SET007 Axioms: SET007+809.ax
%------------------------------------------------------------------------------
% File : SET007+809 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Banach Algebra of Bounded Linear Operators
% 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 : lopban_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 70 ( 1 unt; 0 def)
% Number of atoms : 964 ( 77 equ)
% Maximal formula atoms : 45 ( 13 avg)
% Number of connectives : 980 ( 86 ~; 0 |; 761 &)
% ( 6 <=>; 127 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 12 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 42 ( 41 usr; 0 prp; 1-4 aty)
% Number of functors : 46 ( 46 usr; 3 con; 0-7 aty)
% Number of variables : 166 ( 156 !; 10 ?)
% 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_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ( ~ v3_struct_0(k8_lopban_2(A))
& v3_vectsp_1(k8_lopban_2(A)) ) ) ).
fof(fc2_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ( ~ v3_struct_0(k8_lopban_2(A))
& v2_group_1(k8_lopban_2(A))
& v3_vectsp_1(k8_lopban_2(A))
& v6_vectsp_1(k8_lopban_2(A))
& v8_vectsp_1(k8_lopban_2(A)) ) ) ).
fof(fc3_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ( ~ v3_struct_0(k8_lopban_2(A))
& v3_rlvect_1(k8_lopban_2(A))
& v4_rlvect_1(k8_lopban_2(A))
& v5_rlvect_1(k8_lopban_2(A))
& v6_rlvect_1(k8_lopban_2(A))
& v2_group_1(k8_lopban_2(A))
& v4_group_1(k8_lopban_2(A))
& v3_vectsp_1(k8_lopban_2(A))
& v4_vectsp_1(k8_lopban_2(A))
& v5_vectsp_1(k8_lopban_2(A))
& v6_vectsp_1(k8_lopban_2(A))
& v7_vectsp_1(k8_lopban_2(A))
& v8_vectsp_1(k8_lopban_2(A)) ) ) ).
fof(fc4_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ( ~ v3_struct_0(k9_lopban_2(A))
& v1_funcsdom(k9_lopban_2(A)) ) ) ).
fof(fc5_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ( ~ v3_struct_0(k9_lopban_2(A))
& v2_group_1(k9_lopban_2(A))
& v6_vectsp_1(k9_lopban_2(A))
& v8_vectsp_1(k9_lopban_2(A))
& v1_funcsdom(k9_lopban_2(A)) ) ) ).
fof(fc6_lopban_2,axiom,
( ~ v3_struct_0(k3_rsspace3)
& v3_rlvect_1(k3_rsspace3)
& v4_rlvect_1(k3_rsspace3)
& v5_rlvect_1(k3_rsspace3)
& v6_rlvect_1(k3_rsspace3)
& v7_rlvect_1(k3_rsspace3)
& v2_normsp_1(k3_rsspace3)
& v4_lopban_1(k3_rsspace3) ) ).
fof(fc7_lopban_2,axiom,
( ~ v3_struct_0(k3_rsspace3)
& v3_rlvect_1(k3_rsspace3)
& v4_rlvect_1(k3_rsspace3)
& v5_rlvect_1(k3_rsspace3)
& v6_rlvect_1(k3_rsspace3)
& v7_rlvect_1(k3_rsspace3)
& ~ v3_realset2(k3_rsspace3)
& v2_normsp_1(k3_rsspace3)
& v4_lopban_1(k3_rsspace3) ) ).
fof(rc1_lopban_2,axiom,
? [A] :
( l1_normsp_1(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)
& ~ v3_realset2(A)
& v2_normsp_1(A)
& v4_lopban_1(A) ) ).
fof(rc2_lopban_2,axiom,
? [A] :
( l1_lopban_2(A)
& v1_lopban_2(A) ) ).
fof(rc3_lopban_2,axiom,
? [A] :
( l1_lopban_2(A)
& ~ v3_struct_0(A) ) ).
fof(fc8_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ( ~ v3_struct_0(k10_lopban_2(A))
& v1_lopban_2(k10_lopban_2(A)) ) ) ).
fof(fc9_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ( ~ v3_struct_0(k10_lopban_2(A))
& v2_group_1(k10_lopban_2(A))
& v6_vectsp_1(k10_lopban_2(A))
& v8_vectsp_1(k10_lopban_2(A))
& v1_lopban_2(k10_lopban_2(A)) ) ) ).
fof(rc4_lopban_2,axiom,
? [A] :
( l1_lopban_2(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)
& v4_group_1(A)
& v2_funcsdom(A)
& v2_normsp_1(A)
& v1_lopban_2(A) ) ).
fof(fc10_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ( ~ v3_struct_0(k10_lopban_2(A))
& v3_rlvect_1(k10_lopban_2(A))
& v4_rlvect_1(k10_lopban_2(A))
& v5_rlvect_1(k10_lopban_2(A))
& v6_rlvect_1(k10_lopban_2(A))
& v7_rlvect_1(k10_lopban_2(A))
& v2_group_1(k10_lopban_2(A))
& v4_group_1(k10_lopban_2(A))
& v6_vectsp_1(k10_lopban_2(A))
& v8_vectsp_1(k10_lopban_2(A))
& v2_funcsdom(k10_lopban_2(A))
& v2_normsp_1(k10_lopban_2(A))
& v1_lopban_2(k10_lopban_2(A)) ) ) ).
fof(cc1_lopban_2,axiom,
! [A] :
( l1_lopban_2(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)
& v4_group_1(A)
& v2_funcsdom(A)
& v2_normsp_1(A)
& v5_lopban_2(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)
& v4_group_1(A)
& v5_vectsp_1(A)
& v8_vectsp_1(A)
& v2_funcsdom(A)
& v2_normsp_1(A)
& v4_lopban_1(A)
& v2_lopban_2(A)
& v3_lopban_2(A)
& v4_lopban_2(A) ) ) ) ).
fof(cc2_lopban_2,axiom,
! [A] :
( l1_lopban_2(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)
& v4_group_1(A)
& v5_vectsp_1(A)
& v8_vectsp_1(A)
& v2_funcsdom(A)
& v2_normsp_1(A)
& v4_lopban_1(A)
& v2_lopban_2(A)
& v3_lopban_2(A)
& v4_lopban_2(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)
& v4_group_1(A)
& v2_funcsdom(A)
& v2_normsp_1(A)
& v5_lopban_2(A) ) ) ) ).
fof(fc11_lopban_2,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)
& ~ v3_realset2(A)
& v2_normsp_1(A)
& v4_lopban_1(A)
& l1_normsp_1(A) )
=> ( ~ v3_struct_0(k10_lopban_2(A))
& v3_rlvect_1(k10_lopban_2(A))
& v4_rlvect_1(k10_lopban_2(A))
& v5_rlvect_1(k10_lopban_2(A))
& v6_rlvect_1(k10_lopban_2(A))
& v7_rlvect_1(k10_lopban_2(A))
& v2_group_1(k10_lopban_2(A))
& v4_group_1(k10_lopban_2(A))
& v5_vectsp_1(k10_lopban_2(A))
& v6_vectsp_1(k10_lopban_2(A))
& v8_vectsp_1(k10_lopban_2(A))
& v2_funcsdom(k10_lopban_2(A))
& v2_normsp_1(k10_lopban_2(A))
& v4_lopban_1(k10_lopban_2(A))
& v1_lopban_2(k10_lopban_2(A))
& v2_lopban_2(k10_lopban_2(A))
& v3_lopban_2(k10_lopban_2(A))
& v4_lopban_2(k10_lopban_2(A))
& v5_lopban_2(k10_lopban_2(A)) ) ) ).
fof(rc5_lopban_2,axiom,
? [A] :
( l1_lopban_2(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)
& v4_group_1(A)
& v5_vectsp_1(A)
& v8_vectsp_1(A)
& v2_funcsdom(A)
& v2_normsp_1(A)
& v4_lopban_1(A)
& v2_lopban_2(A)
& v3_lopban_2(A)
& v4_lopban_2(A)
& v5_lopban_2(A) ) ).
fof(t1_lopban_2,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] :
( ( ~ 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] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& l2_rlvect_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v1_lopban_1(D,A,B)
& v2_lopban_1(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& v1_lopban_1(E,B,C)
& v2_lopban_1(E,B,C)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( v1_funct_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E))
& v1_funct_2(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),u1_struct_0(A),u1_struct_0(C))
& v1_lopban_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)
& v2_lopban_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)
& m2_relset_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),u1_struct_0(A),u1_struct_0(C)) ) ) ) ) ) ) ).
fof(t2_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(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)
& v2_normsp_1(B)
& l1_normsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_normsp_1(C)
& l1_normsp_1(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& v1_lopban_1(D,A,B)
& v2_lopban_1(D,A,B)
& v3_lopban_1(D,A,B)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& v1_lopban_1(E,B,C)
& v2_lopban_1(E,B,C)
& v3_lopban_1(E,B,C)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( v1_funct_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E))
& v1_funct_2(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),u1_struct_0(A),u1_struct_0(C))
& v1_lopban_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)
& v2_lopban_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)
& v3_lopban_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),A,C)
& m2_relset_1(k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),u1_struct_0(A),u1_struct_0(C))
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r1_xreal_0(k1_normsp_1(C,k8_funct_2(u1_struct_0(A),u1_struct_0(C),k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E),F)),k4_real_1(k4_real_1(k2_seq_1(k10_lopban_1(B,C),k1_numbers,k15_lopban_1(B,C),E),k2_seq_1(k10_lopban_1(A,B),k1_numbers,k15_lopban_1(A,B),D)),k1_normsp_1(A,F)))
& r1_xreal_0(k2_seq_1(k10_lopban_1(A,C),k1_numbers,k15_lopban_1(A,C),k7_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),D,E)),k4_real_1(k2_seq_1(k10_lopban_1(B,C),k1_numbers,k15_lopban_1(B,C),E),k2_seq_1(k10_lopban_1(A,B),k1_numbers,k15_lopban_1(A,B),D))) ) ) ) ) ) ) ) ) ).
fof(d1_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_struct_0(B,k8_lopban_1(A,A),k10_lopban_1(A,A))
=> ! [C] :
( m1_struct_0(C,k8_lopban_1(A,A),k10_lopban_1(A,A))
=> k3_lopban_2(A,B,C) = k2_binop_1(k10_lopban_1(A,A),k10_lopban_1(A,A),k10_lopban_1(A,A),k8_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),B,C) ) ) ) ).
fof(d2_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_struct_0(B,k8_lopban_1(A,A),k10_lopban_1(A,A))
=> ! [C] :
( m1_struct_0(C,k8_lopban_1(A,A),k10_lopban_1(A,A))
=> k4_lopban_2(A,B,C) = k2_lopban_2(A,k13_lopban_1(A,A,B),k13_lopban_1(A,A,C)) ) ) ) ).
fof(d3_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_struct_0(B,k8_lopban_1(A,A),k10_lopban_1(A,A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k5_lopban_2(A,B,C) = k2_binop_1(k1_numbers,k10_lopban_1(A,A),k10_lopban_1(A,A),k9_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),C,B) ) ) ) ).
fof(d4_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(k10_lopban_1(A,A),k10_lopban_1(A,A)),k10_lopban_1(A,A))
& m2_relset_1(B,k2_zfmisc_1(k10_lopban_1(A,A),k10_lopban_1(A,A)),k10_lopban_1(A,A)) )
=> ( B = k6_lopban_2(A)
<=> ! [C] :
( m1_struct_0(C,k8_lopban_1(A,A),k10_lopban_1(A,A))
=> ! [D] :
( m1_struct_0(D,k8_lopban_1(A,A),k10_lopban_1(A,A))
=> k2_binop_1(k10_lopban_1(A,A),k10_lopban_1(A,A),k10_lopban_1(A,A),B,C,D) = k4_lopban_2(A,D,C) ) ) ) ) ) ).
fof(t3_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ( v1_funct_1(k6_partfun1(u1_struct_0(A)))
& v1_funct_2(k6_partfun1(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(A))
& v1_lopban_1(k6_partfun1(u1_struct_0(A)),A,A)
& v2_lopban_1(k6_partfun1(u1_struct_0(A)),A,A)
& v3_lopban_1(k6_partfun1(u1_struct_0(A)),A,A)
& m2_relset_1(k6_partfun1(u1_struct_0(A)),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(d5_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> k7_lopban_2(A) = k6_partfun1(u1_struct_0(A)) ) ).
fof(t4_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_lopban_1(B,A,A)
& v2_lopban_1(B,A,A)
& v3_lopban_1(B,A,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v1_lopban_1(C,A,A)
& v2_lopban_1(C,A,A)
& v3_lopban_1(C,A,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& v1_lopban_1(D,A,A)
& v2_lopban_1(D,A,A)
& v3_lopban_1(D,A,A)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> ( D = k2_lopban_2(A,C,B)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,E) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,E)) ) ) ) ) ) ) ).
fof(t5_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_lopban_1(B,A,A)
& v2_lopban_1(B,A,A)
& v3_lopban_1(B,A,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v1_lopban_1(C,A,A)
& v2_lopban_1(C,A,A)
& v3_lopban_1(C,A,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
& v1_lopban_1(D,A,A)
& v2_lopban_1(D,A,A)
& v3_lopban_1(D,A,A)
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
=> k2_lopban_2(A,k2_lopban_2(A,D,C),B) = k2_lopban_2(A,D,k2_lopban_2(A,C,B)) ) ) ) ) ).
fof(t6_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_lopban_1(B,A,A)
& v2_lopban_1(B,A,A)
& v3_lopban_1(B,A,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k6_partfun1(u1_struct_0(A)),B) = B
& k7_funct_2(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,k6_partfun1(u1_struct_0(A))) = B ) ) ) ).
fof(t7_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_struct_0(B,k8_lopban_1(A,A),k10_lopban_1(A,A))
=> ! [C] :
( m1_struct_0(C,k8_lopban_1(A,A),k10_lopban_1(A,A))
=> ! [D] :
( m1_struct_0(D,k8_lopban_1(A,A),k10_lopban_1(A,A))
=> k4_lopban_2(A,k4_lopban_2(A,D,C),B) = k4_lopban_2(A,D,k4_lopban_2(A,C,B)) ) ) ) ) ).
fof(t8_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_struct_0(B,k8_lopban_1(A,A),k10_lopban_1(A,A))
=> ( k4_lopban_2(A,k7_lopban_2(A),B) = B
& k4_lopban_2(A,B,k7_lopban_2(A)) = B ) ) ) ).
fof(t9_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_struct_0(B,k8_lopban_1(A,A),k10_lopban_1(A,A))
=> ! [C] :
( m1_struct_0(C,k8_lopban_1(A,A),k10_lopban_1(A,A))
=> ! [D] :
( m1_struct_0(D,k8_lopban_1(A,A),k10_lopban_1(A,A))
=> k4_lopban_2(A,k3_lopban_2(A,C,D),B) = k3_lopban_2(A,k4_lopban_2(A,C,B),k4_lopban_2(A,D,B)) ) ) ) ) ).
fof(t10_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_struct_0(B,k8_lopban_1(A,A),k10_lopban_1(A,A))
=> ! [C] :
( m1_struct_0(C,k8_lopban_1(A,A),k10_lopban_1(A,A))
=> ! [D] :
( m1_struct_0(D,k8_lopban_1(A,A),k10_lopban_1(A,A))
=> k4_lopban_2(A,B,k3_lopban_2(A,C,D)) = k3_lopban_2(A,k4_lopban_2(A,B,C),k4_lopban_2(A,B,D)) ) ) ) ) ).
fof(t11_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_struct_0(B,k8_lopban_1(A,A),k10_lopban_1(A,A))
=> ! [C] :
( m1_struct_0(C,k8_lopban_1(A,A),k10_lopban_1(A,A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> k5_lopban_2(A,k4_lopban_2(A,C,B),k4_real_1(D,E)) = k4_lopban_2(A,k5_lopban_2(A,C,E),k5_lopban_2(A,B,D)) ) ) ) ) ) ).
fof(t12_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_struct_0(B,k8_lopban_1(A,A),k10_lopban_1(A,A))
=> ! [C] :
( m1_struct_0(C,k8_lopban_1(A,A),k10_lopban_1(A,A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> k5_lopban_2(A,k4_lopban_2(A,C,B),D) = k4_lopban_2(A,C,k5_lopban_2(A,B,D)) ) ) ) ) ).
fof(d6_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> k8_lopban_2(A) = g3_vectsp_1(k10_lopban_1(A,A),k8_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),k6_lopban_2(A),k7_lopban_2(A),k10_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A))) ) ).
fof(t13_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k8_lopban_2(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k8_lopban_2(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k8_lopban_2(A)))
=> ( k2_rlvect_1(k8_lopban_2(A),B,C) = k2_rlvect_1(k8_lopban_2(A),C,B)
& k2_rlvect_1(k8_lopban_2(A),k2_rlvect_1(k8_lopban_2(A),B,C),D) = k2_rlvect_1(k8_lopban_2(A),B,k2_rlvect_1(k8_lopban_2(A),C,D))
& k2_rlvect_1(k8_lopban_2(A),B,k1_rlvect_1(k8_lopban_2(A))) = B
& ? [E] :
( m1_subset_1(E,u1_struct_0(k8_lopban_2(A)))
& k2_rlvect_1(k8_lopban_2(A),B,E) = k1_rlvect_1(k8_lopban_2(A)) )
& k1_group_1(k8_lopban_2(A),k1_group_1(k8_lopban_2(A),B,C),D) = k1_group_1(k8_lopban_2(A),B,k1_group_1(k8_lopban_2(A),C,D))
& k1_group_1(k8_lopban_2(A),B,k2_group_1(k8_lopban_2(A))) = B
& k1_group_1(k8_lopban_2(A),k2_group_1(k8_lopban_2(A)),B) = B
& k1_group_1(k8_lopban_2(A),B,k2_rlvect_1(k8_lopban_2(A),C,D)) = k2_rlvect_1(k8_lopban_2(A),k1_group_1(k8_lopban_2(A),B,C),k1_group_1(k8_lopban_2(A),B,D))
& k1_group_1(k8_lopban_2(A),k2_rlvect_1(k8_lopban_2(A),C,D),B) = k2_rlvect_1(k8_lopban_2(A),k1_group_1(k8_lopban_2(A),C,B),k1_group_1(k8_lopban_2(A),D,B)) ) ) ) ) ) ).
fof(t14_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ( ~ v3_struct_0(k8_lopban_2(A))
& v3_rlvect_1(k8_lopban_2(A))
& v4_rlvect_1(k8_lopban_2(A))
& v5_rlvect_1(k8_lopban_2(A))
& v6_rlvect_1(k8_lopban_2(A))
& v4_group_1(k8_lopban_2(A))
& v6_vectsp_1(k8_lopban_2(A))
& v7_vectsp_1(k8_lopban_2(A))
& v8_vectsp_1(k8_lopban_2(A))
& l3_vectsp_1(k8_lopban_2(A)) ) ) ).
fof(d7_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> k9_lopban_2(A) = g1_funcsdom(k10_lopban_1(A,A),k6_lopban_2(A),k8_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),k9_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),k7_lopban_2(A),k10_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A))) ) ).
fof(t15_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k9_lopban_2(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k9_lopban_2(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k9_lopban_2(A)))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( k2_rlvect_1(k9_lopban_2(A),B,C) = k2_rlvect_1(k9_lopban_2(A),C,B)
& k2_rlvect_1(k9_lopban_2(A),k2_rlvect_1(k9_lopban_2(A),B,C),D) = k2_rlvect_1(k9_lopban_2(A),B,k2_rlvect_1(k9_lopban_2(A),C,D))
& k2_rlvect_1(k9_lopban_2(A),B,k1_rlvect_1(k9_lopban_2(A))) = B
& ? [G] :
( m1_subset_1(G,u1_struct_0(k9_lopban_2(A)))
& k2_rlvect_1(k9_lopban_2(A),B,G) = k1_rlvect_1(k9_lopban_2(A)) )
& k1_group_1(k9_lopban_2(A),k1_group_1(k9_lopban_2(A),B,C),D) = k1_group_1(k9_lopban_2(A),B,k1_group_1(k9_lopban_2(A),C,D))
& k1_group_1(k9_lopban_2(A),B,k2_group_1(k9_lopban_2(A))) = B
& k1_group_1(k9_lopban_2(A),k2_group_1(k9_lopban_2(A)),B) = B
& k1_group_1(k9_lopban_2(A),B,k2_rlvect_1(k9_lopban_2(A),C,D)) = k2_rlvect_1(k9_lopban_2(A),k1_group_1(k9_lopban_2(A),B,C),k1_group_1(k9_lopban_2(A),B,D))
& k1_group_1(k9_lopban_2(A),k2_rlvect_1(k9_lopban_2(A),C,D),B) = k2_rlvect_1(k9_lopban_2(A),k1_group_1(k9_lopban_2(A),C,B),k1_group_1(k9_lopban_2(A),D,B))
& k3_rlvect_1(k9_lopban_2(A),k1_group_1(k9_lopban_2(A),B,C),E) = k1_group_1(k9_lopban_2(A),k3_rlvect_1(k9_lopban_2(A),B,E),C)
& k3_rlvect_1(k9_lopban_2(A),k2_rlvect_1(k9_lopban_2(A),B,C),E) = k2_rlvect_1(k9_lopban_2(A),k3_rlvect_1(k9_lopban_2(A),B,E),k3_rlvect_1(k9_lopban_2(A),C,E))
& k3_rlvect_1(k9_lopban_2(A),B,k3_real_1(E,F)) = k2_rlvect_1(k9_lopban_2(A),k3_rlvect_1(k9_lopban_2(A),B,E),k3_rlvect_1(k9_lopban_2(A),B,F))
& k3_rlvect_1(k9_lopban_2(A),B,k4_real_1(E,F)) = k3_rlvect_1(k9_lopban_2(A),k3_rlvect_1(k9_lopban_2(A),B,F),E)
& k3_rlvect_1(k9_lopban_2(A),k1_group_1(k9_lopban_2(A),B,C),k4_real_1(E,F)) = k1_group_1(k9_lopban_2(A),k3_rlvect_1(k9_lopban_2(A),B,E),k3_rlvect_1(k9_lopban_2(A),C,F)) ) ) ) ) ) ) ) ).
fof(t16_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ( ~ v3_struct_0(k9_lopban_2(A))
& v3_rlvect_1(k9_lopban_2(A))
& v4_rlvect_1(k9_lopban_2(A))
& v5_rlvect_1(k9_lopban_2(A))
& v6_rlvect_1(k9_lopban_2(A))
& v4_group_1(k9_lopban_2(A))
& v2_funcsdom(k9_lopban_2(A))
& l1_funcsdom(k9_lopban_2(A)) ) ) ).
fof(t17_lopban_2,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)
& ~ v3_realset2(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& k1_normsp_1(A,B) = np__1 ) ) ).
fof(t18_lopban_2,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)
& ~ v3_realset2(A)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> k2_seq_1(k10_lopban_1(A,A),k1_numbers,k15_lopban_1(A,A),k6_partfun1(u1_struct_0(A))) = np__1 ) ).
fof(d8_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> k10_lopban_2(A) = g1_lopban_2(k10_lopban_1(A,A),k6_lopban_2(A),k8_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),k9_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),k7_lopban_2(A),k10_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),k15_lopban_1(A,A)) ) ).
fof(t19_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k10_lopban_2(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k10_lopban_2(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k10_lopban_2(A)))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( k2_rlvect_1(k10_lopban_2(A),B,C) = k2_rlvect_1(k10_lopban_2(A),C,B)
& k2_rlvect_1(k10_lopban_2(A),k2_rlvect_1(k10_lopban_2(A),B,C),D) = k2_rlvect_1(k10_lopban_2(A),B,k2_rlvect_1(k10_lopban_2(A),C,D))
& k2_rlvect_1(k10_lopban_2(A),B,k1_rlvect_1(k10_lopban_2(A))) = B
& ? [G] :
( m1_subset_1(G,u1_struct_0(k10_lopban_2(A)))
& k2_rlvect_1(k10_lopban_2(A),B,G) = k1_rlvect_1(k10_lopban_2(A)) )
& k1_group_1(k10_lopban_2(A),k1_group_1(k10_lopban_2(A),B,C),D) = k1_group_1(k10_lopban_2(A),B,k1_group_1(k10_lopban_2(A),C,D))
& k1_group_1(k10_lopban_2(A),B,k2_group_1(k10_lopban_2(A))) = B
& k1_group_1(k10_lopban_2(A),k2_group_1(k10_lopban_2(A)),B) = B
& k1_group_1(k10_lopban_2(A),B,k2_rlvect_1(k10_lopban_2(A),C,D)) = k2_rlvect_1(k10_lopban_2(A),k1_group_1(k10_lopban_2(A),B,C),k1_group_1(k10_lopban_2(A),B,D))
& k1_group_1(k10_lopban_2(A),k2_rlvect_1(k10_lopban_2(A),C,D),B) = k2_rlvect_1(k10_lopban_2(A),k1_group_1(k10_lopban_2(A),C,B),k1_group_1(k10_lopban_2(A),D,B))
& k3_rlvect_1(k10_lopban_2(A),k1_group_1(k10_lopban_2(A),B,C),E) = k1_group_1(k10_lopban_2(A),k3_rlvect_1(k10_lopban_2(A),B,E),C)
& k3_rlvect_1(k10_lopban_2(A),k1_group_1(k10_lopban_2(A),B,C),k4_real_1(E,F)) = k1_group_1(k10_lopban_2(A),k3_rlvect_1(k10_lopban_2(A),B,E),k3_rlvect_1(k10_lopban_2(A),C,F))
& k3_rlvect_1(k10_lopban_2(A),k2_rlvect_1(k10_lopban_2(A),B,C),E) = k2_rlvect_1(k10_lopban_2(A),k3_rlvect_1(k10_lopban_2(A),B,E),k3_rlvect_1(k10_lopban_2(A),C,E))
& k3_rlvect_1(k10_lopban_2(A),B,k3_real_1(E,F)) = k2_rlvect_1(k10_lopban_2(A),k3_rlvect_1(k10_lopban_2(A),B,E),k3_rlvect_1(k10_lopban_2(A),B,F))
& k3_rlvect_1(k10_lopban_2(A),B,k4_real_1(E,F)) = k3_rlvect_1(k10_lopban_2(A),k3_rlvect_1(k10_lopban_2(A),B,F),E)
& k3_rlvect_1(k10_lopban_2(A),B,np__1) = B ) ) ) ) ) ) ) ).
fof(t20_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ( v2_normsp_1(k10_lopban_2(A))
& v3_rlvect_1(k10_lopban_2(A))
& v4_rlvect_1(k10_lopban_2(A))
& v5_rlvect_1(k10_lopban_2(A))
& v6_rlvect_1(k10_lopban_2(A))
& v4_group_1(k10_lopban_2(A))
& v2_funcsdom(k10_lopban_2(A))
& v7_rlvect_1(k10_lopban_2(A)) ) ) ).
fof(d9_lopban_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_lopban_2(A) )
=> ( v2_lopban_2(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_xreal_0(k1_normsp_1(A,k1_group_1(A,B,C)),k4_real_1(k1_normsp_1(A,B),k1_normsp_1(A,C))) ) ) ) ) ).
fof(d10_lopban_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_lopban_2(A) )
=> ( v3_lopban_2(A)
<=> k1_normsp_1(A,k2_group_1(A)) = np__1 ) ) ).
fof(d11_lopban_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_lopban_2(A) )
=> ( v4_lopban_2(A)
<=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k3_rlvect_1(A,k1_group_1(A,C,D),B) = k1_group_1(A,C,k3_rlvect_1(A,D,B)) ) ) ) ) ) ).
fof(d12_lopban_2,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)
& v4_group_1(A)
& v2_funcsdom(A)
& v2_normsp_1(A)
& l1_lopban_2(A) )
=> ( v5_lopban_2(A)
<=> ( v2_lopban_2(A)
& v3_lopban_2(A)
& v4_lopban_2(A)
& v8_vectsp_1(A)
& v5_vectsp_1(A)
& v4_lopban_1(A) ) ) ) ).
fof(t21_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> k2_group_1(k8_lopban_2(A)) = k7_lopban_2(A) ) ).
fof(t22_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> k2_group_1(k9_lopban_2(A)) = k7_lopban_2(A) ) ).
fof(t23_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> k2_group_1(k10_lopban_2(A)) = k7_lopban_2(A) ) ).
fof(dt_l1_lopban_2,axiom,
! [A] :
( l1_lopban_2(A)
=> ( l1_funcsdom(A)
& l1_normsp_1(A) ) ) ).
fof(existence_l1_lopban_2,axiom,
? [A] : l1_lopban_2(A) ).
fof(abstractness_v1_lopban_2,axiom,
! [A] :
( l1_lopban_2(A)
=> ( v1_lopban_2(A)
=> A = g1_lopban_2(u1_struct_0(A),u1_group_1(A),u1_rlvect_1(A),u2_rlvect_1(A),u1_vectsp_1(A),u2_struct_0(A),u1_normsp_1(A)) ) ) ).
fof(dt_k1_lopban_2,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k1_fraenkel(A,A))
& m1_subset_1(C,k1_fraenkel(A,A)) )
=> m2_fraenkel(k1_lopban_2(A,B,C),A,A,k1_fraenkel(A,A)) ) ).
fof(redefinition_k1_lopban_2,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k1_fraenkel(A,A))
& m1_subset_1(C,k1_fraenkel(A,A)) )
=> k1_lopban_2(A,B,C) = k5_relat_1(B,C) ) ).
fof(dt_k2_lopban_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_lopban_1(B,A,A)
& v2_lopban_1(B,A,A)
& v3_lopban_1(B,A,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v1_lopban_1(C,A,A)
& v2_lopban_1(C,A,A)
& v3_lopban_1(C,A,A)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( v1_funct_1(k2_lopban_2(A,B,C))
& v1_funct_2(k2_lopban_2(A,B,C),u1_struct_0(A),u1_struct_0(A))
& v1_lopban_1(k2_lopban_2(A,B,C),A,A)
& v2_lopban_1(k2_lopban_2(A,B,C),A,A)
& v3_lopban_1(k2_lopban_2(A,B,C),A,A)
& m2_relset_1(k2_lopban_2(A,B,C),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(redefinition_k2_lopban_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_lopban_1(B,A,A)
& v2_lopban_1(B,A,A)
& v3_lopban_1(B,A,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v1_lopban_1(C,A,A)
& v2_lopban_1(C,A,A)
& v3_lopban_1(C,A,A)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> k2_lopban_2(A,B,C) = k5_relat_1(B,C) ) ).
fof(dt_k3_lopban_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A)
& m1_subset_1(B,k10_lopban_1(A,A))
& m1_subset_1(C,k10_lopban_1(A,A)) )
=> m1_struct_0(k3_lopban_2(A,B,C),k8_lopban_1(A,A),k10_lopban_1(A,A)) ) ).
fof(dt_k4_lopban_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A)
& m1_subset_1(B,k10_lopban_1(A,A))
& m1_subset_1(C,k10_lopban_1(A,A)) )
=> m1_struct_0(k4_lopban_2(A,B,C),k8_lopban_1(A,A),k10_lopban_1(A,A)) ) ).
fof(dt_k5_lopban_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_normsp_1(A)
& l1_normsp_1(A)
& m1_subset_1(B,k10_lopban_1(A,A))
& m1_subset_1(C,k1_numbers) )
=> m1_struct_0(k5_lopban_2(A,B,C),k8_lopban_1(A,A),k10_lopban_1(A,A)) ) ).
fof(dt_k6_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> ( v1_funct_1(k6_lopban_2(A))
& v1_funct_2(k6_lopban_2(A),k2_zfmisc_1(k10_lopban_1(A,A),k10_lopban_1(A,A)),k10_lopban_1(A,A))
& m2_relset_1(k6_lopban_2(A),k2_zfmisc_1(k10_lopban_1(A,A),k10_lopban_1(A,A)),k10_lopban_1(A,A)) ) ) ).
fof(dt_k7_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> m1_struct_0(k7_lopban_2(A),k8_lopban_1(A,A),k10_lopban_1(A,A)) ) ).
fof(dt_k8_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> l3_vectsp_1(k8_lopban_2(A)) ) ).
fof(dt_k9_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> l1_funcsdom(k9_lopban_2(A)) ) ).
fof(dt_k10_lopban_2,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)
& v2_normsp_1(A)
& l1_normsp_1(A) )
=> l1_lopban_2(k10_lopban_2(A)) ) ).
fof(dt_g1_lopban_2,axiom,
! [A,B,C,D,E,F,G] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A)
& m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A)
& m1_subset_1(E,A)
& m1_subset_1(F,A)
& v1_funct_1(G)
& v1_funct_2(G,A,k1_numbers)
& m1_relset_1(G,A,k1_numbers) )
=> ( v1_lopban_2(g1_lopban_2(A,B,C,D,E,F,G))
& l1_lopban_2(g1_lopban_2(A,B,C,D,E,F,G)) ) ) ).
fof(free_g1_lopban_2,axiom,
! [A,B,C,D,E,F,G] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(k1_numbers,A),A)
& m1_relset_1(D,k2_zfmisc_1(k1_numbers,A),A)
& m1_subset_1(E,A)
& m1_subset_1(F,A)
& v1_funct_1(G)
& v1_funct_2(G,A,k1_numbers)
& m1_relset_1(G,A,k1_numbers) )
=> ! [H,I,J,K,L,M,N] :
( g1_lopban_2(A,B,C,D,E,F,G) = g1_lopban_2(H,I,J,K,L,M,N)
=> ( A = H
& B = I
& C = J
& D = K
& E = L
& F = M
& G = N ) ) ) ).
%------------------------------------------------------------------------------