ).
fof(t32_rlvect_5,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)
& v1_rlvect_5(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlsub_1(B,A)
=> ( k1_rlvect_5(A) = k1_rlvect_5(B)
<=> k2_rlsub_1(A) = k2_rlsub_1(B) ) ) ) ).
fof(t33_rlvect_5,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)
& v1_rlvect_5(A)
& l2_rlvect_1(A) )
=> ( k1_rlvect_5(A) = np__0
<=> k2_rlsub_1(A) = k1_rlsub_1(A) ) ) ).
fof(t34_rlvect_5,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)
& v1_rlvect_5(A)
& l2_rlvect_1(A) )
=> ( k1_rlvect_5(A) = np__1
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& B != k1_rlvect_1(A)
& k2_rlsub_1(A) = k1_rlvect_3(A,k7_rlvect_2(A,B)) ) ) ) ).
fof(t35_rlvect_5,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)
& v1_rlvect_5(A)
& l2_rlvect_1(A) )
=> ( k1_rlvect_5(A) = np__2
<=> ? [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)
& k2_rlsub_1(A) = k1_rlvect_3(A,k8_rlvect_2(A,B,C)) ) ) ) ) ).
fof(t36_rlvect_5,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)
& v1_rlvect_5(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlsub_1(B,A)
=> ! [C] :
( m1_rlsub_1(C,A)
=> k1_nat_1(k1_rlvect_5(k1_rlsub_2(A,B,C)),k1_rlvect_5(k2_rlsub_2(A,B,C))) = k1_nat_1(k1_rlvect_5(B),k1_rlvect_5(C)) ) ) ) ).
fof(t37_rlvect_5,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)
& v1_rlvect_5(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlsub_1(B,A)
=> ! [C] :
( m1_rlsub_1(C,A)
=> r1_xreal_0(k5_real_1(k1_nat_1(k1_rlvect_5(B),k1_rlvect_5(C)),k1_rlvect_5(A)),k1_rlvect_5(k2_rlsub_2(A,B,C))) ) ) ) ).
fof(t38_rlvect_5,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)
& v1_rlvect_5(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_rlsub_1(B,A)
=> ! [C] :
( m1_rlsub_1(C,A)
=> ( r1_rlsub_2(A,B,C)
=> k1_rlvect_5(A) = k1_nat_1(k1_rlvect_5(B),k1_rlvect_5(C)) ) ) ) ) ).
fof(t39_rlvect_5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_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)
& v1_rlvect_5(B)
& l2_rlvect_1(B) )
=> ( r1_xreal_0(A,k1_rlvect_5(B))
<=> ? [C] :
( v2_rlvect_1(C)
& m1_rlsub_1(C,B)
& k1_rlvect_5(C) = A ) ) ) ) ).
fof(d4_rlvect_5,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)
& v1_rlvect_5(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( C = k2_rlvect_5(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ? [E] :
( v2_rlvect_1(E)
& m1_rlsub_1(E,A)
& E = D
& k1_rlvect_5(E) = B ) ) ) ) ) ).
fof(t40_rlvect_5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_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)
& v1_rlvect_5(B)
& l2_rlvect_1(B) )
=> ~ ( r1_xreal_0(A,k1_rlvect_5(B))
& v1_xboole_0(k2_rlvect_5(B,A)) ) ) ) ).
fof(t41_rlvect_5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_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)
& v1_rlvect_5(B)
& l2_rlvect_1(B) )
=> ( ~ r1_xreal_0(A,k1_rlvect_5(B))
=> k2_rlvect_5(B,A) = k1_xboole_0 ) ) ) ).
fof(t42_rlvect_5,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_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)
& v1_rlvect_5(B)
& l2_rlvect_1(B) )
=> ! [C] :
( m1_rlsub_1(C,B)
=> r1_tarski(k2_rlvect_5(C,A),k2_rlvect_5(B,A)) ) ) ) ).
fof(dt_k1_rlvect_5,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) )
=> m2_subset_1(k1_rlvect_5(A),k1_numbers,k5_numbers) ) ).
fof(dt_k2_rlvect_5,axiom,
$true ).
%------------------------------------------------------------------------------