SET007 Axioms: SET007+367.ax
%------------------------------------------------------------------------------
% File : SET007+367 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Product of Families of Groups and Vector Spaces
% 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 : prvect_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 91 ( 10 unt; 0 def)
% Number of atoms : 780 ( 48 equ)
% Maximal formula atoms : 20 ( 8 avg)
% Number of connectives : 790 ( 101 ~; 0 |; 502 &)
% ( 14 <=>; 173 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 43 ( 41 usr; 1 prp; 0-3 aty)
% Number of functors : 54 ( 54 usr; 3 con; 0-6 aty)
% Number of variables : 225 ( 220 !; 5 ?)
% 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(fc1_prvect_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A)
& m1_subset_1(B,k5_numbers) )
=> ( ~ v3_struct_0(k5_prvect_1(A,B))
& v1_rlvect_1(k5_prvect_1(A,B))
& v3_rlvect_1(k5_prvect_1(A,B))
& v4_rlvect_1(k5_prvect_1(A,B))
& v5_rlvect_1(k5_prvect_1(A,B))
& v6_rlvect_1(k5_prvect_1(A,B)) ) ) ).
fof(fc2_prvect_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& m1_subset_1(B,k5_numbers) )
=> ( ~ v3_struct_0(k7_prvect_1(A,B))
& v11_vectsp_1(k7_prvect_1(A,B),A) ) ) ).
fof(fc3_prvect_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& m1_subset_1(B,k5_numbers) )
=> ( ~ v3_struct_0(k7_prvect_1(A,B))
& v11_vectsp_1(k7_prvect_1(A,B),A)
& v12_vectsp_1(k7_prvect_1(A,B),A) ) ) ).
fof(rc1_prvect_1,axiom,
? [A] :
( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finset_1(A)
& v1_finseq_1(A) ) ).
fof(fc4_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A) )
=> ~ v1_xboole_0(k1_relat_1(A)) ) ).
fof(fc5_prvect_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& m1_subset_1(B,k1_relat_1(A)) )
=> ~ v1_xboole_0(k1_funct_1(A,B)) ) ).
fof(cc1_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A) )
=> ! [B] :
( m1_prvect_1(B,A)
=> v1_finseq_1(B) ) ) ).
fof(cc2_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A) )
=> ! [B] :
( m2_prvect_1(B,A)
=> v1_finseq_1(B) ) ) ).
fof(rc2_prvect_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finset_1(A)
& v1_finseq_1(A)
& v1_prvect_1(A) ) ).
fof(t1_prvect_1,axiom,
$true ).
fof(t2_prvect_1,axiom,
$true ).
fof(t3_prvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> r3_binop_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A)) ) ).
fof(t4_prvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> r1_finseqop(u1_struct_0(A),k7_vectsp_1(A),u1_rlvect_1(A)) ) ).
fof(t5_prvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ( ( v1_binop_1(u1_rlvect_1(A),u1_struct_0(A))
& v2_binop_1(u1_rlvect_1(A),u1_struct_0(A))
& r3_binop_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A))
& r1_finseqop(u1_struct_0(A),k7_vectsp_1(A),u1_rlvect_1(A)) )
=> ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) ) ) ) ).
fof(t6_prvect_1,axiom,
$true ).
fof(t7_prvect_1,axiom,
$true ).
fof(t8_prvect_1,axiom,
$true ).
fof(t9_prvect_1,axiom,
$true ).
fof(t10_prvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> r3_binop_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A)) ) ).
fof(t11_prvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> r3_binop_1(u1_struct_0(A),k2_group_1(A),u1_group_1(A)) ) ).
fof(d1_prvect_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m2_relset_1(B,k2_zfmisc_1(A,A),A) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(k4_finseq_2(C,A),k4_finseq_2(C,A)),k4_finseq_2(C,A))
& m2_relset_1(D,k2_zfmisc_1(k4_finseq_2(C,A),k4_finseq_2(C,A)),k4_finseq_2(C,A)) )
=> ( D = k2_prvect_1(A,B,C)
<=> ! [E] :
( m2_finseq_2(E,A,k4_finseq_2(C,A))
=> ! [F] :
( m2_finseq_2(F,A,k4_finseq_2(C,A))
=> k2_binop_1(k4_finseq_2(C,A),k4_finseq_2(C,A),k4_finseq_2(C,A),D,E,F) = k1_prvect_1(A,C,B,E,F) ) ) ) ) ) ) ) ).
fof(d2_prvect_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m2_relset_1(B,A,A) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k4_finseq_2(C,A),k4_finseq_2(C,A))
& m2_relset_1(D,k4_finseq_2(C,A),k4_finseq_2(C,A)) )
=> ( D = k3_prvect_1(A,B,C)
<=> ! [E] :
( m2_finseq_2(E,A,k4_finseq_2(C,A))
=> k8_funct_2(k4_finseq_2(C,A),k4_finseq_2(C,A),D,E) = k5_finseqop(A,A,E,B) ) ) ) ) ) ) ).
fof(t12_prvect_1,axiom,
$true ).
fof(t13_prvect_1,axiom,
$true ).
fof(t14_prvect_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ( v1_binop_1(C,B)
=> v1_binop_1(k2_prvect_1(B,C,A),k4_finseq_2(A,B)) ) ) ) ) ).
fof(t15_prvect_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ( v2_binop_1(C,B)
=> v2_binop_1(k2_prvect_1(B,C,A),k4_finseq_2(A,B)) ) ) ) ) ).
fof(t16_prvect_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( m1_subset_1(C,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(B,B),B)
& m2_relset_1(D,k2_zfmisc_1(B,B),B) )
=> ( r3_binop_1(B,C,D)
=> r3_binop_1(k4_finseq_2(A,B),k4_prvect_1(B,A,C),k2_prvect_1(B,D,A)) ) ) ) ) ) ).
fof(t17_prvect_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,B)
& m2_relset_1(D,B,B) )
=> ( ( v1_setwiseo(C,B)
& v2_binop_1(C,B)
& r1_finseqop(B,D,C) )
=> r1_finseqop(k4_finseq_2(A,B),k3_prvect_1(B,D,A),k2_prvect_1(B,C,A)) ) ) ) ) ) ).
fof(d3_prvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A) )
=> k5_prvect_1(A,B) = g1_rlvect_1(k4_finseq_2(B,u1_struct_0(A)),k2_prvect_1(u1_struct_0(A),u1_rlvect_1(A),B),k4_prvect_1(u1_struct_0(A),B,u2_struct_0(A))) ) ) ) ).
fof(d4_prvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),k4_finseq_2(B,u1_struct_0(A))),k4_finseq_2(B,u1_struct_0(A)))
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),k4_finseq_2(B,u1_struct_0(A))),k4_finseq_2(B,u1_struct_0(A))) )
=> ( C = k6_prvect_1(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m2_finseq_2(E,u1_struct_0(A),k4_finseq_2(B,u1_struct_0(A)))
=> k2_binop_1(u1_struct_0(A),k4_finseq_2(B,u1_struct_0(A)),k4_finseq_2(B,u1_struct_0(A)),C,D,E) = k3_finseqop(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_group_1(A),D,E) ) ) ) ) ) ) ).
fof(d5_prvect_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v11_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ( C = k7_prvect_1(A,B)
<=> ( g1_rlvect_1(u1_struct_0(C),u1_rlvect_1(C),u2_struct_0(C)) = k5_prvect_1(A,B)
& u2_vectsp_1(A,C) = k6_prvect_1(A,B) ) ) ) ) ) ).
fof(t18_prvect_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(B,B),B)
& m2_relset_1(C,k2_zfmisc_1(B,B),B) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(B,B),B)
& m2_relset_1(D,k2_zfmisc_1(B,B),B) )
=> ! [E] :
( m1_subset_1(E,B)
=> ! [F] :
( m2_finseq_2(F,B,k4_finseq_2(A,B))
=> ! [G] :
( m2_finseq_2(G,B,k4_finseq_2(A,B))
=> ( r6_binop_1(B,C,D)
=> k3_finseqop(B,B,B,C,E,k1_prvect_1(B,A,D,F,G)) = k1_finseqop(B,B,B,D,k3_finseqop(B,B,B,C,E,F),k3_finseqop(B,B,B,C,E,G)) ) ) ) ) ) ) ) ) ).
fof(d6_prvect_1,axiom,
$true ).
fof(d7_prvect_1,axiom,
$true ).
fof(d8_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( m1_prvect_1(B,A)
<=> ( k1_relat_1(B) = k1_relat_1(A)
& ! [C] :
( m1_subset_1(C,k1_relat_1(A))
=> ( v1_funct_1(k1_funct_1(B,C))
& v1_funct_2(k1_funct_1(B,C),k2_zfmisc_1(k1_funct_1(A,C),k1_funct_1(A,C)),k1_funct_1(A,C))
& m2_relset_1(k1_funct_1(B,C),k2_zfmisc_1(k1_funct_1(A,C),k1_funct_1(A,C)),k1_funct_1(A,C)) ) ) ) ) ) ) ).
fof(d9_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( m2_prvect_1(B,A)
<=> ( k1_relat_1(B) = k1_relat_1(A)
& ! [C] :
( m1_subset_1(C,k1_relat_1(A))
=> ( v1_funct_1(k1_funct_1(B,C))
& v1_funct_2(k1_funct_1(B,C),k1_funct_1(A,C),k1_funct_1(A,C))
& m2_relset_1(k1_funct_1(B,C),k1_funct_1(A,C),k1_funct_1(A,C)) ) ) ) ) ) ) ).
fof(t19_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( m1_prvect_1(B,A)
<=> ( k3_finseq_1(B) = k3_finseq_1(A)
& ! [C] :
( m2_subset_1(C,k5_numbers,k4_finseq_1(A))
=> ( v1_funct_1(k1_funct_1(B,C))
& v1_funct_2(k1_funct_1(B,C),k2_zfmisc_1(k1_funct_1(A,C),k1_funct_1(A,C)),k1_funct_1(A,C))
& m2_relset_1(k1_funct_1(B,C),k2_zfmisc_1(k1_funct_1(A,C),k1_funct_1(A,C)),k1_funct_1(A,C)) ) ) ) ) ) ) ).
fof(t20_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( m2_prvect_1(B,A)
<=> ( k3_finseq_1(B) = k3_finseq_1(A)
& ! [C] :
( m2_subset_1(C,k5_numbers,k4_finseq_1(A))
=> ( v1_funct_1(k1_funct_1(B,C))
& v1_funct_2(k1_funct_1(B,C),k1_funct_1(A,C),k1_funct_1(A,C))
& m2_relset_1(k1_funct_1(B,C),k1_funct_1(A,C),k1_funct_1(A,C)) ) ) ) ) ) ) ).
fof(t21_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k4_card_3(A),k4_card_3(A))
& m2_relset_1(B,k4_card_3(A),k4_card_3(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k4_card_3(A),k4_card_3(A))
& m2_relset_1(C,k4_card_3(A),k4_card_3(A)) )
=> ( ! [D] :
( m1_subset_1(D,k4_card_3(A))
=> ! [E] :
( m2_subset_1(E,k5_numbers,k4_finseq_1(A))
=> k9_prvect_1(A,k12_prvect_1(k4_card_3(A),B,D),E) = k9_prvect_1(A,k12_prvect_1(k4_card_3(A),C,D),E) ) )
=> B = C ) ) ) ) ).
fof(t22_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A) )
=> ! [B] :
( m2_prvect_1(B,A)
=> ( k2_funct_6(B) = A
& r1_tarski(k4_card_3(k3_funct_6(B)),k4_card_3(A)) ) ) ) ).
fof(t23_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A) )
=> ! [B] :
( m2_prvect_1(B,A)
=> ! [C] :
( m1_subset_1(C,k4_card_3(A))
=> ! [D] :
( m2_subset_1(D,k5_numbers,k4_finseq_1(A))
=> k9_prvect_1(A,k12_prvect_1(k4_card_3(A),k13_prvect_1(A,B),C),D) = k8_funct_2(k1_funct_1(A,D),k1_funct_1(A,D),k11_prvect_1(A,B,D),k9_prvect_1(A,C,D)) ) ) ) ) ).
fof(t24_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(k4_card_3(A),k4_card_3(A)),k4_card_3(A))
& m2_relset_1(B,k2_zfmisc_1(k4_card_3(A),k4_card_3(A)),k4_card_3(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(k4_card_3(A),k4_card_3(A)),k4_card_3(A))
& m2_relset_1(C,k2_zfmisc_1(k4_card_3(A),k4_card_3(A)),k4_card_3(A)) )
=> ( ! [D] :
( m1_subset_1(D,k4_card_3(A))
=> ! [E] :
( m1_subset_1(E,k4_card_3(A))
=> ! [F] :
( m2_subset_1(F,k5_numbers,k4_finseq_1(A))
=> k9_prvect_1(A,k14_prvect_1(k4_card_3(A),B,D,E),F) = k9_prvect_1(A,k14_prvect_1(k4_card_3(A),C,D,E),F) ) ) )
=> B = C ) ) ) ) ).
fof(d10_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A) )
=> ! [B] :
( m1_prvect_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(k4_card_3(A),k4_card_3(A)),k4_card_3(A))
& m2_relset_1(C,k2_zfmisc_1(k4_card_3(A),k4_card_3(A)),k4_card_3(A)) )
=> ( C = k15_prvect_1(A,B)
<=> ! [D] :
( m1_subset_1(D,k4_card_3(A))
=> ! [E] :
( m1_subset_1(E,k4_card_3(A))
=> ! [F] :
( m2_subset_1(F,k5_numbers,k4_finseq_1(A))
=> k9_prvect_1(A,k14_prvect_1(k4_card_3(A),C,D,E),F) = k2_binop_1(k1_funct_1(A,F),k1_funct_1(A,F),k1_funct_1(A,F),k10_prvect_1(A,B,F),k9_prvect_1(A,D,F),k9_prvect_1(A,E,F)) ) ) ) ) ) ) ) ).
fof(t25_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A) )
=> ! [B] :
( m1_prvect_1(B,A)
=> ( ! [C] :
( m2_subset_1(C,k5_numbers,k4_finseq_1(A))
=> v1_binop_1(k10_prvect_1(A,B,C),k1_funct_1(A,C)) )
=> v1_binop_1(k15_prvect_1(A,B),k4_card_3(A)) ) ) ) ).
fof(t26_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A) )
=> ! [B] :
( m1_prvect_1(B,A)
=> ( ! [C] :
( m2_subset_1(C,k5_numbers,k4_finseq_1(A))
=> v2_binop_1(k10_prvect_1(A,B,C),k1_funct_1(A,C)) )
=> v2_binop_1(k15_prvect_1(A,B),k4_card_3(A)) ) ) ) ).
fof(t27_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A) )
=> ! [B] :
( m1_prvect_1(B,A)
=> ! [C] :
( m1_subset_1(C,k4_card_3(A))
=> ( ! [D] :
( m2_subset_1(D,k5_numbers,k4_finseq_1(A))
=> r3_binop_1(k1_funct_1(A,D),k9_prvect_1(A,C,D),k10_prvect_1(A,B,D)) )
=> r3_binop_1(k4_card_3(A),C,k15_prvect_1(A,B)) ) ) ) ) ).
fof(t28_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A) )
=> ! [B] :
( m1_prvect_1(B,A)
=> ! [C] :
( m2_prvect_1(C,A)
=> ( ! [D] :
( m2_subset_1(D,k5_numbers,k4_finseq_1(A))
=> ( r1_finseqop(k1_funct_1(A,D),k11_prvect_1(A,C,D),k10_prvect_1(A,B,D))
& v1_setwiseo(k10_prvect_1(A,B,D),k1_funct_1(A,D)) ) )
=> r1_finseqop(k4_card_3(A),k13_prvect_1(A,C),k15_prvect_1(A,B)) ) ) ) ) ).
fof(d11_prvect_1,axiom,
! [A] :
( v1_relat_1(A)
=> ( v1_prvect_1(A)
<=> ! [B] :
( r2_hidden(B,k2_relat_1(A))
=> ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& l1_rlvect_1(B) ) ) ) ) ).
fof(d12_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& v1_prvect_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v2_relat_1(B)
& v1_funct_1(B)
& ~ v1_xboole_0(B)
& v1_finseq_1(B) )
=> ( B = k17_prvect_1(A)
<=> ( k3_finseq_1(B) = k3_finseq_1(A)
& ! [C] :
( m2_subset_1(C,k5_numbers,k4_finseq_1(A))
=> k1_funct_1(B,C) = u1_struct_0(k16_prvect_1(A,C)) ) ) ) ) ) ).
fof(d13_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& v1_prvect_1(A) )
=> ! [B] :
( m1_prvect_1(B,k17_prvect_1(A))
=> ( B = k19_prvect_1(A)
<=> ( k3_finseq_1(B) = k3_finseq_1(k17_prvect_1(A))
& ! [C] :
( m2_subset_1(C,k5_numbers,k4_finseq_1(k17_prvect_1(A)))
=> k10_prvect_1(k17_prvect_1(A),B,C) = u1_rlvect_1(k18_prvect_1(A,C)) ) ) ) ) ) ).
fof(d14_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& v1_prvect_1(A) )
=> ! [B] :
( m2_prvect_1(B,k17_prvect_1(A))
=> ( B = k20_prvect_1(A)
<=> ( k3_finseq_1(B) = k3_finseq_1(k17_prvect_1(A))
& ! [C] :
( m2_subset_1(C,k5_numbers,k4_finseq_1(k17_prvect_1(A)))
=> k11_prvect_1(k17_prvect_1(A),B,C) = k7_vectsp_1(k18_prvect_1(A,C)) ) ) ) ) ) ).
fof(d15_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& v1_prvect_1(A) )
=> ! [B] :
( m1_subset_1(B,k4_card_3(k17_prvect_1(A)))
=> ( B = k21_prvect_1(A)
<=> ! [C] :
( m2_subset_1(C,k5_numbers,k4_finseq_1(k17_prvect_1(A)))
=> k9_prvect_1(k17_prvect_1(A),B,C) = u2_struct_0(k18_prvect_1(A,C)) ) ) ) ) ).
fof(d16_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& v1_prvect_1(A) )
=> k22_prvect_1(A) = g1_rlvect_1(k4_card_3(k17_prvect_1(A)),k15_prvect_1(k17_prvect_1(A),k19_prvect_1(A)),k21_prvect_1(A)) ) ).
fof(s1_prvect_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& k3_finseq_1(A) = k3_finseq_1(f1_s1_prvect_1)
& ! [B] :
( m2_subset_1(B,k5_numbers,k4_finseq_1(f1_s1_prvect_1))
=> k1_funct_1(A,B) = f2_s1_prvect_1(B) ) ) ).
fof(dt_m1_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A) )
=> ! [B] :
( m1_prvect_1(B,A)
=> ( v1_relat_1(B)
& v1_funct_1(B) ) ) ) ).
fof(existence_m1_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A) )
=> ? [B] : m1_prvect_1(B,A) ) ).
fof(dt_m2_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A) )
=> ! [B] :
( m2_prvect_1(B,A)
=> ( v1_relat_1(B)
& v1_funct_1(B) ) ) ) ).
fof(existence_m2_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A) )
=> ? [B] : m2_prvect_1(B,A) ) ).
fof(dt_k1_prvect_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k5_numbers)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& m1_subset_1(D,k4_finseq_2(B,A))
& m1_subset_1(E,k4_finseq_2(B,A)) )
=> m2_finseq_2(k1_prvect_1(A,B,C,D,E),A,k4_finseq_2(B,A)) ) ).
fof(redefinition_k1_prvect_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k5_numbers)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& m1_subset_1(D,k4_finseq_2(B,A))
& m1_subset_1(E,k4_finseq_2(B,A)) )
=> k1_prvect_1(A,B,C,D,E) = k3_funcop_1(C,D,E) ) ).
fof(dt_k2_prvect_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& m1_subset_1(C,k5_numbers) )
=> ( v1_funct_1(k2_prvect_1(A,B,C))
& v1_funct_2(k2_prvect_1(A,B,C),k2_zfmisc_1(k4_finseq_2(C,A),k4_finseq_2(C,A)),k4_finseq_2(C,A))
& m2_relset_1(k2_prvect_1(A,B,C),k2_zfmisc_1(k4_finseq_2(C,A),k4_finseq_2(C,A)),k4_finseq_2(C,A)) ) ) ).
fof(dt_k3_prvect_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,A,A)
& m1_relset_1(B,A,A)
& m1_subset_1(C,k5_numbers) )
=> ( v1_funct_1(k3_prvect_1(A,B,C))
& v1_funct_2(k3_prvect_1(A,B,C),k4_finseq_2(C,A),k4_finseq_2(C,A))
& m2_relset_1(k3_prvect_1(A,B,C),k4_finseq_2(C,A),k4_finseq_2(C,A)) ) ) ).
fof(dt_k4_prvect_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,A) )
=> m2_finseq_2(k4_prvect_1(A,B,C),A,k4_finseq_2(B,A)) ) ).
fof(redefinition_k4_prvect_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,A) )
=> k4_prvect_1(A,B,C) = k2_finseq_2(B,C) ) ).
fof(dt_k5_prvect_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& m1_subset_1(B,k5_numbers) )
=> ( ~ v3_struct_0(k5_prvect_1(A,B))
& v1_rlvect_1(k5_prvect_1(A,B))
& v3_rlvect_1(k5_prvect_1(A,B))
& v4_rlvect_1(k5_prvect_1(A,B))
& v5_rlvect_1(k5_prvect_1(A,B))
& v6_rlvect_1(k5_prvect_1(A,B))
& l1_rlvect_1(k5_prvect_1(A,B)) ) ) ).
fof(dt_k6_prvect_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& m1_subset_1(B,k5_numbers) )
=> ( v1_funct_1(k6_prvect_1(A,B))
& v1_funct_2(k6_prvect_1(A,B),k2_zfmisc_1(u1_struct_0(A),k4_finseq_2(B,u1_struct_0(A))),k4_finseq_2(B,u1_struct_0(A)))
& m2_relset_1(k6_prvect_1(A,B),k2_zfmisc_1(u1_struct_0(A),k4_finseq_2(B,u1_struct_0(A))),k4_finseq_2(B,u1_struct_0(A))) ) ) ).
fof(dt_k7_prvect_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& m1_subset_1(B,k5_numbers) )
=> ( v11_vectsp_1(k7_prvect_1(A,B),A)
& l4_vectsp_1(k7_prvect_1(A,B),A) ) ) ).
fof(dt_k8_prvect_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k5_numbers)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& m1_subset_1(D,A)
& m1_subset_1(E,k4_finseq_2(B,A)) )
=> m2_finseq_2(k8_prvect_1(A,B,C,D,E),A,k4_finseq_2(B,A)) ) ).
fof(redefinition_k8_prvect_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k5_numbers)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& m1_subset_1(D,A)
& m1_subset_1(E,k4_finseq_2(B,A)) )
=> k8_prvect_1(A,B,C,D,E) = k5_funcop_1(C,D,E) ) ).
fof(dt_k9_prvect_1,axiom,
! [A,B,C] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& m1_subset_1(B,k4_card_3(A))
& m1_subset_1(C,k1_relat_1(A)) )
=> m1_subset_1(k9_prvect_1(A,B,C),k1_funct_1(A,C)) ) ).
fof(redefinition_k9_prvect_1,axiom,
! [A,B,C] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& m1_subset_1(B,k4_card_3(A))
& m1_subset_1(C,k1_relat_1(A)) )
=> k9_prvect_1(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k10_prvect_1,axiom,
! [A,B,C] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& m1_prvect_1(B,A)
& m1_subset_1(C,k4_finseq_1(A)) )
=> ( v1_funct_1(k10_prvect_1(A,B,C))
& v1_funct_2(k10_prvect_1(A,B,C),k2_zfmisc_1(k1_funct_1(A,C),k1_funct_1(A,C)),k1_funct_1(A,C))
& m2_relset_1(k10_prvect_1(A,B,C),k2_zfmisc_1(k1_funct_1(A,C),k1_funct_1(A,C)),k1_funct_1(A,C)) ) ) ).
fof(redefinition_k10_prvect_1,axiom,
! [A,B,C] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& m1_prvect_1(B,A)
& m1_subset_1(C,k4_finseq_1(A)) )
=> k10_prvect_1(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k11_prvect_1,axiom,
! [A,B,C] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& m2_prvect_1(B,A)
& m1_subset_1(C,k4_finseq_1(A)) )
=> ( v1_funct_1(k11_prvect_1(A,B,C))
& v1_funct_2(k11_prvect_1(A,B,C),k1_funct_1(A,C),k1_funct_1(A,C))
& m2_relset_1(k11_prvect_1(A,B,C),k1_funct_1(A,C),k1_funct_1(A,C)) ) ) ).
fof(redefinition_k11_prvect_1,axiom,
! [A,B,C] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& m2_prvect_1(B,A)
& m1_subset_1(C,k4_finseq_1(A)) )
=> k11_prvect_1(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k12_prvect_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_fraenkel(A)
& v1_funct_1(B)
& v1_funct_2(B,A,A)
& m1_relset_1(B,A,A)
& m1_subset_1(C,A) )
=> m1_subset_1(k12_prvect_1(A,B,C),A) ) ).
fof(redefinition_k12_prvect_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_fraenkel(A)
& v1_funct_1(B)
& v1_funct_2(B,A,A)
& m1_relset_1(B,A,A)
& m1_subset_1(C,A) )
=> k12_prvect_1(A,B,C) = k1_funct_1(B,C) ) ).
fof(dt_k13_prvect_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& m2_prvect_1(B,A) )
=> ( v1_funct_1(k13_prvect_1(A,B))
& v1_funct_2(k13_prvect_1(A,B),k4_card_3(A),k4_card_3(A))
& m2_relset_1(k13_prvect_1(A,B),k4_card_3(A),k4_card_3(A)) ) ) ).
fof(redefinition_k13_prvect_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& m2_prvect_1(B,A) )
=> k13_prvect_1(A,B) = k7_funct_6(B) ) ).
fof(dt_k14_prvect_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v1_fraenkel(A)
& v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& m1_subset_1(C,A)
& m1_subset_1(D,A) )
=> m1_subset_1(k14_prvect_1(A,B,C,D),A) ) ).
fof(redefinition_k14_prvect_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v1_fraenkel(A)
& v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& m1_subset_1(C,A)
& m1_subset_1(D,A) )
=> k14_prvect_1(A,B,C,D) = k1_binop_1(B,C,D) ) ).
fof(dt_k15_prvect_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& m1_prvect_1(B,A) )
=> ( v1_funct_1(k15_prvect_1(A,B))
& v1_funct_2(k15_prvect_1(A,B),k2_zfmisc_1(k4_card_3(A),k4_card_3(A)),k4_card_3(A))
& m2_relset_1(k15_prvect_1(A,B),k2_zfmisc_1(k4_card_3(A),k4_card_3(A)),k4_card_3(A)) ) ) ).
fof(dt_k16_prvect_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& v1_prvect_1(A)
& m1_subset_1(B,k4_finseq_1(A)) )
=> ( ~ v3_struct_0(k16_prvect_1(A,B))
& v3_rlvect_1(k16_prvect_1(A,B))
& v4_rlvect_1(k16_prvect_1(A,B))
& v5_rlvect_1(k16_prvect_1(A,B))
& v6_rlvect_1(k16_prvect_1(A,B))
& l1_rlvect_1(k16_prvect_1(A,B)) ) ) ).
fof(redefinition_k16_prvect_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& v1_prvect_1(A)
& m1_subset_1(B,k4_finseq_1(A)) )
=> k16_prvect_1(A,B) = k1_funct_1(A,B) ) ).
fof(dt_k17_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& v1_prvect_1(A) )
=> ( v1_relat_1(k17_prvect_1(A))
& v2_relat_1(k17_prvect_1(A))
& v1_funct_1(k17_prvect_1(A))
& ~ v1_xboole_0(k17_prvect_1(A))
& v1_finseq_1(k17_prvect_1(A)) ) ) ).
fof(dt_k18_prvect_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& v1_prvect_1(A)
& m1_subset_1(B,k4_finseq_1(k17_prvect_1(A))) )
=> ( ~ v3_struct_0(k18_prvect_1(A,B))
& v3_rlvect_1(k18_prvect_1(A,B))
& v4_rlvect_1(k18_prvect_1(A,B))
& v5_rlvect_1(k18_prvect_1(A,B))
& v6_rlvect_1(k18_prvect_1(A,B))
& l1_rlvect_1(k18_prvect_1(A,B)) ) ) ).
fof(redefinition_k18_prvect_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& v1_prvect_1(A)
& m1_subset_1(B,k4_finseq_1(k17_prvect_1(A))) )
=> k18_prvect_1(A,B) = k1_funct_1(A,B) ) ).
fof(dt_k19_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& v1_prvect_1(A) )
=> m1_prvect_1(k19_prvect_1(A),k17_prvect_1(A)) ) ).
fof(dt_k20_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& v1_prvect_1(A) )
=> m2_prvect_1(k20_prvect_1(A),k17_prvect_1(A)) ) ).
fof(dt_k21_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& v1_prvect_1(A) )
=> m1_subset_1(k21_prvect_1(A),k4_card_3(k17_prvect_1(A))) ) ).
fof(dt_k22_prvect_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& ~ v1_xboole_0(A)
& v1_finseq_1(A)
& v1_prvect_1(A) )
=> ( ~ v3_struct_0(k22_prvect_1(A))
& v1_rlvect_1(k22_prvect_1(A))
& v3_rlvect_1(k22_prvect_1(A))
& v4_rlvect_1(k22_prvect_1(A))
& v5_rlvect_1(k22_prvect_1(A))
& v6_rlvect_1(k22_prvect_1(A))
& l1_rlvect_1(k22_prvect_1(A)) ) ) ).
%------------------------------------------------------------------------------