SET007 Axioms: SET007+653.ax
%------------------------------------------------------------------------------
% File : SET007+653 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Hahn Banach Theorem
% Version : [Urb08] axioms.
% English : The Hahn Banach Theorem in the Vector Space over the Field of
% Complex Numbers
% 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 : hahnban1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 114 ( 11 unt; 0 def)
% Number of atoms : 1080 ( 60 equ)
% Maximal formula atoms : 40 ( 9 avg)
% Number of connectives : 1103 ( 137 ~; 0 |; 714 &)
% ( 18 <=>; 234 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 49 ( 47 usr; 1 prp; 0-6 aty)
% Number of functors : 59 ( 59 usr; 8 con; 0-4 aty)
% Number of variables : 288 ( 285 !; 3 ?)
% 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(cc1_hahnban1,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_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(B),u1_struct_0(A))
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v2_hahnban1(C,A,B) )
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v3_hahnban1(C,A,B) ) ) ) ) ).
fof(fc1_hahnban1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v5_rlvect_1(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ( v1_relat_1(k7_hahnban1(A,B))
& v1_funct_1(k7_hahnban1(A,B))
& v1_funct_2(k7_hahnban1(A,B),u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(k7_hahnban1(A,B),A,B) ) ) ).
fof(fc2_hahnban1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ( v1_relat_1(k7_hahnban1(A,B))
& v1_funct_1(k7_hahnban1(A,B))
& v1_funct_2(k7_hahnban1(A,B),u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(k7_hahnban1(A,B),A,B)
& v2_hahnban1(k7_hahnban1(A,B),A,B) ) ) ).
fof(fc3_hahnban1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ( v1_relat_1(k7_hahnban1(A,B))
& v1_funct_1(k7_hahnban1(A,B))
& v1_funct_2(k7_hahnban1(A,B),u1_struct_0(B),u1_struct_0(A))
& v3_hahnban1(k7_hahnban1(A,B),A,B) ) ) ).
fof(rc1_hahnban1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ? [C] :
( m1_relset_1(C,u1_struct_0(B),u1_struct_0(A))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(C,A,B)
& v2_hahnban1(C,A,B)
& v3_hahnban1(C,A,B) ) ) ).
fof(fc4_hahnban1,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)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(C,A,B)
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(A))
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(D,A,B)
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_relat_1(k3_hahnban1(A,B,C,D))
& v1_funct_1(k3_hahnban1(A,B,C,D))
& v1_funct_2(k3_hahnban1(A,B,C,D),u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(k3_hahnban1(A,B,C,D),A,B) ) ) ).
fof(fc5_hahnban1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(C,A,B)
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_relat_1(k4_hahnban1(A,B,C))
& v1_funct_1(k4_hahnban1(A,B,C))
& v1_funct_2(k4_hahnban1(A,B,C),u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(k4_hahnban1(A,B,C),A,B) ) ) ).
fof(fc6_hahnban1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& m1_subset_1(C,u1_struct_0(A))
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(D,A,B)
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_relat_1(k6_hahnban1(A,B,C,D))
& v1_funct_1(k6_hahnban1(A,B,C,D))
& v1_funct_2(k6_hahnban1(A,B,C,D),u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(k6_hahnban1(A,B,C,D),A,B) ) ) ).
fof(fc7_hahnban1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v2_hahnban1(C,A,B)
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(A))
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& v2_hahnban1(D,A,B)
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_relat_1(k3_hahnban1(A,B,C,D))
& v1_funct_1(k3_hahnban1(A,B,C,D))
& v1_funct_2(k3_hahnban1(A,B,C,D),u1_struct_0(B),u1_struct_0(A))
& v2_hahnban1(k3_hahnban1(A,B,C,D),A,B) ) ) ).
fof(fc8_hahnban1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& v2_hahnban1(C,A,B)
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_relat_1(k4_hahnban1(A,B,C))
& v1_funct_1(k4_hahnban1(A,B,C))
& v1_funct_2(k4_hahnban1(A,B,C),u1_struct_0(B),u1_struct_0(A))
& v2_hahnban1(k4_hahnban1(A,B,C),A,B) ) ) ).
fof(fc9_hahnban1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& m1_subset_1(C,u1_struct_0(A))
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& v2_hahnban1(D,A,B)
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_relat_1(k6_hahnban1(A,B,C,D))
& v1_funct_1(k6_hahnban1(A,B,C,D))
& v1_funct_2(k6_hahnban1(A,B,C,D),u1_struct_0(B),u1_struct_0(A))
& v2_hahnban1(k6_hahnban1(A,B,C,D),A,B) ) ) ).
fof(fc10_hahnban1,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)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ( ~ v3_struct_0(k8_hahnban1(A,B))
& v3_rlvect_1(k8_hahnban1(A,B))
& v11_vectsp_1(k8_hahnban1(A,B),A) ) ) ).
fof(fc11_hahnban1,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)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ( ~ v3_struct_0(k8_hahnban1(A,B))
& v3_rlvect_1(k8_hahnban1(A,B))
& v4_rlvect_1(k8_hahnban1(A,B))
& v11_vectsp_1(k8_hahnban1(A,B),A) ) ) ).
fof(fc12_hahnban1,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)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ( ~ v3_struct_0(k8_hahnban1(A,B))
& v3_rlvect_1(k8_hahnban1(A,B))
& v5_rlvect_1(k8_hahnban1(A,B))
& v11_vectsp_1(k8_hahnban1(A,B),A) ) ) ).
fof(fc13_hahnban1,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)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ( ~ v3_struct_0(k8_hahnban1(A,B))
& v3_rlvect_1(k8_hahnban1(A,B))
& v6_rlvect_1(k8_hahnban1(A,B))
& v11_vectsp_1(k8_hahnban1(A,B),A) ) ) ).
fof(fc14_hahnban1,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)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ( ~ v3_struct_0(k8_hahnban1(A,B))
& v3_rlvect_1(k8_hahnban1(A,B))
& v4_rlvect_1(k8_hahnban1(A,B))
& v5_rlvect_1(k8_hahnban1(A,B))
& v6_rlvect_1(k8_hahnban1(A,B))
& v11_vectsp_1(k8_hahnban1(A,B),A)
& v12_vectsp_1(k8_hahnban1(A,B),A) ) ) ).
fof(cc2_hahnban1,axiom,
! [A,B] :
( ( l1_struct_0(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(B),k1_numbers)
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),k1_numbers)
& v5_hahnban1(C,A,B) )
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),k1_numbers)
& v4_hahnban1(C,A,B) ) ) ) ) ).
fof(cc3_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v12_vectsp_1(A,k1_complfld)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( m1_relset_1(B,u1_struct_0(A),k1_numbers)
=> ( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& v6_hahnban1(B,A) )
=> ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& v8_hahnban1(B,k1_complfld,A) ) ) ) ) ).
fof(fc15_hahnban1,axiom,
! [A,B] :
( ( l1_struct_0(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ( v1_relat_1(k9_hahnban1(A,B))
& v1_funct_1(k9_hahnban1(A,B))
& v1_funct_2(k9_hahnban1(A,B),u1_struct_0(B),k1_numbers)
& v4_hahnban1(k9_hahnban1(A,B),A,B)
& v5_hahnban1(k9_hahnban1(A,B),A,B) ) ) ).
fof(fc16_hahnban1,axiom,
! [A,B] :
( ( l1_struct_0(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ( v1_relat_1(k9_hahnban1(A,B))
& v1_funct_1(k9_hahnban1(A,B))
& v1_funct_2(k9_hahnban1(A,B),u1_struct_0(B),k1_numbers)
& v8_hahnban1(k9_hahnban1(A,B),A,B) ) ) ).
fof(fc17_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ( v1_relat_1(k9_hahnban1(k1_complfld,A))
& v1_funct_1(k9_hahnban1(k1_complfld,A))
& v1_funct_2(k9_hahnban1(k1_complfld,A),u1_struct_0(A),k1_numbers)
& v4_hahnban1(k9_hahnban1(k1_complfld,A),k1_complfld,A)
& v5_hahnban1(k9_hahnban1(k1_complfld,A),k1_complfld,A)
& v6_hahnban1(k9_hahnban1(k1_complfld,A),A)
& v8_hahnban1(k9_hahnban1(k1_complfld,A),k1_complfld,A) ) ) ).
fof(fc18_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ( v1_relat_1(k9_hahnban1(k1_complfld,A))
& v1_funct_1(k9_hahnban1(k1_complfld,A))
& v1_funct_2(k9_hahnban1(k1_complfld,A),u1_struct_0(A),k1_numbers)
& v4_hahnban1(k9_hahnban1(k1_complfld,A),k1_complfld,A)
& v5_hahnban1(k9_hahnban1(k1_complfld,A),k1_complfld,A)
& v7_hahnban1(k9_hahnban1(k1_complfld,A),A)
& v8_hahnban1(k9_hahnban1(k1_complfld,A),k1_complfld,A) ) ) ).
fof(rc2_hahnban1,axiom,
! [A,B] :
( ( l1_struct_0(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ? [C] :
( m1_relset_1(C,u1_struct_0(B),k1_numbers)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),k1_numbers)
& v4_hahnban1(C,A,B)
& v5_hahnban1(C,A,B)
& v8_hahnban1(C,A,B) ) ) ).
fof(rc3_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),k1_numbers)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& v4_hahnban1(B,k1_complfld,A)
& v5_hahnban1(B,k1_complfld,A)
& v6_hahnban1(B,A)
& v7_hahnban1(B,A) ) ) ).
fof(fc19_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ( ~ v3_struct_0(k10_hahnban1(A))
& v2_rlvect_1(k10_hahnban1(A)) ) ) ).
fof(fc20_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& l4_vectsp_1(A,k1_complfld) )
=> ( ~ v3_struct_0(k10_hahnban1(A))
& v2_rlvect_1(k10_hahnban1(A))
& v3_rlvect_1(k10_hahnban1(A)) ) ) ).
fof(fc21_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& l4_vectsp_1(A,k1_complfld) )
=> ( ~ v3_struct_0(k10_hahnban1(A))
& v2_rlvect_1(k10_hahnban1(A))
& v4_rlvect_1(k10_hahnban1(A)) ) ) ).
fof(fc22_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v5_rlvect_1(A)
& l4_vectsp_1(A,k1_complfld) )
=> ( ~ v3_struct_0(k10_hahnban1(A))
& v2_rlvect_1(k10_hahnban1(A))
& v5_rlvect_1(k10_hahnban1(A)) ) ) ).
fof(fc23_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_rlvect_1(A)
& l4_vectsp_1(A,k1_complfld) )
=> ( ~ v3_struct_0(k10_hahnban1(A))
& v2_rlvect_1(k10_hahnban1(A))
& v6_rlvect_1(k10_hahnban1(A)) ) ) ).
fof(fc24_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v12_vectsp_1(A,k1_complfld)
& l4_vectsp_1(A,k1_complfld) )
=> ( ~ v3_struct_0(k10_hahnban1(A))
& v2_rlvect_1(k10_hahnban1(A))
& v7_rlvect_1(k10_hahnban1(A)) ) ) ).
fof(fc25_hahnban1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v12_vectsp_1(A,k1_complfld)
& l4_vectsp_1(A,k1_complfld)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1)
& v2_hahnban(B,k10_hahnban1(A))
& m1_relset_1(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) )
=> ( v1_relat_1(k13_hahnban1(A,B))
& v1_funct_1(k13_hahnban1(A,B))
& v1_funct_2(k13_hahnban1(A,B),u1_struct_0(A),k1_numbers)
& v4_hahnban1(k13_hahnban1(A,B),k1_complfld,A)
& v5_hahnban1(k13_hahnban1(A,B),k1_complfld,A) ) ) ).
fof(fc26_hahnban1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v12_vectsp_1(A,k1_complfld)
& l4_vectsp_1(A,k1_complfld)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& v5_hahnban1(B,k1_complfld,A)
& m1_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ( v1_relat_1(k14_hahnban1(A,B))
& v1_funct_1(k14_hahnban1(A,B))
& v1_funct_2(k14_hahnban1(A,B),u1_struct_0(k10_hahnban1(A)),k6_supinf_1)
& v1_hahnban(k14_hahnban1(A,B),k10_hahnban1(A))
& v2_hahnban(k14_hahnban1(A,B),k10_hahnban1(A)) ) ) ).
fof(fc27_hahnban1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v12_vectsp_1(A,k1_complfld)
& l4_vectsp_1(A,k1_complfld)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1)
& v3_hahnban(B,k10_hahnban1(A))
& m1_relset_1(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) )
=> ( v1_relat_1(k13_hahnban1(A,B))
& v1_funct_1(k13_hahnban1(A,B))
& v1_funct_2(k13_hahnban1(A,B),u1_struct_0(A),k1_numbers)
& v6_hahnban1(k13_hahnban1(A,B),A)
& v8_hahnban1(k13_hahnban1(A,B),k1_complfld,A) ) ) ).
fof(fc28_hahnban1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v12_vectsp_1(A,k1_complfld)
& l4_vectsp_1(A,k1_complfld)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& v6_hahnban1(B,A)
& m1_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ( v1_relat_1(k14_hahnban1(A,B))
& v1_funct_1(k14_hahnban1(A,B))
& v1_funct_2(k14_hahnban1(A,B),u1_struct_0(k10_hahnban1(A)),k6_supinf_1)
& v3_hahnban(k14_hahnban1(A,B),k10_hahnban1(A))
& v4_hahnban(k14_hahnban1(A,B),k10_hahnban1(A)) ) ) ).
fof(t1_hahnban1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k18_complex1(k17_complex1(A)) = k17_complex1(A) ) ).
fof(t2_hahnban1,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> k3_xcmplx_0(k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1)),k2_xcmplx_0(C,k3_xcmplx_0(D,k7_complex1))) = k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)),k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(C,B)),k7_complex1)) ) ) ) ) ).
fof(t3_hahnban1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> k9_complex1(k5_arytm_0(A,np__0),k7_complex1) = k5_arytm_0(np__0,A) ) ).
fof(t4_hahnban1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> k17_complex1(k5_arytm_0(A,np__0)) = k18_complex1(A) ) ).
fof(t5_hahnban1,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> k2_xcmplx_0(k17_complex1(A),k3_xcmplx_0(np__0,k7_complex1)) = k3_xcmplx_0(k7_xcmplx_0(k15_complex1(A),k2_xcmplx_0(k17_complex1(A),k3_xcmplx_0(np__0,k7_complex1))),A) ) ).
fof(d1_hahnban1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> k1_hahnban1(A,B) = k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1)) ) ) ).
fof(d2_hahnban1,axiom,
k2_hahnban1 = k7_complex1 ).
fof(t6_hahnban1,axiom,
( k2_hahnban1 = k5_arytm_0(np__0,np__1)
& k2_hahnban1 = k1_hahnban1(np__0,np__1) ) ).
fof(t7_hahnban1,axiom,
k3_complfld(k2_hahnban1) = np__1 ).
fof(t8_hahnban1,axiom,
k10_group_1(k1_complfld,k2_hahnban1,k2_hahnban1) = k5_rlvect_1(k1_complfld,k2_group_1(k1_complfld)) ).
fof(t9_hahnban1,axiom,
k10_group_1(k1_complfld,k5_rlvect_1(k1_complfld,k2_group_1(k1_complfld)),k5_rlvect_1(k1_complfld,k2_group_1(k1_complfld))) = k2_group_1(k1_complfld) ).
fof(t10_hahnban1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> k4_rlvect_1(k1_complfld,k1_hahnban1(A,B),k1_hahnban1(C,D)) = k1_hahnban1(k3_real_1(A,C),k3_real_1(B,D)) ) ) ) ) ).
fof(t11_hahnban1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> k10_group_1(k1_complfld,k1_hahnban1(A,B),k1_hahnban1(C,D)) = k1_hahnban1(k5_real_1(k4_real_1(A,C),k4_real_1(B,D)),k3_real_1(k4_real_1(A,D),k4_real_1(C,B))) ) ) ) ) ).
fof(t12_hahnban1,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k18_complex1(k17_complex1(A)) = k17_complex1(A) ) ).
fof(t13_hahnban1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> k3_complfld(k1_hahnban1(A,np__0)) = k18_complex1(A) ) ).
fof(t14_hahnban1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> k10_group_1(k1_complfld,k1_hahnban1(A,np__0),k2_hahnban1) = k1_hahnban1(np__0,A) ) ).
fof(t15_hahnban1,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( k3_complex1(k1_hahnban1(A,B)) = A
& k4_complex1(k1_hahnban1(A,B)) = B ) ) ) ).
fof(t16_hahnban1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k1_complfld))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k1_complfld))
=> ( k3_complex1(k4_rlvect_1(k1_complfld,A,B)) = k3_real_1(k3_complex1(A),k3_complex1(B))
& k4_complex1(k4_rlvect_1(k1_complfld,A,B)) = k3_real_1(k4_complex1(A),k4_complex1(B)) ) ) ) ).
fof(t17_hahnban1,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k1_complfld))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k1_complfld))
=> ( k3_complex1(k10_group_1(k1_complfld,A,B)) = k5_real_1(k4_real_1(k3_complex1(A),k3_complex1(B)),k4_real_1(k4_complex1(A),k4_complex1(B)))
& k4_complex1(k10_group_1(k1_complfld,A,B)) = k3_real_1(k4_real_1(k3_complex1(A),k4_complex1(B)),k4_real_1(k3_complex1(B),k4_complex1(A))) ) ) ) ).
fof(d3_hahnban1,axiom,
$true ).
fof(d4_hahnban1,axiom,
$true ).
fof(d5_hahnban1,axiom,
$true ).
fof(d6_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
=> ( E = k3_hahnban1(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,F) = k2_rlvect_1(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,F),k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,F)) ) ) ) ) ) ) ) ).
fof(d7_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( D = k4_hahnban1(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,E) = k5_rlvect_1(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E)) ) ) ) ) ) ) ).
fof(d8_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> k5_hahnban1(A,B,C,D) = k3_hahnban1(A,B,C,k4_hahnban1(A,B,D)) ) ) ) ) ).
fof(d9_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
=> ( E = k6_hahnban1(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,F) = k1_group_1(A,C,k8_funct_2(u1_struct_0(B),u1_struct_0(A),D,F)) ) ) ) ) ) ) ) ).
fof(d10_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A) )
=> ! [B] :
( l4_vectsp_1(B,A)
=> k7_hahnban1(A,B) = k1_borsuk_1(u1_struct_0(A),k2_pre_topc(B),k1_rlvect_1(A)) ) ) ).
fof(d11_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_hahnban1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,k2_rlvect_1(B,D,E)) = k2_rlvect_1(A,k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,D),k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,E)) ) ) ) ) ) ) ).
fof(d12_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v2_hahnban1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,k6_vectsp_1(A,B,E,D)) = k1_group_1(A,E,k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,D)) ) ) ) ) ) ) ).
fof(d13_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v3_hahnban1(C,A,B)
<=> k8_funct_2(u1_struct_0(B),u1_struct_0(A),C,k1_rlvect_1(B)) = k1_rlvect_1(A) ) ) ) ) ).
fof(t18_hahnban1,axiom,
$true ).
fof(t19_hahnban1,axiom,
$true ).
fof(t20_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> r4_nattra_1(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),k3_hahnban1(A,B,C,D),k3_hahnban1(A,B,D,C)) ) ) ) ) ).
fof(t21_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
=> r4_nattra_1(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),k3_hahnban1(A,B,k3_hahnban1(A,B,C,D),E),k3_hahnban1(A,B,C,k3_hahnban1(A,B,D,E))) ) ) ) ) ) ).
fof(t22_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> k8_funct_2(u1_struct_0(B),u1_struct_0(A),k7_hahnban1(A,B),C) = k1_rlvect_1(A) ) ) ) ).
fof(t23_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v5_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> r4_nattra_1(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),k3_hahnban1(A,B,C,k7_hahnban1(A,B)),C) ) ) ) ).
fof(t24_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> r4_nattra_1(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),k5_hahnban1(A,B,C,C),k7_hahnban1(A,B)) ) ) ) ).
fof(t25_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
=> r4_nattra_1(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),k6_hahnban1(A,B,C,k3_hahnban1(A,B,D,E)),k3_hahnban1(A,B,k6_hahnban1(A,B,C,D),k6_hahnban1(A,B,C,E))) ) ) ) ) ) ).
fof(t26_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v5_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
=> r4_nattra_1(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),k6_hahnban1(A,B,k2_rlvect_1(A,C,D),E),k3_hahnban1(A,B,k6_hahnban1(A,B,C,E),k6_hahnban1(A,B,D,E))) ) ) ) ) ) ).
fof(t27_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
=> r4_nattra_1(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),k6_hahnban1(A,B,k1_group_1(A,C,D),E),k6_hahnban1(A,B,C,k6_hahnban1(A,B,D,E))) ) ) ) ) ) ).
fof(t28_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> r4_nattra_1(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),k6_hahnban1(A,B,k2_group_1(A),C),C) ) ) ) ).
fof(d14_hahnban1,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)
& v4_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v11_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ( C = k8_hahnban1(A,B)
<=> ( ! [D] :
( r2_hidden(D,u1_struct_0(C))
<=> ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(D,A,B)
& v2_hahnban1(D,A,B)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) ) )
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(D,A,B)
& v2_hahnban1(D,A,B)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(E,A,B)
& v2_hahnban1(E,A,B)
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
=> k1_binop_1(u1_rlvect_1(C),D,E) = k3_hahnban1(A,B,D,E) ) )
& u2_struct_0(C) = k7_hahnban1(A,B)
& ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& v1_hahnban1(D,A,B)
& v2_hahnban1(D,A,B)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k1_binop_1(u2_vectsp_1(A,C),E,D) = k6_hahnban1(A,B,E,D) ) ) ) ) ) ) ) ).
fof(d15_hahnban1,axiom,
$true ).
fof(d16_hahnban1,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),k1_numbers)
& m2_relset_1(C,u1_struct_0(B),k1_numbers) )
=> ( v4_hahnban1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> r1_xreal_0(k8_funct_2(u1_struct_0(B),k1_numbers,C,k2_rlvect_1(B,D,E)),k3_real_1(k8_funct_2(u1_struct_0(B),k1_numbers,C,D),k8_funct_2(u1_struct_0(B),k1_numbers,C,E))) ) ) ) ) ) ) ).
fof(d17_hahnban1,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),k1_numbers)
& m2_relset_1(C,u1_struct_0(B),k1_numbers) )
=> ( v5_hahnban1(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k8_funct_2(u1_struct_0(B),k1_numbers,C,k2_rlvect_1(B,D,E)) = k3_real_1(k8_funct_2(u1_struct_0(B),k1_numbers,C,D),k8_funct_2(u1_struct_0(B),k1_numbers,C,E)) ) ) ) ) ) ) ).
fof(d18_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ( v6_hahnban1(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> k8_funct_2(u1_struct_0(A),k1_numbers,B,k6_vectsp_1(k1_complfld,A,k1_hahnban1(D,np__0),C)) = k4_real_1(D,k8_funct_2(u1_struct_0(A),k1_numbers,B,C)) ) ) ) ) ) ).
fof(t29_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v12_vectsp_1(A,k1_complfld)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ( v6_hahnban1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> k8_funct_2(u1_struct_0(A),k1_numbers,B,k6_vectsp_1(k1_complfld,A,k1_hahnban1(np__0,D),C)) = k4_real_1(D,k8_funct_2(u1_struct_0(A),k1_numbers,B,k6_vectsp_1(k1_complfld,A,k2_hahnban1,C))) ) ) ) ) ) ).
fof(d19_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ( v7_hahnban1(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k1_complfld))
=> k8_funct_2(u1_struct_0(A),k1_numbers,B,k6_vectsp_1(k1_complfld,A,D,C)) = k4_real_1(k3_complfld(D),k8_funct_2(u1_struct_0(A),k1_numbers,B,C)) ) ) ) ) ) ).
fof(d20_hahnban1,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l4_vectsp_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),k1_numbers)
& m2_relset_1(C,u1_struct_0(B),k1_numbers) )
=> ( v8_hahnban1(C,A,B)
<=> k1_funct_1(C,k1_rlvect_1(B)) = np__0 ) ) ) ) ).
fof(d21_hahnban1,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l4_vectsp_1(B,A)
=> k9_hahnban1(A,B) = k1_borsuk_1(k1_numbers,k2_pre_topc(B),np__0) ) ) ).
fof(d22_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v2_rlvect_1(B)
& l2_rlvect_1(B) )
=> ( B = k10_hahnban1(A)
<=> ( g1_rlvect_1(u1_struct_0(B),u1_rlvect_1(B),u2_struct_0(B)) = g1_rlvect_1(u1_struct_0(A),u1_rlvect_1(A),u2_struct_0(A))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_binop_1(u2_rlvect_1(B),C,D) = k6_vectsp_1(k1_complfld,A,k1_hahnban1(C,np__0),D) ) ) ) ) ) ) ).
fof(t30_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v12_vectsp_1(A,k1_complfld)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( m1_vectsp_4(B,k1_complfld,A)
=> m1_rlsub_1(k10_hahnban1(B),k10_hahnban1(A)) ) ) ).
fof(t31_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1)
& m2_relset_1(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) ) ) ) ).
fof(t32_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v12_vectsp_1(A,k1_complfld)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& v4_hahnban1(B,k1_complfld,A)
& v7_hahnban1(B,A)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1)
& v1_hahnban(B,k10_hahnban1(A))
& v4_hahnban(B,k10_hahnban1(A))
& m2_relset_1(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) ) ) ) ).
fof(d23_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_complfld))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k10_hahnban1(A)),k6_supinf_1)
& m2_relset_1(C,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) )
=> ( C = k11_hahnban1(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_funct_1(C,D) = k3_complex1(k8_funct_2(u1_struct_0(A),u1_struct_0(k1_complfld),B,D)) ) ) ) ) ) ).
fof(d24_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_complfld))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k10_hahnban1(A)),k6_supinf_1)
& m2_relset_1(C,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) )
=> ( C = k12_hahnban1(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_funct_1(C,D) = k4_complex1(k8_funct_2(u1_struct_0(A),u1_struct_0(k1_complfld),B,D)) ) ) ) ) ) ).
fof(d25_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1)
& m2_relset_1(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) )
=> k13_hahnban1(A,B) = B ) ) ).
fof(d26_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> k14_hahnban1(A,B) = B ) ) ).
fof(d27_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),k1_numbers)
& m2_relset_1(C,u1_struct_0(A),k1_numbers) )
=> ( C = k15_hahnban1(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),k1_numbers,C,D) = k8_funct_2(u1_struct_0(A),k1_numbers,B,k6_vectsp_1(k1_complfld,A,k2_hahnban1,D)) ) ) ) ) ) ).
fof(d28_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1)
& m2_relset_1(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k1_complfld))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ( C = k16_hahnban1(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(k1_complfld),C,D) = k1_hahnban1(k8_funct_2(u1_struct_0(A),k1_numbers,k13_hahnban1(A,B),D),k1_real_1(k8_funct_2(u1_struct_0(A),k1_numbers,k15_hahnban1(A,k13_hahnban1(A,B)),D))) ) ) ) ) ) ).
fof(t33_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v12_vectsp_1(A,k1_complfld)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_complfld))
& v1_hahnban1(B,k1_complfld,A)
& v2_hahnban1(B,k1_complfld,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ( v1_funct_1(k11_hahnban1(A,B))
& v1_funct_2(k11_hahnban1(A,B),u1_struct_0(k10_hahnban1(A)),k6_supinf_1)
& v2_hahnban(k11_hahnban1(A,B),k10_hahnban1(A))
& v3_hahnban(k11_hahnban1(A,B),k10_hahnban1(A))
& m2_relset_1(k11_hahnban1(A,B),u1_struct_0(k10_hahnban1(A)),k6_supinf_1) ) ) ) ).
fof(t34_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v12_vectsp_1(A,k1_complfld)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_complfld))
& v1_hahnban1(B,k1_complfld,A)
& v2_hahnban1(B,k1_complfld,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ( v1_funct_1(k12_hahnban1(A,B))
& v1_funct_2(k12_hahnban1(A,B),u1_struct_0(k10_hahnban1(A)),k6_supinf_1)
& v2_hahnban(k12_hahnban1(A,B),k10_hahnban1(A))
& v3_hahnban(k12_hahnban1(A,B),k10_hahnban1(A))
& m2_relset_1(k12_hahnban1(A,B),u1_struct_0(k10_hahnban1(A)),k6_supinf_1) ) ) ) ).
fof(t35_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v12_vectsp_1(A,k1_complfld)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1)
& v2_hahnban(B,k10_hahnban1(A))
& v3_hahnban(B,k10_hahnban1(A))
& m2_relset_1(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) )
=> ( v1_funct_1(k16_hahnban1(A,B))
& v1_funct_2(k16_hahnban1(A,B),u1_struct_0(A),u1_struct_0(k1_complfld))
& v1_hahnban1(k16_hahnban1(A,B),k1_complfld,A)
& v2_hahnban1(k16_hahnban1(A,B),k1_complfld,A)
& m2_relset_1(k16_hahnban1(A,B),u1_struct_0(A),u1_struct_0(k1_complfld)) ) ) ) ).
fof(t36_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v12_vectsp_1(A,k1_complfld)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& v4_hahnban1(B,k1_complfld,A)
& v7_hahnban1(B,A)
& m2_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ! [C] :
( m1_vectsp_4(C,k1_complfld,A)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(k1_complfld))
& v1_hahnban1(D,k1_complfld,C)
& v2_hahnban1(D,k1_complfld,C)
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(k1_complfld)) )
=> ~ ( ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( F = E
=> r1_xreal_0(k3_complfld(k8_funct_2(u1_struct_0(C),u1_struct_0(k1_complfld),D,E)),k8_funct_2(u1_struct_0(A),k1_numbers,B,F)) ) ) )
& ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(k1_complfld))
& v1_hahnban1(E,k1_complfld,A)
& v2_hahnban1(E,k1_complfld,A)
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ~ ( k8_relset_1(u1_struct_0(A),u1_struct_0(k1_complfld),E,u1_struct_0(C)) = D
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> r1_xreal_0(k3_complfld(k8_funct_2(u1_struct_0(A),u1_struct_0(k1_complfld),E,F)),k8_funct_2(u1_struct_0(A),k1_numbers,B,F)) ) ) ) ) ) ) ) ) ).
fof(dt_k1_hahnban1,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_numbers)
& m1_subset_1(B,k1_numbers) )
=> m1_subset_1(k1_hahnban1(A,B),u1_struct_0(k1_complfld)) ) ).
fof(dt_k2_hahnban1,axiom,
m1_subset_1(k2_hahnban1,u1_struct_0(k1_complfld)) ).
fof(dt_k3_hahnban1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(A))
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_funct_1(k3_hahnban1(A,B,C,D))
& v1_funct_2(k3_hahnban1(A,B,C,D),u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(k3_hahnban1(A,B,C,D),u1_struct_0(B),u1_struct_0(A)) ) ) ).
fof(dt_k4_hahnban1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_funct_1(k4_hahnban1(A,B,C))
& v1_funct_2(k4_hahnban1(A,B,C),u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(k4_hahnban1(A,B,C),u1_struct_0(B),u1_struct_0(A)) ) ) ).
fof(dt_k5_hahnban1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(B),u1_struct_0(A))
& m1_relset_1(C,u1_struct_0(B),u1_struct_0(A))
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_funct_1(k5_hahnban1(A,B,C,D))
& v1_funct_2(k5_hahnban1(A,B,C,D),u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(k5_hahnban1(A,B,C,D),u1_struct_0(B),u1_struct_0(A)) ) ) ).
fof(dt_k6_hahnban1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_group_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A)
& m1_subset_1(C,u1_struct_0(A))
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
=> ( v1_funct_1(k6_hahnban1(A,B,C,D))
& v1_funct_2(k6_hahnban1(A,B,C,D),u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(k6_hahnban1(A,B,C,D),u1_struct_0(B),u1_struct_0(A)) ) ) ).
fof(dt_k7_hahnban1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_struct_0(A)
& l4_vectsp_1(B,A) )
=> ( v1_funct_1(k7_hahnban1(A,B))
& v1_funct_2(k7_hahnban1(A,B),u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(k7_hahnban1(A,B),u1_struct_0(B),u1_struct_0(A)) ) ) ).
fof(dt_k8_hahnban1,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)
& v4_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ( ~ v3_struct_0(k8_hahnban1(A,B))
& v11_vectsp_1(k8_hahnban1(A,B),A)
& l4_vectsp_1(k8_hahnban1(A,B),A) ) ) ).
fof(dt_k9_hahnban1,axiom,
! [A,B] :
( ( l1_struct_0(A)
& l4_vectsp_1(B,A) )
=> ( v1_funct_1(k9_hahnban1(A,B))
& v1_funct_2(k9_hahnban1(A,B),u1_struct_0(B),k1_numbers)
& m2_relset_1(k9_hahnban1(A,B),u1_struct_0(B),k1_numbers) ) ) ).
fof(dt_k10_hahnban1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ( v2_rlvect_1(k10_hahnban1(A))
& l2_rlvect_1(k10_hahnban1(A)) ) ) ).
fof(dt_k11_hahnban1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_complfld))
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ( v1_funct_1(k11_hahnban1(A,B))
& v1_funct_2(k11_hahnban1(A,B),u1_struct_0(k10_hahnban1(A)),k6_supinf_1)
& m2_relset_1(k11_hahnban1(A,B),u1_struct_0(k10_hahnban1(A)),k6_supinf_1) ) ) ).
fof(dt_k12_hahnban1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_complfld))
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ( v1_funct_1(k12_hahnban1(A,B))
& v1_funct_2(k12_hahnban1(A,B),u1_struct_0(k10_hahnban1(A)),k6_supinf_1)
& m2_relset_1(k12_hahnban1(A,B),u1_struct_0(k10_hahnban1(A)),k6_supinf_1) ) ) ).
fof(dt_k13_hahnban1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1)
& m1_relset_1(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) )
=> ( v1_funct_1(k13_hahnban1(A,B))
& v1_funct_2(k13_hahnban1(A,B),u1_struct_0(A),k1_numbers)
& m2_relset_1(k13_hahnban1(A,B),u1_struct_0(A),k1_numbers) ) ) ).
fof(dt_k14_hahnban1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m1_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ( v1_funct_1(k14_hahnban1(A,B))
& v1_funct_2(k14_hahnban1(A,B),u1_struct_0(k10_hahnban1(A)),k6_supinf_1)
& m2_relset_1(k14_hahnban1(A,B),u1_struct_0(k10_hahnban1(A)),k6_supinf_1) ) ) ).
fof(dt_k15_hahnban1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),k1_numbers)
& m1_relset_1(B,u1_struct_0(A),k1_numbers) )
=> ( v1_funct_1(k15_hahnban1(A,B))
& v1_funct_2(k15_hahnban1(A,B),u1_struct_0(A),k1_numbers)
& m2_relset_1(k15_hahnban1(A,B),u1_struct_0(A),k1_numbers) ) ) ).
fof(dt_k16_hahnban1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1)
& m1_relset_1(B,u1_struct_0(k10_hahnban1(A)),k6_supinf_1) )
=> ( v1_funct_1(k16_hahnban1(A,B))
& v1_funct_2(k16_hahnban1(A,B),u1_struct_0(A),u1_struct_0(k1_complfld))
& m2_relset_1(k16_hahnban1(A,B),u1_struct_0(A),u1_struct_0(k1_complfld)) ) ) ).
%------------------------------------------------------------------------------