SET007 Axioms: SET007+802.ax
%------------------------------------------------------------------------------
% File : SET007+802 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Banach Space 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_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 104 ( 2 unt; 0 def)
% Number of atoms : 1748 ( 74 equ)
% Maximal formula atoms : 26 ( 16 avg)
% Number of connectives : 1860 ( 216 ~; 0 |;1343 &)
% ( 24 <=>; 277 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 14 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 37 ( 35 usr; 1 prp; 0-4 aty)
% Number of functors : 55 ( 55 usr; 4 con; 0-6 aty)
% Number of variables : 342 ( 334 !; 8 ?)
% 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_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ 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) )
=> ( ~ v3_struct_0(k5_lopban_1(A,B))
& v2_rlvect_1(k5_lopban_1(A,B))
& v3_rlvect_1(k5_lopban_1(A,B))
& v4_rlvect_1(k5_lopban_1(A,B))
& v5_rlvect_1(k5_lopban_1(A,B))
& v6_rlvect_1(k5_lopban_1(A,B))
& v7_rlvect_1(k5_lopban_1(A,B)) ) ) ).
fof(fc2_lopban_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ 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) )
=> ( ~ v3_struct_0(k5_lopban_1(A,B))
& v2_rlvect_1(k5_lopban_1(A,B))
& v3_rlvect_1(k5_lopban_1(A,B))
& v4_rlvect_1(k5_lopban_1(A,B))
& v5_rlvect_1(k5_lopban_1(A,B))
& v6_rlvect_1(k5_lopban_1(A,B))
& v7_rlvect_1(k5_lopban_1(A,B))
& v1_monoid_0(k5_lopban_1(A,B)) ) ) ).
fof(rc1_lopban_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A)
& ~ 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_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_lopban_1(C,A,B)
& v2_lopban_1(C,A,B) ) ) ).
fof(fc3_lopban_1,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)
& ~ 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) )
=> ( ~ v1_xboole_0(k7_lopban_1(A,B))
& v1_fraenkel(k7_lopban_1(A,B)) ) ) ).
fof(fc4_lopban_1,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)
& ~ 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) )
=> ( ~ v3_struct_0(g2_rlvect_1(k7_lopban_1(A,B),k10_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k8_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k9_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B))))
& v2_rlvect_1(g2_rlvect_1(k7_lopban_1(A,B),k10_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k8_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k9_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B))))
& v3_rlvect_1(g2_rlvect_1(k7_lopban_1(A,B),k10_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k8_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k9_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B))))
& v4_rlvect_1(g2_rlvect_1(k7_lopban_1(A,B),k10_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k8_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k9_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B))))
& v5_rlvect_1(g2_rlvect_1(k7_lopban_1(A,B),k10_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k8_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k9_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B))))
& v6_rlvect_1(g2_rlvect_1(k7_lopban_1(A,B),k10_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k8_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k9_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B))))
& v7_rlvect_1(g2_rlvect_1(k7_lopban_1(A,B),k10_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k8_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k9_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)))) ) ) ).
fof(fc5_lopban_1,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)
& ~ 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) )
=> ( ~ v3_struct_0(k8_lopban_1(A,B))
& v2_rlvect_1(k8_lopban_1(A,B))
& v3_rlvect_1(k8_lopban_1(A,B))
& v4_rlvect_1(k8_lopban_1(A,B))
& v5_rlvect_1(k8_lopban_1(A,B))
& v6_rlvect_1(k8_lopban_1(A,B))
& v7_rlvect_1(k8_lopban_1(A,B)) ) ) ).
fof(fc6_lopban_1,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)
& ~ 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) )
=> ( ~ v3_struct_0(k8_lopban_1(A,B))
& v2_rlvect_1(k8_lopban_1(A,B))
& v3_rlvect_1(k8_lopban_1(A,B))
& v4_rlvect_1(k8_lopban_1(A,B))
& v5_rlvect_1(k8_lopban_1(A,B))
& v6_rlvect_1(k8_lopban_1(A,B))
& v7_rlvect_1(k8_lopban_1(A,B))
& v1_monoid_0(k8_lopban_1(A,B)) ) ) ).
fof(rc2_lopban_1,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)
& v2_normsp_1(A)
& l1_normsp_1(A)
& ~ 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] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_lopban_1(C,A,B)
& v2_lopban_1(C,A,B)
& v3_lopban_1(C,A,B) ) ) ).
fof(fc7_lopban_1,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)
& v2_normsp_1(A)
& l1_normsp_1(A)
& ~ 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) )
=> ~ v1_xboole_0(k10_lopban_1(A,B)) ) ).
fof(fc8_lopban_1,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)
& v2_normsp_1(A)
& l1_normsp_1(A)
& ~ 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) )
=> ( ~ v3_struct_0(g2_rlvect_1(k10_lopban_1(A,B),k10_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B))))
& v2_rlvect_1(g2_rlvect_1(k10_lopban_1(A,B),k10_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B))))
& v3_rlvect_1(g2_rlvect_1(k10_lopban_1(A,B),k10_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B))))
& v4_rlvect_1(g2_rlvect_1(k10_lopban_1(A,B),k10_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B))))
& v5_rlvect_1(g2_rlvect_1(k10_lopban_1(A,B),k10_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B))))
& v6_rlvect_1(g2_rlvect_1(k10_lopban_1(A,B),k10_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B))))
& v7_rlvect_1(g2_rlvect_1(k10_lopban_1(A,B),k10_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)))) ) ) ).
fof(fc9_lopban_1,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)
& v2_normsp_1(A)
& l1_normsp_1(A)
& ~ 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) )
=> ( ~ v3_struct_0(k11_lopban_1(A,B))
& v2_rlvect_1(k11_lopban_1(A,B))
& v3_rlvect_1(k11_lopban_1(A,B))
& v4_rlvect_1(k11_lopban_1(A,B))
& v5_rlvect_1(k11_lopban_1(A,B))
& v6_rlvect_1(k11_lopban_1(A,B))
& v7_rlvect_1(k11_lopban_1(A,B)) ) ) ).
fof(cc1_lopban_1,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)
& v2_normsp_1(A)
& l1_normsp_1(A)
& ~ 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] :
( m1_subset_1(C,u1_struct_0(k11_lopban_1(A,B)))
=> ( v1_relat_1(C)
& v1_funct_1(C) ) ) ) ).
fof(cc2_lopban_1,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)
& v2_normsp_1(A)
& l1_normsp_1(A)
& ~ 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] :
( m1_subset_1(C,u1_struct_0(k16_lopban_1(A,B)))
=> ( v1_relat_1(C)
& v1_funct_1(C) ) ) ) ).
fof(fc10_lopban_1,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)
& v2_normsp_1(A)
& l1_normsp_1(A)
& ~ 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) )
=> ( ~ v3_struct_0(k16_lopban_1(A,B))
& v3_rlvect_1(k16_lopban_1(A,B))
& v4_rlvect_1(k16_lopban_1(A,B))
& v5_rlvect_1(k16_lopban_1(A,B))
& v6_rlvect_1(k16_lopban_1(A,B))
& v7_rlvect_1(k16_lopban_1(A,B))
& v2_normsp_1(k16_lopban_1(A,B)) ) ) ).
fof(rc3_lopban_1,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)
& v2_normsp_1(A)
& v4_lopban_1(A) ) ).
fof(fc11_lopban_1,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)
& v2_normsp_1(A)
& l1_normsp_1(A)
& ~ 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)
& v4_lopban_1(B)
& l1_normsp_1(B) )
=> ( ~ v3_struct_0(k16_lopban_1(A,B))
& v3_rlvect_1(k16_lopban_1(A,B))
& v4_rlvect_1(k16_lopban_1(A,B))
& v5_rlvect_1(k16_lopban_1(A,B))
& v6_rlvect_1(k16_lopban_1(A,B))
& v7_rlvect_1(k16_lopban_1(A,B))
& v2_normsp_1(k16_lopban_1(A,B))
& v4_lopban_1(k16_lopban_1(A,B)) ) ) ).
fof(t1_lopban_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_rlvect_1(B) )
=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(k1_fraenkel(A,u1_struct_0(B)),k1_fraenkel(A,u1_struct_0(B))),k1_fraenkel(A,u1_struct_0(B)))
& m2_relset_1(C,k2_zfmisc_1(k1_fraenkel(A,u1_struct_0(B)),k1_fraenkel(A,u1_struct_0(B))),k1_fraenkel(A,u1_struct_0(B)))
& ! [D] :
( m2_fraenkel(D,A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B)))
=> ! [E] :
( m2_fraenkel(E,A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B)))
=> k1_funcsdom(A,u1_struct_0(B),C,D,E) = k4_funcsdom(u1_struct_0(B),A,u1_rlvect_1(B),D,E) ) ) ) ) ) ).
fof(t2_lopban_1,axiom,
! [A] :
( ~ v1_xboole_0(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] :
( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(k1_numbers,k1_fraenkel(A,u1_struct_0(B))),k1_fraenkel(A,u1_struct_0(B)))
& m2_relset_1(C,k2_zfmisc_1(k1_numbers,k1_fraenkel(A,u1_struct_0(B))),k1_fraenkel(A,u1_struct_0(B)))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m2_fraenkel(E,A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B)))
=> ! [F] :
( m1_subset_1(F,A)
=> k8_funct_2(A,u1_struct_0(B),k2_funcsdom(A,u1_struct_0(B),k1_numbers,k1_fraenkel(A,u1_struct_0(B)),C,k1_domain_1(k1_numbers,k1_fraenkel(A,u1_struct_0(B)),D,E)),F) = k3_rlvect_1(B,k8_funct_2(A,u1_struct_0(B),E,F),D) ) ) ) ) ) ) ).
fof(d1_lopban_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(k1_fraenkel(A,u1_struct_0(B)),k1_fraenkel(A,u1_struct_0(B))),k1_fraenkel(A,u1_struct_0(B)))
& m2_relset_1(C,k2_zfmisc_1(k1_fraenkel(A,u1_struct_0(B)),k1_fraenkel(A,u1_struct_0(B))),k1_fraenkel(A,u1_struct_0(B))) )
=> ( C = k2_lopban_1(A,B)
<=> ! [D] :
( m2_fraenkel(D,A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B)))
=> ! [E] :
( m2_fraenkel(E,A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B)))
=> k1_funcsdom(A,u1_struct_0(B),C,D,E) = k4_funcsdom(u1_struct_0(B),A,u1_rlvect_1(B),D,E) ) ) ) ) ) ) ).
fof(d2_lopban_1,axiom,
! [A] :
( ~ v1_xboole_0(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] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(k1_numbers,k1_fraenkel(A,u1_struct_0(B))),k1_fraenkel(A,u1_struct_0(B)))
& m2_relset_1(C,k2_zfmisc_1(k1_numbers,k1_fraenkel(A,u1_struct_0(B))),k1_fraenkel(A,u1_struct_0(B))) )
=> ( C = k3_lopban_1(A,B)
<=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m2_fraenkel(E,A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B)))
=> ! [F] :
( m1_subset_1(F,A)
=> k8_funct_2(A,u1_struct_0(B),k2_funcsdom(A,u1_struct_0(B),k1_numbers,k1_fraenkel(A,u1_struct_0(B)),C,k1_domain_1(k1_numbers,k1_fraenkel(A,u1_struct_0(B)),D,E)),F) = k3_rlvect_1(B,k8_funct_2(A,u1_struct_0(B),E,F),D) ) ) ) ) ) ) ) ).
fof(d3_lopban_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l2_struct_0(B) )
=> k4_lopban_1(A,B) = k2_funcop_1(A,k1_rlvect_1(B)) ) ).
fof(t3_lopban_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_rlvect_1(B) )
=> ! [C] :
( m2_fraenkel(C,A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B)))
=> ! [D] :
( m2_fraenkel(D,A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B)))
=> ! [E] :
( m2_fraenkel(E,A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B)))
=> ( E = k1_funcsdom(A,u1_struct_0(B),k2_lopban_1(A,B),C,D)
<=> ! [F] :
( m1_subset_1(F,A)
=> k8_funct_2(A,u1_struct_0(B),E,F) = k2_rlvect_1(B,k8_funct_2(A,u1_struct_0(B),C,F),k8_funct_2(A,u1_struct_0(B),D,F)) ) ) ) ) ) ) ) ).
fof(t4_lopban_1,axiom,
! [A] :
( ~ v1_xboole_0(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,A)
=> k8_funct_2(A,u1_struct_0(B),k4_lopban_1(A,B),C) = k1_rlvect_1(B) ) ) ) ).
fof(t5_lopban_1,axiom,
! [A] :
( ~ v1_xboole_0(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] :
( m2_fraenkel(C,A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B)))
=> ! [D] :
( m2_fraenkel(D,A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B)))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( C = k2_funcsdom(A,u1_struct_0(B),k1_numbers,k1_fraenkel(A,u1_struct_0(B)),k3_lopban_1(A,B),k1_domain_1(k1_numbers,k1_fraenkel(A,u1_struct_0(B)),E,D))
<=> ! [F] :
( m1_subset_1(F,A)
=> k8_funct_2(A,u1_struct_0(B),C,F) = k3_rlvect_1(B,k8_funct_2(A,u1_struct_0(B),D,F),E) ) ) ) ) ) ) ) ).
fof(t6_lopban_1,axiom,
! [A] :
( ~ v1_xboole_0(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] :
( m2_fraenkel(C,A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B)))
=> ! [D] :
( m2_fraenkel(D,A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B)))
=> k1_funcsdom(A,u1_struct_0(B),k2_lopban_1(A,B),C,D) = k1_funcsdom(A,u1_struct_0(B),k2_lopban_1(A,B),D,C) ) ) ) ) ).
fof(t7_lopban_1,axiom,
! [A] :
( ~ v1_xboole_0(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] :
( m2_fraenkel(C,A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B)))
=> ! [D] :
( m2_fraenkel(D,A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B)))
=> ! [E] :
( m2_fraenkel(E,A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B)))
=> k1_funcsdom(A,u1_struct_0(B),k2_lopban_1(A,B),C,k1_funcsdom(A,u1_struct_0(B),k2_lopban_1(A,B),D,E)) = k1_funcsdom(A,u1_struct_0(B),k2_lopban_1(A,B),k1_funcsdom(A,u1_struct_0(B),k2_lopban_1(A,B),C,D),E) ) ) ) ) ) ).
fof(t8_lopban_1,axiom,
! [A] :
( ~ v1_xboole_0(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] :
( m2_fraenkel(C,A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B)))
=> k1_funcsdom(A,u1_struct_0(B),k2_lopban_1(A,B),k4_lopban_1(A,B),C) = C ) ) ) ).
fof(t9_lopban_1,axiom,
! [A] :
( ~ v1_xboole_0(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] :
( m2_fraenkel(C,A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B)))
=> k1_funcsdom(A,u1_struct_0(B),k2_lopban_1(A,B),C,k2_funcsdom(A,u1_struct_0(B),k1_numbers,k1_fraenkel(A,u1_struct_0(B)),k3_lopban_1(A,B),k1_domain_1(k1_numbers,k1_fraenkel(A,u1_struct_0(B)),k1_real_1(np__1),C))) = k4_lopban_1(A,B) ) ) ) ).
fof(t10_lopban_1,axiom,
! [A] :
( ~ v1_xboole_0(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] :
( m2_fraenkel(C,A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B)))
=> k1_funct_1(k3_lopban_1(A,B),k1_domain_1(k5_numbers,k1_fraenkel(A,u1_struct_0(B)),np__1,C)) = C ) ) ) ).
fof(t11_lopban_1,axiom,
! [A] :
( ~ v1_xboole_0(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] :
( m2_fraenkel(C,A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B)))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> k2_funcsdom(A,u1_struct_0(B),k1_numbers,k1_fraenkel(A,u1_struct_0(B)),k3_lopban_1(A,B),k1_domain_1(k1_numbers,k1_fraenkel(A,u1_struct_0(B)),D,k2_funcsdom(A,u1_struct_0(B),k1_numbers,k1_fraenkel(A,u1_struct_0(B)),k3_lopban_1(A,B),k1_domain_1(k1_numbers,k1_fraenkel(A,u1_struct_0(B)),E,C)))) = k2_funcsdom(A,u1_struct_0(B),k1_numbers,k1_fraenkel(A,u1_struct_0(B)),k3_lopban_1(A,B),k1_domain_1(k1_numbers,k1_fraenkel(A,u1_struct_0(B)),k4_real_1(D,E),C)) ) ) ) ) ) ).
fof(t12_lopban_1,axiom,
! [A] :
( ~ v1_xboole_0(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] :
( m2_fraenkel(C,A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B)))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> k1_funcsdom(A,u1_struct_0(B),k2_lopban_1(A,B),k2_funcsdom(A,u1_struct_0(B),k1_numbers,k1_fraenkel(A,u1_struct_0(B)),k3_lopban_1(A,B),k1_domain_1(k1_numbers,k1_fraenkel(A,u1_struct_0(B)),D,C)),k2_funcsdom(A,u1_struct_0(B),k1_numbers,k1_fraenkel(A,u1_struct_0(B)),k3_lopban_1(A,B),k1_domain_1(k1_numbers,k1_fraenkel(A,u1_struct_0(B)),E,C))) = k2_funcsdom(A,u1_struct_0(B),k1_numbers,k1_fraenkel(A,u1_struct_0(B)),k3_lopban_1(A,B),k1_domain_1(k1_numbers,k1_fraenkel(A,u1_struct_0(B)),k3_real_1(D,E),C)) ) ) ) ) ) ).
fof(t13_lopban_1,axiom,
! [A] :
( ~ v1_xboole_0(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) )
=> ( ~ v3_struct_0(g2_rlvect_1(k1_fraenkel(A,u1_struct_0(B)),k4_lopban_1(A,B),k2_lopban_1(A,B),k3_lopban_1(A,B)))
& v3_rlvect_1(g2_rlvect_1(k1_fraenkel(A,u1_struct_0(B)),k4_lopban_1(A,B),k2_lopban_1(A,B),k3_lopban_1(A,B)))
& v4_rlvect_1(g2_rlvect_1(k1_fraenkel(A,u1_struct_0(B)),k4_lopban_1(A,B),k2_lopban_1(A,B),k3_lopban_1(A,B)))
& v5_rlvect_1(g2_rlvect_1(k1_fraenkel(A,u1_struct_0(B)),k4_lopban_1(A,B),k2_lopban_1(A,B),k3_lopban_1(A,B)))
& v6_rlvect_1(g2_rlvect_1(k1_fraenkel(A,u1_struct_0(B)),k4_lopban_1(A,B),k2_lopban_1(A,B),k3_lopban_1(A,B)))
& v7_rlvect_1(g2_rlvect_1(k1_fraenkel(A,u1_struct_0(B)),k4_lopban_1(A,B),k2_lopban_1(A,B),k3_lopban_1(A,B)))
& l2_rlvect_1(g2_rlvect_1(k1_fraenkel(A,u1_struct_0(B)),k4_lopban_1(A,B),k2_lopban_1(A,B),k3_lopban_1(A,B))) ) ) ) ).
fof(d4_lopban_1,axiom,
! [A] :
( ~ v1_xboole_0(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) )
=> k5_lopban_1(A,B) = g2_rlvect_1(k1_fraenkel(A,u1_struct_0(B)),k4_lopban_1(A,B),k2_lopban_1(A,B),k3_lopban_1(A,B)) ) ) ).
fof(t14_lopban_1,axiom,
! [A] :
( ~ v1_xboole_0(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,u1_struct_0(k5_lopban_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k5_lopban_1(A,B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k5_lopban_1(A,B)))
=> ( E = k4_rlvect_1(k5_lopban_1(A,B),C,D)
<=> ! [F] :
( m1_subset_1(F,A)
=> k6_lopban_1(A,B,E,F) = k4_rlvect_1(B,k6_lopban_1(A,B,C,F),k6_lopban_1(A,B,D,F)) ) ) ) ) ) ) ) ).
fof(t15_lopban_1,axiom,
! [A] :
( ~ v1_xboole_0(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,u1_struct_0(k5_lopban_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k5_lopban_1(A,B)))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( D = k3_rlvect_1(k5_lopban_1(A,B),C,E)
<=> ! [F] :
( m1_subset_1(F,A)
=> k6_lopban_1(A,B,D,F) = k3_rlvect_1(B,k6_lopban_1(A,B,C,F),E) ) ) ) ) ) ) ) ).
fof(t16_lopban_1,axiom,
! [A] :
( ~ v1_xboole_0(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) )
=> k1_rlvect_1(k5_lopban_1(A,B)) = k2_funcop_1(A,k1_rlvect_1(B)) ) ) ).
fof(d5_lopban_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_lopban_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k2_rlvect_1(A,D,E)) = k2_rlvect_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) ) ) ) ) ) ) ).
fof(d6_lopban_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l2_rlvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v2_lopban_1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k3_rlvect_1(A,D,E)) = k3_rlvect_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),E) ) ) ) ) ) ) ).
fof(d7_lopban_1,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] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_lopban_1(u1_struct_0(A),B))))
=> ( C = k7_lopban_1(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ( 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)) ) ) ) ) ) ) ).
fof(t17_lopban_1,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) )
=> v1_rlsub_1(k7_lopban_1(A,B),k5_lopban_1(u1_struct_0(A),B)) ) ) ).
fof(t18_lopban_1,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) )
=> m1_rlsub_1(g2_rlvect_1(k7_lopban_1(A,B),k10_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k8_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k9_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B))),k5_lopban_1(u1_struct_0(A),B)) ) ) ).
fof(d8_lopban_1,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) )
=> k8_lopban_1(A,B) = g2_rlvect_1(k7_lopban_1(A,B),k10_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k8_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k9_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B))) ) ) ).
fof(t19_lopban_1,axiom,
$true ).
fof(t20_lopban_1,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] :
( m1_subset_1(C,u1_struct_0(k8_lopban_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k8_lopban_1(A,B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k8_lopban_1(A,B)))
=> ( E = k4_rlvect_1(k8_lopban_1(A,B),C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k9_lopban_1(A,B,E,F) = k4_rlvect_1(B,k9_lopban_1(A,B,C,F),k9_lopban_1(A,B,D,F)) ) ) ) ) ) ) ) ).
fof(t21_lopban_1,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] :
( m1_subset_1(C,u1_struct_0(k8_lopban_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k8_lopban_1(A,B)))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( D = k3_rlvect_1(k8_lopban_1(A,B),C,E)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k9_lopban_1(A,B,D,F) = k3_rlvect_1(B,k9_lopban_1(A,B,C,F),E) ) ) ) ) ) ) ) ).
fof(t22_lopban_1,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) )
=> k1_rlvect_1(k8_lopban_1(A,B)) = k2_funcop_1(u1_struct_0(A),k1_rlvect_1(B)) ) ) ).
fof(t23_lopban_1,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) )
=> ( v1_funct_1(k2_funcop_1(u1_struct_0(A),k1_rlvect_1(B)))
& v1_funct_2(k2_funcop_1(u1_struct_0(A),k1_rlvect_1(B)),u1_struct_0(A),u1_struct_0(B))
& v1_lopban_1(k2_funcop_1(u1_struct_0(A),k1_rlvect_1(B)),A,B)
& v2_lopban_1(k2_funcop_1(u1_struct_0(A),k1_rlvect_1(B)),A,B)
& m2_relset_1(k2_funcop_1(u1_struct_0(A),k1_rlvect_1(B)),u1_struct_0(A),u1_struct_0(B)) ) ) ) ).
fof(t24_lopban_1,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,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( v4_normsp_1(B,A)
& k8_normsp_1(A,B) = C )
=> ( v4_seq_2(k7_normsp_1(A,B))
& k2_seq_2(k7_normsp_1(A,B)) = k1_normsp_1(A,C) ) ) ) ) ) ).
fof(d9_lopban_1,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_lopban_1(C,A,B)
& v2_lopban_1(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v3_lopban_1(C,A,B)
<=> ? [D] :
( m1_subset_1(D,k1_numbers)
& r1_xreal_0(np__0,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> r1_xreal_0(k1_normsp_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)),k4_real_1(D,k1_normsp_1(A,E))) ) ) ) ) ) ) ).
fof(t25_lopban_1,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_lopban_1(C,A,B)
& v2_lopban_1(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D) = k1_rlvect_1(B) )
=> v3_lopban_1(C,A,B) ) ) ) ) ).
fof(d10_lopban_1,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] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k8_lopban_1(A,B))))
=> ( C = k10_lopban_1(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ( 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)) ) ) ) ) ) ) ).
fof(t26_lopban_1,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) )
=> v1_rlsub_1(k10_lopban_1(A,B),k8_lopban_1(A,B)) ) ) ).
fof(t27_lopban_1,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) )
=> m1_rlsub_1(g2_rlvect_1(k10_lopban_1(A,B),k10_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B))),k8_lopban_1(A,B)) ) ) ).
fof(d11_lopban_1,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) )
=> k11_lopban_1(A,B) = g2_rlvect_1(k10_lopban_1(A,B),k10_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B))) ) ) ).
fof(t28_lopban_1,axiom,
$true ).
fof(t29_lopban_1,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] :
( m1_subset_1(C,u1_struct_0(k11_lopban_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k11_lopban_1(A,B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k11_lopban_1(A,B)))
=> ( E = k4_rlvect_1(k11_lopban_1(A,B),C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k12_lopban_1(A,B,E,F) = k4_rlvect_1(B,k12_lopban_1(A,B,C,F),k12_lopban_1(A,B,D,F)) ) ) ) ) ) ) ) ).
fof(t30_lopban_1,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] :
( m1_subset_1(C,u1_struct_0(k11_lopban_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k11_lopban_1(A,B)))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( D = k3_rlvect_1(k11_lopban_1(A,B),C,E)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k12_lopban_1(A,B,D,F) = k3_rlvect_1(B,k12_lopban_1(A,B,C,F),E) ) ) ) ) ) ) ) ).
fof(t31_lopban_1,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) )
=> k1_rlvect_1(k11_lopban_1(A,B)) = k2_funcop_1(u1_struct_0(A),k1_rlvect_1(B)) ) ) ).
fof(d12_lopban_1,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] :
( r2_hidden(C,k10_lopban_1(A,B))
=> k13_lopban_1(A,B,C) = C ) ) ) ).
fof(t32_lopban_1,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_lopban_1(C,A,B)
& v2_lopban_1(C,A,B)
& v3_lopban_1(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( ~ v1_xboole_0(k14_lopban_1(A,B,C))
& v1_seq_4(k14_lopban_1(A,B,C)) ) ) ) ) ).
fof(t33_lopban_1,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_lopban_1(C,A,B)
& v2_lopban_1(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v3_lopban_1(C,A,B)
<=> v1_seq_4(k14_lopban_1(A,B,C)) ) ) ) ) ).
fof(t34_lopban_1,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] :
( v1_funct_1(C)
& v1_funct_2(C,k10_lopban_1(A,B),k1_numbers)
& m2_relset_1(C,k10_lopban_1(A,B),k1_numbers)
& ! [D] :
( r2_hidden(D,k10_lopban_1(A,B))
=> k2_seq_1(k10_lopban_1(A,B),k1_numbers,C,D) = k3_pscomp_1(k14_lopban_1(A,B,k13_lopban_1(A,B,D))) ) ) ) ) ).
fof(d14_lopban_1,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,k10_lopban_1(A,B),k1_numbers)
& m2_relset_1(C,k10_lopban_1(A,B),k1_numbers) )
=> ( C = k15_lopban_1(A,B)
<=> ! [D] :
( r2_hidden(D,k10_lopban_1(A,B))
=> k2_seq_1(k10_lopban_1(A,B),k1_numbers,C,D) = k3_pscomp_1(k14_lopban_1(A,B,k13_lopban_1(A,B,D))) ) ) ) ) ) ).
fof(t35_lopban_1,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_lopban_1(C,A,B)
& v2_lopban_1(C,A,B)
& v3_lopban_1(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> k13_lopban_1(A,B,C) = C ) ) ) ).
fof(t36_lopban_1,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_lopban_1(C,A,B)
& v2_lopban_1(C,A,B)
& v3_lopban_1(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> k2_seq_1(k10_lopban_1(A,B),k1_numbers,k15_lopban_1(A,B),C) = k3_pscomp_1(k14_lopban_1(A,B,C)) ) ) ) ).
fof(d15_lopban_1,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) )
=> k16_lopban_1(A,B) = g1_normsp_1(k10_lopban_1(A,B),k10_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k15_lopban_1(A,B)) ) ) ).
fof(t37_lopban_1,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) )
=> k2_funcop_1(u1_struct_0(A),k1_rlvect_1(B)) = k1_rlvect_1(k16_lopban_1(A,B)) ) ) ).
fof(t38_lopban_1,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] :
( m1_subset_1(C,u1_struct_0(k16_lopban_1(A,B)))
=> ! [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)) )
=> ( D = C
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> r1_xreal_0(k1_normsp_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),D,E)),k4_real_1(k1_normsp_1(k16_lopban_1(A,B),C),k1_normsp_1(A,E))) ) ) ) ) ) ) ).
fof(t39_lopban_1,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] :
( m1_subset_1(C,u1_struct_0(k16_lopban_1(A,B)))
=> r1_xreal_0(np__0,k1_normsp_1(k16_lopban_1(A,B),C)) ) ) ) ).
fof(t40_lopban_1,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] :
( m1_subset_1(C,u1_struct_0(k16_lopban_1(A,B)))
=> ( C = k1_rlvect_1(k16_lopban_1(A,B))
=> np__0 = k1_normsp_1(k16_lopban_1(A,B),C) ) ) ) ) ).
fof(t41_lopban_1,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] :
( m1_subset_1(C,u1_struct_0(k16_lopban_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k16_lopban_1(A,B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k16_lopban_1(A,B)))
=> ( E = k2_rlvect_1(k16_lopban_1(A,B),C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k17_lopban_1(A,B,E,F) = k4_rlvect_1(B,k17_lopban_1(A,B,C,F),k17_lopban_1(A,B,D,F)) ) ) ) ) ) ) ) ).
fof(t42_lopban_1,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] :
( m1_subset_1(C,u1_struct_0(k16_lopban_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k16_lopban_1(A,B)))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( D = k3_rlvect_1(k16_lopban_1(A,B),C,E)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k17_lopban_1(A,B,D,F) = k3_rlvect_1(B,k17_lopban_1(A,B,C,F),E) ) ) ) ) ) ) ) ).
fof(t43_lopban_1,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] :
( m1_subset_1(C,u1_struct_0(k16_lopban_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k16_lopban_1(A,B)))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( ( k1_normsp_1(k16_lopban_1(A,B),C) = np__0
=> C = k1_rlvect_1(k16_lopban_1(A,B)) )
& ( C = k1_rlvect_1(k16_lopban_1(A,B))
=> k1_normsp_1(k16_lopban_1(A,B),C) = np__0 )
& k1_normsp_1(k16_lopban_1(A,B),k3_rlvect_1(k16_lopban_1(A,B),C,E)) = k4_real_1(k18_complex1(E),k1_normsp_1(k16_lopban_1(A,B),C))
& r1_xreal_0(k1_normsp_1(k16_lopban_1(A,B),k2_rlvect_1(k16_lopban_1(A,B),C,D)),k3_real_1(k1_normsp_1(k16_lopban_1(A,B),C),k1_normsp_1(k16_lopban_1(A,B),D))) ) ) ) ) ) ) ).
fof(t44_lopban_1,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) )
=> v2_normsp_1(k16_lopban_1(A,B)) ) ) ).
fof(t45_lopban_1,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) )
=> ( ~ v3_struct_0(k16_lopban_1(A,B))
& v3_rlvect_1(k16_lopban_1(A,B))
& v4_rlvect_1(k16_lopban_1(A,B))
& v5_rlvect_1(k16_lopban_1(A,B))
& v6_rlvect_1(k16_lopban_1(A,B))
& v7_rlvect_1(k16_lopban_1(A,B))
& v2_normsp_1(k16_lopban_1(A,B))
& l1_normsp_1(k16_lopban_1(A,B)) ) ) ) ).
fof(t46_lopban_1,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] :
( m1_subset_1(C,u1_struct_0(k16_lopban_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k16_lopban_1(A,B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k16_lopban_1(A,B)))
=> ( E = k6_rlvect_1(k16_lopban_1(A,B),C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k17_lopban_1(A,B,E,F) = k6_rlvect_1(B,k17_lopban_1(A,B,C,F),k17_lopban_1(A,B,D,F)) ) ) ) ) ) ) ) ).
fof(d16_lopban_1,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) )
=> ( v4_lopban_1(A)
<=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_rsspace3(B,A)
=> v4_normsp_1(B,A) ) ) ) ) ).
fof(t47_lopban_1,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,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v4_normsp_1(B,A)
=> ( v4_seq_2(k7_normsp_1(A,B))
& k2_seq_2(k7_normsp_1(A,B)) = k1_normsp_1(A,k8_normsp_1(A,B)) ) ) ) ) ).
fof(t48_lopban_1,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) )
=> ( v4_lopban_1(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(k16_lopban_1(A,B)))
& m2_relset_1(C,k5_numbers,u1_struct_0(k16_lopban_1(A,B))) )
=> ( v1_rsspace3(C,k16_lopban_1(A,B))
=> v4_normsp_1(C,k16_lopban_1(A,B)) ) ) ) ) ) ).
fof(t49_lopban_1,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)
& v4_lopban_1(B)
& l1_normsp_1(B) )
=> ( ~ v3_struct_0(k16_lopban_1(A,B))
& v3_rlvect_1(k16_lopban_1(A,B))
& v4_rlvect_1(k16_lopban_1(A,B))
& v5_rlvect_1(k16_lopban_1(A,B))
& v6_rlvect_1(k16_lopban_1(A,B))
& v7_rlvect_1(k16_lopban_1(A,B))
& v2_normsp_1(k16_lopban_1(A,B))
& v4_lopban_1(k16_lopban_1(A,B))
& l1_normsp_1(k16_lopban_1(A,B)) ) ) ) ).
fof(dt_k1_lopban_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(k1_numbers,B),B)
& m1_relset_1(C,k2_zfmisc_1(k1_numbers,B),B)
& v1_xreal_0(D)
& v1_funct_1(E)
& v1_funct_2(E,A,B)
& m1_relset_1(E,A,B) )
=> m2_fraenkel(k1_lopban_1(A,B,C,D,E),A,B,k1_fraenkel(A,B)) ) ).
fof(redefinition_k1_lopban_1,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(k1_numbers,B),B)
& m1_relset_1(C,k2_zfmisc_1(k1_numbers,B),B)
& v1_xreal_0(D)
& v1_funct_1(E)
& v1_funct_2(E,A,B)
& m1_relset_1(E,A,B) )
=> k1_lopban_1(A,B,C,D,E) = k5_funcop_1(C,D,E) ) ).
fof(dt_k2_lopban_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v3_struct_0(B)
& l1_rlvect_1(B) )
=> ( v1_funct_1(k2_lopban_1(A,B))
& v1_funct_2(k2_lopban_1(A,B),k2_zfmisc_1(k1_fraenkel(A,u1_struct_0(B)),k1_fraenkel(A,u1_struct_0(B))),k1_fraenkel(A,u1_struct_0(B)))
& m2_relset_1(k2_lopban_1(A,B),k2_zfmisc_1(k1_fraenkel(A,u1_struct_0(B)),k1_fraenkel(A,u1_struct_0(B))),k1_fraenkel(A,u1_struct_0(B))) ) ) ).
fof(dt_k3_lopban_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ 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) )
=> ( v1_funct_1(k3_lopban_1(A,B))
& v1_funct_2(k3_lopban_1(A,B),k2_zfmisc_1(k1_numbers,k1_fraenkel(A,u1_struct_0(B))),k1_fraenkel(A,u1_struct_0(B)))
& m2_relset_1(k3_lopban_1(A,B),k2_zfmisc_1(k1_numbers,k1_fraenkel(A,u1_struct_0(B))),k1_fraenkel(A,u1_struct_0(B))) ) ) ).
fof(dt_k4_lopban_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l2_struct_0(B) )
=> m2_fraenkel(k4_lopban_1(A,B),A,u1_struct_0(B),k1_fraenkel(A,u1_struct_0(B))) ) ).
fof(dt_k5_lopban_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ 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) )
=> ( ~ v3_struct_0(k5_lopban_1(A,B))
& v3_rlvect_1(k5_lopban_1(A,B))
& v4_rlvect_1(k5_lopban_1(A,B))
& v5_rlvect_1(k5_lopban_1(A,B))
& v6_rlvect_1(k5_lopban_1(A,B))
& v7_rlvect_1(k5_lopban_1(A,B))
& l2_rlvect_1(k5_lopban_1(A,B)) ) ) ).
fof(dt_k6_lopban_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ 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,u1_struct_0(k5_lopban_1(A,B)))
& m1_subset_1(D,A) )
=> m1_subset_1(k6_lopban_1(A,B,C,D),u1_struct_0(B)) ) ).
fof(redefinition_k6_lopban_1,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ 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,u1_struct_0(k5_lopban_1(A,B)))
& m1_subset_1(D,A) )
=> k6_lopban_1(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k7_lopban_1,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)
& ~ 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(k7_lopban_1(A,B),k1_zfmisc_1(u1_struct_0(k5_lopban_1(u1_struct_0(A),B)))) ) ).
fof(dt_k8_lopban_1,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)
& ~ 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) )
=> ( ~ v3_struct_0(k8_lopban_1(A,B))
& v3_rlvect_1(k8_lopban_1(A,B))
& v4_rlvect_1(k8_lopban_1(A,B))
& v5_rlvect_1(k8_lopban_1(A,B))
& v6_rlvect_1(k8_lopban_1(A,B))
& v7_rlvect_1(k8_lopban_1(A,B))
& l2_rlvect_1(k8_lopban_1(A,B)) ) ) ).
fof(dt_k9_lopban_1,axiom,
! [A,B,C,D] :
( ( ~ 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)
& ~ 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,u1_struct_0(k8_lopban_1(A,B)))
& m1_subset_1(D,u1_struct_0(A)) )
=> m1_subset_1(k9_lopban_1(A,B,C,D),u1_struct_0(B)) ) ).
fof(redefinition_k9_lopban_1,axiom,
! [A,B,C,D] :
( ( ~ 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)
& ~ 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,u1_struct_0(k8_lopban_1(A,B)))
& m1_subset_1(D,u1_struct_0(A)) )
=> k9_lopban_1(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k10_lopban_1,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)
& v2_normsp_1(A)
& l1_normsp_1(A)
& ~ 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) )
=> m1_subset_1(k10_lopban_1(A,B),k1_zfmisc_1(u1_struct_0(k8_lopban_1(A,B)))) ) ).
fof(dt_k11_lopban_1,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)
& v2_normsp_1(A)
& l1_normsp_1(A)
& ~ 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) )
=> ( ~ v3_struct_0(k11_lopban_1(A,B))
& v3_rlvect_1(k11_lopban_1(A,B))
& v4_rlvect_1(k11_lopban_1(A,B))
& v5_rlvect_1(k11_lopban_1(A,B))
& v6_rlvect_1(k11_lopban_1(A,B))
& v7_rlvect_1(k11_lopban_1(A,B))
& l2_rlvect_1(k11_lopban_1(A,B)) ) ) ).
fof(dt_k12_lopban_1,axiom,
! [A,B,C,D] :
( ( ~ 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(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)
& m1_subset_1(C,u1_struct_0(k11_lopban_1(A,B)))
& m1_subset_1(D,u1_struct_0(A)) )
=> m1_subset_1(k12_lopban_1(A,B,C,D),u1_struct_0(B)) ) ).
fof(redefinition_k12_lopban_1,axiom,
! [A,B,C,D] :
( ( ~ 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(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)
& m1_subset_1(C,u1_struct_0(k11_lopban_1(A,B)))
& m1_subset_1(D,u1_struct_0(A)) )
=> k12_lopban_1(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(dt_k13_lopban_1,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)
& ~ 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) )
=> ( v1_funct_1(k13_lopban_1(A,B,C))
& v1_funct_2(k13_lopban_1(A,B,C),u1_struct_0(A),u1_struct_0(B))
& v1_lopban_1(k13_lopban_1(A,B,C),A,B)
& v2_lopban_1(k13_lopban_1(A,B,C),A,B)
& v3_lopban_1(k13_lopban_1(A,B,C),A,B)
& m2_relset_1(k13_lopban_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) ) ) ).
fof(dt_k14_lopban_1,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)
& ~ 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)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_lopban_1(C,A,B)
& v2_lopban_1(C,A,B)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( ~ v1_xboole_0(k14_lopban_1(A,B,C))
& m1_subset_1(k14_lopban_1(A,B,C),k1_zfmisc_1(k1_numbers)) ) ) ).
fof(dt_k15_lopban_1,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)
& v2_normsp_1(A)
& l1_normsp_1(A)
& ~ 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) )
=> ( v1_funct_1(k15_lopban_1(A,B))
& v1_funct_2(k15_lopban_1(A,B),k10_lopban_1(A,B),k1_numbers)
& m2_relset_1(k15_lopban_1(A,B),k10_lopban_1(A,B),k1_numbers) ) ) ).
fof(dt_k16_lopban_1,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)
& v2_normsp_1(A)
& l1_normsp_1(A)
& ~ 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) )
=> ( ~ v3_struct_0(k16_lopban_1(A,B))
& l1_normsp_1(k16_lopban_1(A,B)) ) ) ).
fof(dt_k17_lopban_1,axiom,
! [A,B,C,D] :
( ( ~ 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(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)
& m1_subset_1(C,u1_struct_0(k16_lopban_1(A,B)))
& m1_subset_1(D,u1_struct_0(A)) )
=> m1_subset_1(k17_lopban_1(A,B,C,D),u1_struct_0(B)) ) ).
fof(redefinition_k17_lopban_1,axiom,
! [A,B,C,D] :
( ( ~ 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(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)
& m1_subset_1(C,u1_struct_0(k16_lopban_1(A,B)))
& m1_subset_1(D,u1_struct_0(A)) )
=> k17_lopban_1(A,B,C,D) = k1_funct_1(C,D) ) ).
fof(d13_lopban_1,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] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_lopban_1(C,A,B)
& v2_lopban_1(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> k14_lopban_1(A,B,C) = a_3_0_lopban_1(A,B,C) ) ) ) ).
fof(fraenkel_a_3_0_lopban_1,axiom,
! [A,B,C,D] :
( ( ~ 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)
& ~ 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)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& v1_lopban_1(D,B,C)
& v2_lopban_1(D,B,C)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ( r2_hidden(A,a_3_0_lopban_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k1_normsp_1(C,k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,E))
& r1_xreal_0(k1_normsp_1(B,E),np__1) ) ) ) ).
%------------------------------------------------------------------------------