SET007 Axioms: SET007+749.ax
%------------------------------------------------------------------------------
% File : SET007+749 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Hermitan Functionals
% Version : [Urb08] axioms.
% English : Canonical Construction of Scalar Product in Quotient Vector Space
% 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 : hermitan [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 144 ( 3 unt; 0 def)
% Number of atoms : 1950 ( 118 equ)
% Maximal formula atoms : 36 ( 13 avg)
% Number of connectives : 2025 ( 219 ~; 1 |;1441 &)
% ( 11 <=>; 353 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 12 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 45 ( 43 usr; 1 prp; 0-4 aty)
% Number of functors : 79 ( 79 usr; 9 con; 0-5 aty)
% Number of variables : 410 ( 402 !; 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_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ( v1_relat_1(k7_hahnban1(k1_complfld,A))
& v1_funct_1(k7_hahnban1(k1_complfld,A))
& v1_funct_2(k7_hahnban1(k1_complfld,A),u1_struct_0(A),u1_struct_0(k1_complfld))
& v5_seqm_3(k7_hahnban1(k1_complfld,A))
& v1_hahnban1(k7_hahnban1(k1_complfld,A),k1_complfld,A)
& v2_hahnban1(k7_hahnban1(k1_complfld,A),k1_complfld,A)
& v3_hahnban1(k7_hahnban1(k1_complfld,A),k1_complfld,A)
& v1_hermitan(k7_hahnban1(k1_complfld,A),A) ) ) ).
fof(cc1_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(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),u1_struct_0(k1_complfld))
=> ( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_complfld))
& v1_hermitan(B,A) )
=> ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_complfld))
& v3_hahnban1(B,k1_complfld,A) ) ) ) ) ).
fof(rc1_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld))
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_complfld))
& v1_hahnban1(B,k1_complfld,A)
& v3_hahnban1(B,k1_complfld,A)
& v1_hermitan(B,A) ) ) ).
fof(fc2_hermitan,axiom,
! [A,B,C] :
( ( ~ 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))
& v1_hermitan(B,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld))
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k1_complfld))
& v1_hermitan(C,A)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k3_hahnban1(k1_complfld,A,B,C))
& v1_funct_1(k3_hahnban1(k1_complfld,A,B,C))
& v1_funct_2(k3_hahnban1(k1_complfld,A,B,C),u1_struct_0(A),u1_struct_0(k1_complfld))
& v1_hermitan(k3_hahnban1(k1_complfld,A,B,C),A) ) ) ).
fof(fc3_hermitan,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))
& v1_hermitan(B,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k4_hahnban1(k1_complfld,A,B))
& v1_funct_1(k4_hahnban1(k1_complfld,A,B))
& v1_funct_2(k4_hahnban1(k1_complfld,A,B),u1_struct_0(A),u1_struct_0(k1_complfld))
& v1_hermitan(k4_hahnban1(k1_complfld,A,B),A) ) ) ).
fof(fc4_hermitan,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& m1_subset_1(B,u1_struct_0(k1_complfld))
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k1_complfld))
& v1_hermitan(C,A)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k6_hahnban1(k1_complfld,A,B,C))
& v1_funct_1(k6_hahnban1(k1_complfld,A,B,C))
& v1_funct_2(k6_hahnban1(k1_complfld,A,B,C),u1_struct_0(A),u1_struct_0(k1_complfld))
& v1_hermitan(k6_hahnban1(k1_complfld,A,B,C),A) ) ) ).
fof(fc5_hermitan,axiom,
! [A,B,C] :
( ( ~ 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))
& v1_hermitan(B,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld))
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k1_complfld))
& v1_hermitan(C,A)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k5_hahnban1(k1_complfld,A,B,C))
& v1_funct_1(k5_hahnban1(k1_complfld,A,B,C))
& v1_funct_2(k5_hahnban1(k1_complfld,A,B,C),u1_struct_0(A),u1_struct_0(k1_complfld))
& v1_hermitan(k5_hahnban1(k1_complfld,A,B,C),A) ) ) ).
fof(fc6_hermitan,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))
& v1_hahnban1(B,k1_complfld,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k1_hermitan(A,B))
& v1_funct_1(k1_hermitan(A,B))
& v1_funct_2(k1_hermitan(A,B),u1_struct_0(A),u1_struct_0(k1_complfld))
& v1_hahnban1(k1_hermitan(A,B),k1_complfld,A) ) ) ).
fof(fc7_hermitan,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))
& v2_hahnban1(B,k1_complfld,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k1_hermitan(A,B))
& v1_funct_1(k1_hermitan(A,B))
& v1_funct_2(k1_hermitan(A,B),u1_struct_0(A),u1_struct_0(k1_complfld))
& v1_hermitan(k1_hermitan(A,B),A) ) ) ).
fof(fc8_hermitan,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))
& v1_hermitan(B,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k1_hermitan(A,B))
& v1_funct_1(k1_hermitan(A,B))
& v1_funct_2(k1_hermitan(A,B),u1_struct_0(A),u1_struct_0(k1_complfld))
& v2_hahnban1(k1_hermitan(A,B),k1_complfld,A) ) ) ).
fof(fc9_hermitan,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)
& ~ v3_realset2(A)
& l4_vectsp_1(A,k1_complfld)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_complfld))
& ~ v5_seqm_3(B)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k1_hermitan(A,B))
& v1_funct_1(k1_hermitan(A,B))
& v1_funct_2(k1_hermitan(A,B),u1_struct_0(A),u1_struct_0(k1_complfld))
& ~ v5_seqm_3(k1_hermitan(A,B))
& ~ v1_realset1(k1_hermitan(A,B)) ) ) ).
fof(rc2_hermitan,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)
& ~ v3_realset2(A)
& l4_vectsp_1(A,k1_complfld) )
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld))
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_complfld))
& ~ v5_seqm_3(B)
& v1_hahnban1(B,k1_complfld,A)
& v3_hahnban1(B,k1_complfld,A)
& ~ v1_realset1(B)
& v1_hermitan(B,A) ) ) ).
fof(fc10_hermitan,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)
& ~ v3_realset2(A)
& l4_vectsp_1(A,k1_complfld)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_complfld))
& ~ v5_seqm_3(B)
& v1_hahnban1(B,k1_complfld,A)
& v1_hermitan(B,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k2_hermitan(A,B))
& v1_funct_1(k2_hermitan(A,B))
& v1_funct_2(k2_hermitan(A,B),u1_struct_0(k6_vectsp10(k1_complfld,A,k9_vectsp10(k1_complfld,A,k1_hermitan(A,B)))),u1_struct_0(k1_complfld))
& ~ v5_seqm_3(k2_hermitan(A,B))
& v1_hahnban1(k2_hermitan(A,B),k1_complfld,k6_vectsp10(k1_complfld,A,k9_vectsp10(k1_complfld,A,k1_hermitan(A,B))))
& v3_hahnban1(k2_hermitan(A,B),k1_complfld,k6_vectsp10(k1_complfld,A,k9_vectsp10(k1_complfld,A,k1_hermitan(A,B))))
& ~ v1_realset1(k2_hermitan(A,B))
& v1_hermitan(k2_hermitan(A,B),k6_vectsp10(k1_complfld,A,k9_vectsp10(k1_complfld,A,k1_hermitan(A,B)))) ) ) ).
fof(fc11_hermitan,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),u1_struct_0(k1_complfld))
& v1_hahnban1(B,k1_complfld,A)
& v1_hermitan(B,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k2_hermitan(A,B))
& v1_funct_1(k2_hermitan(A,B))
& v1_funct_2(k2_hermitan(A,B),u1_struct_0(k6_vectsp10(k1_complfld,A,k9_vectsp10(k1_complfld,A,k1_hermitan(A,B)))),u1_struct_0(k1_complfld))
& v1_hahnban1(k2_hermitan(A,B),k1_complfld,k6_vectsp10(k1_complfld,A,k9_vectsp10(k1_complfld,A,k1_hermitan(A,B))))
& v3_hahnban1(k2_hermitan(A,B),k1_complfld,k6_vectsp10(k1_complfld,A,k9_vectsp10(k1_complfld,A,k1_hermitan(A,B))))
& ~ v2_vectsp10(k2_hermitan(A,B),k1_complfld,k6_vectsp10(k1_complfld,A,k9_vectsp10(k1_complfld,A,k1_hermitan(A,B))))
& v1_hermitan(k2_hermitan(A,B),k6_vectsp10(k1_complfld,A,k9_vectsp10(k1_complfld,A,k1_hermitan(A,B)))) ) ) ).
fof(fc12_hermitan,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld) )
=> ( v1_relat_1(k1_bilinear(k1_complfld,A,B))
& v1_funct_1(k1_bilinear(k1_complfld,A,B))
& v1_funct_2(k1_bilinear(k1_complfld,A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(k1_bilinear(k1_complfld,A,B),k1_complfld,A,B)
& v2_bilinear(k1_bilinear(k1_complfld,A,B),k1_complfld,A,B)
& v3_bilinear(k1_bilinear(k1_complfld,A,B),k1_complfld,A,B)
& v4_bilinear(k1_bilinear(k1_complfld,A,B),k1_complfld,A,B)
& v2_hermitan(k1_bilinear(k1_complfld,A,B),A,B) ) ) ).
fof(fc13_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ( v1_relat_1(k1_bilinear(k1_complfld,A,A))
& v1_funct_1(k1_bilinear(k1_complfld,A,A))
& v1_funct_2(k1_bilinear(k1_complfld,A,A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v1_bilinear(k1_bilinear(k1_complfld,A,A),k1_complfld,A,A)
& v2_bilinear(k1_bilinear(k1_complfld,A,A),k1_complfld,A,A)
& v3_bilinear(k1_bilinear(k1_complfld,A,A),k1_complfld,A,A)
& v4_bilinear(k1_bilinear(k1_complfld,A,A),k1_complfld,A,A)
& v7_bilinear(k1_bilinear(k1_complfld,A,A),k1_complfld,A)
& v8_bilinear(k1_bilinear(k1_complfld,A,A),k1_complfld,A)
& v2_hermitan(k1_bilinear(k1_complfld,A,A),A,A)
& v3_hermitan(k1_bilinear(k1_complfld,A,A),A) ) ) ).
fof(fc14_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ( v1_relat_1(k1_bilinear(k1_complfld,A,A))
& v1_funct_1(k1_bilinear(k1_complfld,A,A))
& v1_funct_2(k1_bilinear(k1_complfld,A,A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v1_bilinear(k1_bilinear(k1_complfld,A,A),k1_complfld,A,A)
& v2_bilinear(k1_bilinear(k1_complfld,A,A),k1_complfld,A,A)
& v3_bilinear(k1_bilinear(k1_complfld,A,A),k1_complfld,A,A)
& v4_bilinear(k1_bilinear(k1_complfld,A,A),k1_complfld,A,A)
& v7_bilinear(k1_bilinear(k1_complfld,A,A),k1_complfld,A)
& v8_bilinear(k1_bilinear(k1_complfld,A,A),k1_complfld,A)
& v2_hermitan(k1_bilinear(k1_complfld,A,A),A,A)
& v5_hermitan(k1_bilinear(k1_complfld,A,A),A) ) ) ).
fof(cc2_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
=> ( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v3_hermitan(B,A) )
=> ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v4_hermitan(B,A) ) ) ) ) ).
fof(rc3_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ? [B] :
( m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v1_bilinear(B,k1_complfld,A,A)
& v2_bilinear(B,k1_complfld,A,A)
& v4_bilinear(B,k1_complfld,A,A)
& v2_hermitan(B,A,A)
& v3_hermitan(B,A)
& v4_hermitan(B,A)
& v5_hermitan(B,A) ) ) ).
fof(rc4_hermitan,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld) )
=> ? [C] :
( m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(C,k1_complfld,A,B)
& v2_bilinear(C,k1_complfld,A,B)
& v4_bilinear(C,k1_complfld,A,B)
& v2_hermitan(C,A,B) ) ) ).
fof(cc3_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
=> ( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v1_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A) )
=> ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(B,k1_complfld,A,A) ) ) ) ) ).
fof(cc4_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
=> ( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A) )
=> ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v1_bilinear(B,k1_complfld,A,A) ) ) ) ) ).
fof(cc5_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
=> ( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v4_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A) )
=> ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_hermitan(B,A,A) ) ) ) ) ).
fof(cc6_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
=> ( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_hermitan(B,A,A)
& v3_hermitan(B,A) )
=> ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v4_bilinear(B,k1_complfld,A,A) ) ) ) ) ).
fof(fc15_hermitan,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k1_complfld))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(k1_complfld))
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(k1_complfld))
& v1_hermitan(D,B)
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k11_bilinear(k1_complfld,A,B,C,D))
& v1_funct_1(k11_bilinear(k1_complfld,A,B,C,D))
& v1_funct_2(k11_bilinear(k1_complfld,A,B,C,D),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v2_hermitan(k11_bilinear(k1_complfld,A,B,C,D),A,B) ) ) ).
fof(fc16_hermitan,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v2_hermitan(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& m1_subset_1(D,u1_struct_0(A)) )
=> ( v1_relat_1(k9_bilinear(k1_complfld,A,B,C,D))
& v1_funct_1(k9_bilinear(k1_complfld,A,B,C,D))
& v1_funct_2(k9_bilinear(k1_complfld,A,B,C,D),u1_struct_0(B),u1_struct_0(k1_complfld))
& v1_hermitan(k9_bilinear(k1_complfld,A,B,C,D),B) ) ) ).
fof(fc17_hermitan,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v2_hermitan(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v2_hermitan(D,A,B)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k2_bilinear(k1_complfld,A,B,C,D))
& v1_funct_1(k2_bilinear(k1_complfld,A,B,C,D))
& v1_funct_2(k2_bilinear(k1_complfld,A,B,C,D),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v2_hermitan(k2_bilinear(k1_complfld,A,B,C,D),A,B) ) ) ).
fof(fc18_hermitan,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v2_hermitan(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& m1_subset_1(D,u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k3_bilinear(k1_complfld,A,B,C,D))
& v1_funct_1(k3_bilinear(k1_complfld,A,B,C,D))
& v1_funct_2(k3_bilinear(k1_complfld,A,B,C,D),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v2_hermitan(k3_bilinear(k1_complfld,A,B,C,D),A,B) ) ) ).
fof(fc19_hermitan,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v2_hermitan(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k4_bilinear(k1_complfld,A,B,C))
& v1_funct_1(k4_bilinear(k1_complfld,A,B,C))
& v1_funct_2(k4_bilinear(k1_complfld,A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v2_hermitan(k4_bilinear(k1_complfld,A,B,C),A,B) ) ) ).
fof(fc20_hermitan,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v2_hermitan(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v2_hermitan(D,A,B)
& m1_relset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k6_bilinear(k1_complfld,A,B,C,D))
& v1_funct_1(k6_bilinear(k1_complfld,A,B,C,D))
& v1_funct_2(k6_bilinear(k1_complfld,A,B,C,D),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v2_hermitan(k6_bilinear(k1_complfld,A,B,C,D),A,B) ) ) ).
fof(rc5_hermitan,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)
& ~ v3_realset2(A)
& l4_vectsp_1(A,k1_complfld)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& ~ v3_realset2(B)
& l4_vectsp_1(B,k1_complfld) )
=> ? [C] :
( m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& ~ v5_seqm_3(C)
& ~ v1_realset1(C)
& v1_bilinear(C,k1_complfld,A,B)
& v2_bilinear(C,k1_complfld,A,B)
& v4_bilinear(C,k1_complfld,A,B)
& v2_hermitan(C,A,B) ) ) ).
fof(fc21_hermitan,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(C,k1_complfld,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k3_hermitan(A,B,C))
& v1_funct_1(k3_hermitan(A,B,C))
& v1_funct_2(k3_hermitan(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(k3_hermitan(A,B,C),k1_complfld,A,B) ) ) ).
fof(fc22_hermitan,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v2_bilinear(C,k1_complfld,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k3_hermitan(A,B,C))
& v1_funct_1(k3_hermitan(A,B,C))
& v1_funct_2(k3_hermitan(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v2_bilinear(k3_hermitan(A,B,C),k1_complfld,A,B) ) ) ).
fof(fc23_hermitan,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v3_bilinear(C,k1_complfld,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k3_hermitan(A,B,C))
& v1_funct_1(k3_hermitan(A,B,C))
& v1_funct_2(k3_hermitan(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v2_hermitan(k3_hermitan(A,B,C),A,B) ) ) ).
fof(fc24_hermitan,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v2_hermitan(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k3_hermitan(A,B,C))
& v1_funct_1(k3_hermitan(A,B,C))
& v1_funct_2(k3_hermitan(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v3_bilinear(k3_hermitan(A,B,C),k1_complfld,A,B) ) ) ).
fof(fc25_hermitan,axiom,
! [A,B,C] :
( ( ~ 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)
& ~ v3_realset2(A)
& l4_vectsp_1(A,k1_complfld)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& ~ v3_realset2(B)
& l4_vectsp_1(B,k1_complfld)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& ~ v5_seqm_3(C)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k3_hermitan(A,B,C))
& v1_funct_1(k3_hermitan(A,B,C))
& v1_funct_2(k3_hermitan(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& ~ v5_seqm_3(k3_hermitan(A,B,C)) ) ) ).
fof(fc26_hermitan,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_relat_1(k11_bilinear(k1_complfld,A,A,B,k1_hermitan(A,B)))
& v1_funct_1(k11_bilinear(k1_complfld,A,A,B,k1_hermitan(A,B)))
& v1_funct_2(k11_bilinear(k1_complfld,A,A,B,k1_hermitan(A,B)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v3_hermitan(k11_bilinear(k1_complfld,A,A,B,k1_hermitan(A,B)),A)
& v4_hermitan(k11_bilinear(k1_complfld,A,A,B,k1_hermitan(A,B)),A)
& v5_hermitan(k11_bilinear(k1_complfld,A,A,B,k1_hermitan(A,B)),A) ) ) ).
fof(rc6_hermitan,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)
& ~ v3_realset2(A)
& l4_vectsp_1(A,k1_complfld) )
=> ? [B] :
( m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& ~ v5_seqm_3(B)
& ~ v1_realset1(B)
& v1_bilinear(B,k1_complfld,A,A)
& v2_bilinear(B,k1_complfld,A,A)
& v4_bilinear(B,k1_complfld,A,A)
& v2_hermitan(B,A,A)
& v3_hermitan(B,A)
& v4_hermitan(B,A)
& v5_hermitan(B,A) ) ) ).
fof(fc27_hermitan,axiom,
! [A,B] :
( ( ~ v3_struct_0(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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_hermitan(B,A,A)
& m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ~ v1_xboole_0(k14_bilinear(k1_complfld,A,B)) ) ).
fof(fc28_hermitan,axiom,
! [A,B,C] :
( ( ~ 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)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& l4_vectsp_1(B,k1_complfld)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(C,k1_complfld,A,B)
& v2_bilinear(C,k1_complfld,A,B)
& v4_bilinear(C,k1_complfld,A,B)
& v2_hermitan(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k17_bilinear(k1_complfld,A,B,C))
& v1_funct_1(k17_bilinear(k1_complfld,A,B,C))
& v1_funct_2(k17_bilinear(k1_complfld,A,B,C),k2_zfmisc_1(u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C))),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(k17_bilinear(k1_complfld,A,B,C),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B)
& v2_bilinear(k17_bilinear(k1_complfld,A,B,C),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B)
& v4_bilinear(k17_bilinear(k1_complfld,A,B,C),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B)
& ~ v5_bilinear(k17_bilinear(k1_complfld,A,B,C),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B)
& v2_hermitan(k17_bilinear(k1_complfld,A,B,C),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B) ) ) ).
fof(fc29_hermitan,axiom,
! [A,B,C] :
( ( ~ 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)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& l4_vectsp_1(B,k1_complfld)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(C,k1_complfld,A,B)
& v2_bilinear(C,k1_complfld,A,B)
& v4_bilinear(C,k1_complfld,A,B)
& v2_hermitan(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k7_hermitan(A,B,C))
& v1_funct_1(k7_hermitan(A,B,C))
& v1_funct_2(k7_hermitan(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))),u1_struct_0(k1_complfld))
& v1_bilinear(k7_hermitan(A,B,C),k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& v2_bilinear(k7_hermitan(A,B,C),k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& v4_bilinear(k7_hermitan(A,B,C),k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& v2_hermitan(k7_hermitan(A,B,C),A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C)))) ) ) ).
fof(fc30_hermitan,axiom,
! [A,B,C] :
( ( ~ 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)
& ~ v3_realset2(A)
& l4_vectsp_1(A,k1_complfld)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& ~ v3_realset2(B)
& l4_vectsp_1(B,k1_complfld)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& ~ v5_seqm_3(C)
& v1_bilinear(C,k1_complfld,A,B)
& v2_bilinear(C,k1_complfld,A,B)
& v4_bilinear(C,k1_complfld,A,B)
& v2_hermitan(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k8_hermitan(A,B,C))
& v1_funct_1(k8_hermitan(A,B,C))
& v1_funct_2(k8_hermitan(A,B,C),k2_zfmisc_1(u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C))),u1_struct_0(k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))),u1_struct_0(k1_complfld))
& ~ v5_seqm_3(k8_hermitan(A,B,C))
& v1_bilinear(k8_hermitan(A,B,C),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& v2_bilinear(k8_hermitan(A,B,C),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& v4_bilinear(k8_hermitan(A,B,C),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& v2_hermitan(k8_hermitan(A,B,C),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C)))) ) ) ).
fof(fc31_hermitan,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v5_rlvect_1(A)
& l4_vectsp_1(A,k1_complfld)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& l4_vectsp_1(B,k1_complfld)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(C,k1_complfld,A,B)
& v2_hermitan(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k7_hermitan(A,B,C))
& v1_funct_1(k7_hermitan(A,B,C))
& v1_funct_2(k7_hermitan(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))),u1_struct_0(k1_complfld))
& v1_bilinear(k7_hermitan(A,B,C),k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& ~ v6_bilinear(k7_hermitan(A,B,C),k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& v2_hermitan(k7_hermitan(A,B,C),A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C)))) ) ) ).
fof(fc32_hermitan,axiom,
! [A,B,C] :
( ( ~ 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)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& l4_vectsp_1(B,k1_complfld)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(C,k1_complfld,A,B)
& v2_bilinear(C,k1_complfld,A,B)
& v4_bilinear(C,k1_complfld,A,B)
& v2_hermitan(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k7_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C)))
& v1_funct_1(k7_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C)))
& v1_funct_2(k7_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C)),k2_zfmisc_1(u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C))),u1_struct_0(k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k3_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C)))))),u1_struct_0(k1_complfld))
& v1_bilinear(k7_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C)),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k3_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C)))))
& v2_bilinear(k7_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C)),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k3_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C)))))
& v4_bilinear(k7_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C)),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k3_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C)))))
& ~ v5_bilinear(k7_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C)),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k3_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C)))))
& ~ v6_bilinear(k7_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C)),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k3_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C)))))
& v2_hermitan(k7_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k3_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C))))) ) ) ).
fof(fc33_hermitan,axiom,
! [A,B,C] :
( ( ~ 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)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& l4_vectsp_1(B,k1_complfld)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(C,k1_complfld,A,B)
& v2_bilinear(C,k1_complfld,A,B)
& v4_bilinear(C,k1_complfld,A,B)
& v2_hermitan(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k17_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C)))
& v1_funct_1(k17_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C)))
& v1_funct_2(k17_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C)),k2_zfmisc_1(u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C)))),u1_struct_0(k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))),u1_struct_0(k1_complfld))
& v1_bilinear(k17_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C)),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C))),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& v2_bilinear(k17_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C)),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C))),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& v4_bilinear(k17_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C)),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C))),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& ~ v5_bilinear(k17_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C)),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C))),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& ~ v6_bilinear(k17_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C)),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C))),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& v2_hermitan(k17_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C)),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C))),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C)))) ) ) ).
fof(fc34_hermitan,axiom,
! [A,B,C] :
( ( ~ 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)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& l4_vectsp_1(B,k1_complfld)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(C,k1_complfld,A,B)
& v2_bilinear(C,k1_complfld,A,B)
& v4_bilinear(C,k1_complfld,A,B)
& v2_hermitan(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k8_hermitan(A,B,C))
& v1_funct_1(k8_hermitan(A,B,C))
& v1_funct_2(k8_hermitan(A,B,C),k2_zfmisc_1(u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C))),u1_struct_0(k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))),u1_struct_0(k1_complfld))
& v1_bilinear(k8_hermitan(A,B,C),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& v2_bilinear(k8_hermitan(A,B,C),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& v4_bilinear(k8_hermitan(A,B,C),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& ~ v5_bilinear(k8_hermitan(A,B,C),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& ~ v6_bilinear(k8_hermitan(A,B,C),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& v2_hermitan(k8_hermitan(A,B,C),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C)))) ) ) ).
fof(cc7_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v5_rlvect_1(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
=> ( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(B,k1_complfld,A,A)
& v6_hermitan(B,A) )
=> ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v5_hermitan(B,A) ) ) ) ) ).
fof(cc8_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v5_rlvect_1(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
=> ( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v1_bilinear(B,k1_complfld,A,A)
& v6_hermitan(B,A) )
=> ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v5_hermitan(B,A) ) ) ) ) ).
fof(fc35_hermitan,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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(B,k1_complfld,A,A)
& v4_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A)
& v5_hermitan(B,A)
& m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k9_hermitan(A,B))
& v1_funct_1(k9_hermitan(A,B))
& v1_funct_2(k9_hermitan(A,B),k2_zfmisc_1(u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B))),u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))),u1_struct_0(k1_complfld))
& v1_bilinear(k9_hermitan(A,B),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& v2_bilinear(k9_hermitan(A,B),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& v4_bilinear(k9_hermitan(A,B),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& ~ v5_bilinear(k9_hermitan(A,B),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& ~ v6_bilinear(k9_hermitan(A,B),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& v2_hermitan(k9_hermitan(A,B),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& v3_hermitan(k9_hermitan(A,B),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& v4_hermitan(k9_hermitan(A,B),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& v5_hermitan(k9_hermitan(A,B),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& v6_hermitan(k9_hermitan(A,B),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B))) ) ) ).
fof(fc36_hermitan,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)
& ~ v3_realset2(A)
& l4_vectsp_1(A,k1_complfld)
& v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& ~ v5_seqm_3(B)
& v2_bilinear(B,k1_complfld,A,A)
& v4_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A)
& v5_hermitan(B,A)
& m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ( v1_relat_1(k9_hermitan(A,B))
& v1_funct_1(k9_hermitan(A,B))
& v1_funct_2(k9_hermitan(A,B),k2_zfmisc_1(u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B))),u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))),u1_struct_0(k1_complfld))
& ~ v5_seqm_3(k9_hermitan(A,B))
& v1_bilinear(k9_hermitan(A,B),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& v2_bilinear(k9_hermitan(A,B),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& v4_bilinear(k9_hermitan(A,B),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& ~ v5_bilinear(k9_hermitan(A,B),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& ~ v6_bilinear(k9_hermitan(A,B),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& v2_hermitan(k9_hermitan(A,B),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& v3_hermitan(k9_hermitan(A,B),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& v4_hermitan(k9_hermitan(A,B),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& v5_hermitan(k9_hermitan(A,B),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& v6_hermitan(k9_hermitan(A,B),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B))) ) ) ).
fof(t1_hermitan,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ( A = k15_complex1(A)
=> k4_complex1(A) = np__0 ) ) ).
fof(t2_hermitan,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ( A != k5_complex1
=> ( k17_complex1(k5_arytm_0(k6_real_1(k3_complex1(A),k17_complex1(A)),k6_real_1(k1_real_1(k4_complex1(A)),k17_complex1(A)))) = np__1
& k3_complex1(k9_complex1(k5_arytm_0(k6_real_1(k3_complex1(A),k17_complex1(A)),k6_real_1(k1_real_1(k4_complex1(A)),k17_complex1(A))),A)) = k17_complex1(A)
& k4_complex1(k9_complex1(k5_arytm_0(k6_real_1(k3_complex1(A),k17_complex1(A)),k6_real_1(k1_real_1(k4_complex1(A)),k17_complex1(A))),A)) = np__0 ) ) ) ).
fof(t3_hermitan,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ? [B] :
( m1_subset_1(B,k2_numbers)
& k17_complex1(B) = np__1
& k3_complex1(k9_complex1(B,A)) = k17_complex1(A)
& k4_complex1(k9_complex1(B,A)) = np__0 ) ) ).
fof(t4_hermitan,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> k9_complex1(A,k15_complex1(A)) = k2_xcmplx_0(k7_square_1(k17_complex1(A)),k3_xcmplx_0(np__0,k7_complex1)) ) ).
fof(t5_hermitan,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k1_complfld))
=> ( A = k2_complfld(A)
=> k4_complex1(A) = np__0 ) ) ).
fof(t6_hermitan,axiom,
$true ).
fof(t7_hermitan,axiom,
k10_group_1(k1_complfld,k2_hahnban1,k2_complfld(k2_hahnban1)) = k2_group_1(k1_complfld) ).
fof(t8_hermitan,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k1_complfld))
=> ( A != k1_rlvect_1(k1_complfld)
=> ( k3_complfld(k1_hahnban1(k6_real_1(k3_complex1(A),k3_complfld(A)),k6_real_1(k1_real_1(k4_complex1(A)),k3_complfld(A)))) = np__1
& k3_complex1(k10_group_1(k1_complfld,k1_hahnban1(k6_real_1(k3_complex1(A),k3_complfld(A)),k6_real_1(k1_real_1(k4_complex1(A)),k3_complfld(A))),A)) = k3_complfld(A)
& k4_complex1(k10_group_1(k1_complfld,k1_hahnban1(k6_real_1(k3_complex1(A),k3_complfld(A)),k6_real_1(k1_real_1(k4_complex1(A)),k3_complfld(A))),A)) = np__0 ) ) ) ).
fof(t9_hermitan,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k1_complfld))
=> ? [B] :
( m1_subset_1(B,u1_struct_0(k1_complfld))
& k3_complfld(B) = np__1
& k3_complex1(k10_group_1(k1_complfld,B,A)) = k3_complfld(A)
& k4_complex1(k10_group_1(k1_complfld,B,A)) = np__0 ) ) ).
fof(t10_hermitan,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k1_complfld))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k1_complfld))
=> ( k3_complex1(k6_rlvect_1(k1_complfld,A,B)) = k5_real_1(k3_complex1(A),k3_complex1(B))
& k4_complex1(k6_rlvect_1(k1_complfld,A,B)) = k5_real_1(k4_complex1(A),k4_complex1(B)) ) ) ) ).
fof(t11_hermitan,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k1_complfld))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k1_complfld))
=> ( k4_complex1(A) = np__0
=> ( k3_complex1(k10_group_1(k1_complfld,A,B)) = k4_real_1(k3_complex1(A),k3_complex1(B))
& k4_complex1(k10_group_1(k1_complfld,A,B)) = k4_real_1(k3_complex1(A),k4_complex1(B)) ) ) ) ) ).
fof(t12_hermitan,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k1_complfld))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k1_complfld))
=> ( ( k4_complex1(A) = np__0
& k4_complex1(B) = np__0 )
=> k4_complex1(k10_group_1(k1_complfld,A,B)) = np__0 ) ) ) ).
fof(t13_hermitan,axiom,
$true ).
fof(t14_hermitan,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k1_complfld))
=> ( k4_complex1(A) = np__0
=> A = k2_complfld(A) ) ) ).
fof(t15_hermitan,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> k10_group_1(k1_complfld,k1_hahnban1(A,np__0),k1_hahnban1(B,np__0)) = k1_hahnban1(k4_real_1(A,B),np__0) ) ) ).
fof(t16_hermitan,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k1_complfld))
=> k10_group_1(k1_complfld,A,k2_complfld(A)) = k1_hahnban1(k7_square_1(k3_complfld(A)),np__0) ) ).
fof(t17_hermitan,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k1_complfld))
=> ( ( r1_xreal_0(np__0,k3_complex1(A))
& k4_complex1(A) = np__0 )
=> k3_complfld(A) = k3_complex1(A) ) ) ).
fof(t18_hermitan,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k1_complfld))
=> k3_real_1(k3_complex1(A),k3_complex1(k2_complfld(A))) = k4_real_1(np__2,k3_complex1(A)) ) ).
fof(d1_hermitan,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)) )
=> ( v1_hermitan(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),u1_struct_0(k1_complfld),B,k6_vectsp_1(k1_complfld,A,D,C)) = k10_group_1(k1_complfld,k2_complfld(D),k8_funct_2(u1_struct_0(A),u1_struct_0(k1_complfld),B,C)) ) ) ) ) ) ).
fof(d2_hermitan,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(A),u1_struct_0(k1_complfld))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ( C = k1_hermitan(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) = k2_complfld(k8_funct_2(u1_struct_0(A),u1_struct_0(k1_complfld),B,D)) ) ) ) ) ) ).
fof(t19_hermitan,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)) )
=> k1_hermitan(A,k1_hermitan(A,B)) = B ) ) ).
fof(t20_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> k1_hermitan(A,k7_hahnban1(k1_complfld,A)) = k7_hahnban1(k1_complfld,A) ) ).
fof(t21_hermitan,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(A),u1_struct_0(k1_complfld))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> k1_hermitan(A,k3_hahnban1(k1_complfld,A,B,C)) = k3_hahnban1(k1_complfld,A,k1_hermitan(A,B),k1_hermitan(A,C)) ) ) ) ).
fof(t22_hermitan,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)) )
=> k1_hermitan(A,k4_hahnban1(k1_complfld,A,B)) = k4_hahnban1(k1_complfld,A,k1_hermitan(A,B)) ) ) ).
fof(t23_hermitan,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] :
( m1_subset_1(C,u1_struct_0(k1_complfld))
=> k1_hermitan(A,k6_hahnban1(k1_complfld,A,C,B)) = k6_hahnban1(k1_complfld,A,k2_complfld(C),k1_hermitan(A,B)) ) ) ) ).
fof(t24_hermitan,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(A),u1_struct_0(k1_complfld))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> k1_hermitan(A,k5_hahnban1(k1_complfld,A,B,C)) = k5_hahnban1(k1_complfld,A,k1_hermitan(A,B),k1_hermitan(A,C)) ) ) ) ).
fof(t25_hermitan,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] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k8_funct_2(u1_struct_0(A),u1_struct_0(k1_complfld),B,C) = k1_rlvect_1(k1_complfld)
<=> k8_funct_2(u1_struct_0(A),u1_struct_0(k1_complfld),k1_hermitan(A,B),C) = k1_rlvect_1(k1_complfld) ) ) ) ) ).
fof(t26_hermitan,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)) )
=> k8_vectsp10(k1_complfld,A,B) = k8_vectsp10(k1_complfld,A,k1_hermitan(A,B)) ) ) ).
fof(t27_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(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)
& v1_hermitan(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> v1_vectsp_4(k8_vectsp10(k1_complfld,A,B),k1_complfld,A) ) ) ).
fof(t28_hermitan,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)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(k1_complfld))
& v1_hahnban1(C,k1_complfld,A)
& v1_hermitan(C,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ( r1_tarski(u1_struct_0(B),k8_vectsp10(k1_complfld,A,k1_hermitan(A,C)))
=> v1_hermitan(k10_vectsp10(k1_complfld,A,B,C),k6_vectsp10(k1_complfld,A,B)) ) ) ) ) ).
fof(d3_hermitan,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)
& v1_hermitan(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> k2_hermitan(A,B) = k10_vectsp10(k1_complfld,A,k9_vectsp10(k1_complfld,A,k1_hermitan(A,B)),B) ) ) ).
fof(t29_hermitan,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)
& v1_hermitan(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_vectsp10(k1_complfld,A,k9_vectsp10(k1_complfld,A,k1_hermitan(A,B)))))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( C = k3_vectsp_4(k1_complfld,A,D,k9_vectsp10(k1_complfld,A,k1_hermitan(A,B)))
=> k8_funct_2(u1_struct_0(k6_vectsp10(k1_complfld,A,k9_vectsp10(k1_complfld,A,k1_hermitan(A,B)))),u1_struct_0(k1_complfld),k2_hermitan(A,B),C) = k8_funct_2(u1_struct_0(A),u1_struct_0(k1_complfld),B,D) ) ) ) ) ) ).
fof(d4_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( v2_hermitan(C,A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> v1_hermitan(k9_bilinear(k1_complfld,A,B,C,D),B) ) ) ) ) ) ).
fof(t30_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k1_complfld))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& m2_relset_1(F,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( v2_hermitan(F,A,B)
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),F,k1_domain_1(u1_struct_0(A),u1_struct_0(B),C,k6_vectsp_1(k1_complfld,B,E,D))) = k10_group_1(k1_complfld,k2_complfld(E),k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),F,k1_domain_1(u1_struct_0(A),u1_struct_0(B),C,D))) ) ) ) ) ) ) ) ).
fof(d5_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ( v3_hermitan(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,D)) = k2_complfld(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,C))) ) ) ) ) ) ).
fof(d6_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ( v4_hermitan(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k4_complex1(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,C))) = np__0 ) ) ) ) ).
fof(d7_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ( v5_hermitan(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_xreal_0(np__0,k3_complex1(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,C)))) ) ) ) ) ).
fof(d8_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( D = k3_hermitan(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(B),E,F)) = k2_complfld(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),C,k1_domain_1(u1_struct_0(A),u1_struct_0(B),E,F))) ) ) ) ) ) ) ) ).
fof(t31_hermitan,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] :
( m1_subset_1(C,u1_struct_0(A))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),k11_bilinear(k1_complfld,A,A,B,k1_hermitan(A,B)),k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,C)) = k1_hahnban1(k7_square_1(k3_complfld(k8_funct_2(u1_struct_0(A),u1_struct_0(k1_complfld),B,C))),np__0) ) ) ) ).
fof(t32_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> k3_hermitan(A,B,k3_hermitan(A,B,C)) = C ) ) ) ).
fof(t33_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld) )
=> k3_hermitan(A,B,k1_bilinear(k1_complfld,A,B)) = k1_bilinear(k1_complfld,A,B) ) ) ).
fof(t34_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> k3_hermitan(A,B,k8_bilinear(k1_complfld,A,B,C,D)) = k8_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C),k3_hermitan(A,B,D)) ) ) ) ) ).
fof(t35_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> k3_hermitan(A,B,k5_bilinear(k1_complfld,A,B,C)) = k5_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C)) ) ) ) ).
fof(t36_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k1_complfld))
=> k3_hermitan(A,B,k3_bilinear(k1_complfld,A,B,C,D)) = k3_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C),k2_complfld(D)) ) ) ) ) ).
fof(t37_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> k3_hermitan(A,B,k7_bilinear(k1_complfld,A,B,C,D)) = k7_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C),k3_hermitan(A,B,D)) ) ) ) ) ).
fof(t38_hermitan,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] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& l4_vectsp_1(B,k1_complfld) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(F,k1_complfld,A,B)
& v2_hermitan(F,A,B)
& m2_relset_1(F,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),F,k1_domain_1(u1_struct_0(A),u1_struct_0(B),C,k6_rlvect_1(B,D,E))) = k6_rlvect_1(k1_complfld,k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),F,k1_domain_1(u1_struct_0(A),u1_struct_0(B),C,D)),k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),F,k1_domain_1(u1_struct_0(A),u1_struct_0(B),C,E))) ) ) ) ) ) ) ).
fof(t39_hermitan,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] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& l4_vectsp_1(B,k1_complfld) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(G,k1_complfld,A,B)
& v2_bilinear(G,k1_complfld,A,B)
& v4_bilinear(G,k1_complfld,A,B)
& v2_hermitan(G,A,B)
& m2_relset_1(G,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),G,k1_domain_1(u1_struct_0(A),u1_struct_0(B),k6_rlvect_1(A,C,D),k6_rlvect_1(B,E,F))) = k6_rlvect_1(k1_complfld,k6_rlvect_1(k1_complfld,k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),G,k1_domain_1(u1_struct_0(A),u1_struct_0(B),C,E)),k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),G,k1_domain_1(u1_struct_0(A),u1_struct_0(B),C,F))),k6_rlvect_1(k1_complfld,k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),G,k1_domain_1(u1_struct_0(A),u1_struct_0(B),D,E)),k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),G,k1_domain_1(u1_struct_0(A),u1_struct_0(B),D,F)))) ) ) ) ) ) ) ) ).
fof(t40_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(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] :
( ( ~ v3_struct_0(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& l4_vectsp_1(B,k1_complfld) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k1_complfld))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k1_complfld))
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(I,k1_complfld,A,B)
& v2_bilinear(I,k1_complfld,A,B)
& v4_bilinear(I,k1_complfld,A,B)
& v2_hermitan(I,A,B)
& m2_relset_1(I,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),I,k1_domain_1(u1_struct_0(A),u1_struct_0(B),k2_rlvect_1(A,C,k6_vectsp_1(k1_complfld,A,G,D)),k2_rlvect_1(B,E,k6_vectsp_1(k1_complfld,B,H,F)))) = k4_rlvect_1(k1_complfld,k4_rlvect_1(k1_complfld,k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),I,k1_domain_1(u1_struct_0(A),u1_struct_0(B),C,E)),k10_group_1(k1_complfld,k2_complfld(H),k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),I,k1_domain_1(u1_struct_0(A),u1_struct_0(B),C,F)))),k4_rlvect_1(k1_complfld,k10_group_1(k1_complfld,G,k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),I,k1_domain_1(u1_struct_0(A),u1_struct_0(B),D,E))),k10_group_1(k1_complfld,G,k10_group_1(k1_complfld,k2_complfld(H),k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),I,k1_domain_1(u1_struct_0(A),u1_struct_0(B),D,F)))))) ) ) ) ) ) ) ) ) ) ).
fof(t41_hermitan,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] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& l4_vectsp_1(B,k1_complfld) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k1_complfld))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k1_complfld))
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(I,k1_complfld,A,B)
& v2_bilinear(I,k1_complfld,A,B)
& v4_bilinear(I,k1_complfld,A,B)
& v2_hermitan(I,A,B)
& m2_relset_1(I,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),I,k1_domain_1(u1_struct_0(A),u1_struct_0(B),k6_rlvect_1(A,C,k6_vectsp_1(k1_complfld,A,G,D)),k6_rlvect_1(B,E,k6_vectsp_1(k1_complfld,B,H,F)))) = k6_rlvect_1(k1_complfld,k6_rlvect_1(k1_complfld,k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),I,k1_domain_1(u1_struct_0(A),u1_struct_0(B),C,E)),k10_group_1(k1_complfld,k2_complfld(H),k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),I,k1_domain_1(u1_struct_0(A),u1_struct_0(B),C,F)))),k6_rlvect_1(k1_complfld,k10_group_1(k1_complfld,G,k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),I,k1_domain_1(u1_struct_0(A),u1_struct_0(B),D,E))),k10_group_1(k1_complfld,G,k10_group_1(k1_complfld,k2_complfld(H),k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),I,k1_domain_1(u1_struct_0(A),u1_struct_0(B),D,F)))))) ) ) ) ) ) ) ) ) ) ).
fof(t42_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_hermitan(B,A,A)
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,k1_rlvect_1(A))) = k1_rlvect_1(k1_complfld) ) ) ) ).
fof(t43_hermitan,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_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(D,k1_complfld,A,A)
& v4_bilinear(D,k1_complfld,A,A)
& v3_hermitan(D,A)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> k4_rlvect_1(k1_complfld,k4_rlvect_1(k1_complfld,k4_rlvect_1(k1_complfld,k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)),k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C))),k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C))),k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C))) = k6_rlvect_1(k1_complfld,k4_rlvect_1(k1_complfld,k6_rlvect_1(k1_complfld,k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),k4_rlvect_1(A,B,C),k4_rlvect_1(A,B,C))),k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),k6_rlvect_1(A,B,C),k6_rlvect_1(A,B,C)))),k10_group_1(k1_complfld,k2_hahnban1,k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),k4_rlvect_1(A,B,k6_vectsp_1(k1_complfld,A,k2_hahnban1,C)),k4_rlvect_1(A,B,k6_vectsp_1(k1_complfld,A,k2_hahnban1,C)))))),k10_group_1(k1_complfld,k2_hahnban1,k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),k6_rlvect_1(A,B,k6_vectsp_1(k1_complfld,A,k2_hahnban1,C)),k6_rlvect_1(A,B,k6_vectsp_1(k1_complfld,A,k2_hahnban1,C)))))) ) ) ) ) ).
fof(d9_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k4_hermitan(A,B,C) = k3_complex1(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,C))) ) ) ) ).
fof(t44_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v4_hermitan(B,A)
& v5_hermitan(B,A)
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k3_complfld(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,C))) = k3_complex1(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,C)))
& k4_hermitan(A,B,C) = k3_complfld(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,C))) ) ) ) ) ).
fof(t45_hermitan,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_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v1_bilinear(D,k1_complfld,A,A)
& v2_bilinear(D,k1_complfld,A,A)
& v4_bilinear(D,k1_complfld,A,A)
& v2_hermitan(D,A,A)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k1_complfld))
=> ( ( k3_complfld(F) = np__1
& k3_complex1(k10_group_1(k1_complfld,F,k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,B)))) = k3_complfld(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,B)))
& k4_complex1(k10_group_1(k1_complfld,F,k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,B)))) = np__0 )
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),k6_rlvect_1(A,B,k6_vectsp_1(k1_complfld,A,k10_group_1(k1_complfld,k1_hahnban1(E,np__0),F),C)),k6_rlvect_1(A,B,k6_vectsp_1(k1_complfld,A,k10_group_1(k1_complfld,k1_hahnban1(E,np__0),F),C)))) = k4_rlvect_1(k1_complfld,k6_rlvect_1(k1_complfld,k6_rlvect_1(k1_complfld,k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,B)),k10_group_1(k1_complfld,k1_hahnban1(E,np__0),k10_group_1(k1_complfld,F,k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,B))))),k10_group_1(k1_complfld,k1_hahnban1(E,np__0),k10_group_1(k1_complfld,k2_complfld(F),k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C))))),k10_group_1(k1_complfld,k1_hahnban1(k7_square_1(E),np__0),k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,C)))) ) ) ) ) ) ) ) ).
fof(t46_hermitan,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_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(D,k1_complfld,A,A)
& v4_bilinear(D,k1_complfld,A,A)
& v3_hermitan(D,A)
& v5_hermitan(D,A)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k1_complfld))
=> ( ( k3_complfld(F) = np__1
& k3_complex1(k10_group_1(k1_complfld,F,k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,B)))) = k3_complfld(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,B)))
& k4_complex1(k10_group_1(k1_complfld,F,k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,B)))) = np__0 )
=> ( k3_complex1(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),k6_rlvect_1(A,B,k6_vectsp_1(k1_complfld,A,k10_group_1(k1_complfld,k1_hahnban1(E,np__0),F),C)),k6_rlvect_1(A,B,k6_vectsp_1(k1_complfld,A,k10_group_1(k1_complfld,k1_hahnban1(E,np__0),F),C))))) = k2_xcmplx_0(k6_xcmplx_0(k4_hermitan(A,D,B),k4_real_1(k4_real_1(np__2,k3_complfld(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,B)))),E)),k3_xcmplx_0(k4_hermitan(A,D,C),k7_square_1(E)))
& r1_xreal_0(np__0,k2_xcmplx_0(k6_xcmplx_0(k4_hermitan(A,D,B),k4_real_1(k4_real_1(np__2,k3_complfld(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,B)))),E)),k3_xcmplx_0(k4_hermitan(A,D,C),k7_square_1(E)))) ) ) ) ) ) ) ) ) ).
fof(t47_hermitan,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_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(D,k1_complfld,A,A)
& v4_bilinear(D,k1_complfld,A,A)
& v3_hermitan(D,A)
& v5_hermitan(D,A)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ( k4_hermitan(A,D,C) = np__0
=> k3_complfld(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,B))) = np__0 ) ) ) ) ) ).
fof(t48_hermitan,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_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(D,k1_complfld,A,A)
& v4_bilinear(D,k1_complfld,A,A)
& v3_hermitan(D,A)
& v5_hermitan(D,A)
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> r1_xreal_0(k7_square_1(k3_complfld(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C)))),k3_xcmplx_0(k4_hermitan(A,D,B),k4_hermitan(A,D,C))) ) ) ) ) ).
fof(t49_hermitan,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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(B,k1_complfld,A,A)
& v4_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A)
& v5_hermitan(B,A)
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r1_xreal_0(k7_square_1(k3_complfld(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,D)))),k4_real_1(k3_complfld(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,C))),k3_complfld(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,D))))) ) ) ) ) ).
fof(t50_hermitan,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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(B,k1_complfld,A,A)
& v4_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A)
& v5_hermitan(B,A)
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r1_xreal_0(k4_hermitan(A,B,k4_rlvect_1(A,C,D)),k5_square_1(k2_xcmplx_0(k8_square_1(k4_hermitan(A,B,C)),k8_square_1(k4_hermitan(A,B,D))))) ) ) ) ) ).
fof(t51_hermitan,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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(B,k1_complfld,A,A)
& v4_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A)
& v5_hermitan(B,A)
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r1_xreal_0(k3_complfld(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),k4_rlvect_1(A,C,D),k4_rlvect_1(A,C,D)))),k7_square_1(k3_real_1(k9_square_1(k3_complfld(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,C)))),k9_square_1(k3_complfld(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,D))))))) ) ) ) ) ).
fof(t52_hermitan,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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(B,k1_complfld,A,A)
& v4_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A)
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k2_xcmplx_0(k4_hermitan(A,B,k4_rlvect_1(A,C,D)),k4_hermitan(A,B,k6_rlvect_1(A,C,D))) = k2_xcmplx_0(k3_xcmplx_0(np__2,k4_hermitan(A,B,C)),k3_xcmplx_0(np__2,k4_hermitan(A,B,D))) ) ) ) ) ).
fof(t53_hermitan,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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(B,k1_complfld,A,A)
& v4_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A)
& v5_hermitan(B,A)
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k3_real_1(k3_complfld(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),k4_rlvect_1(A,C,D),k4_rlvect_1(A,C,D)))),k3_complfld(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),k6_rlvect_1(A,C,D),k6_rlvect_1(A,C,D))))) = k3_real_1(k4_real_1(np__2,k3_complfld(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,C)))),k4_real_1(np__2,k3_complfld(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,D))))) ) ) ) ) ).
fof(d10_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ! [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 = k5_hermitan(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),k1_numbers,C,D) = k8_square_1(k4_hermitan(A,B,D)) ) ) ) ) ) ).
fof(t54_hermitan,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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(B,k1_complfld,A,A)
& v4_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A)
& v5_hermitan(B,A)
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> v1_vectsp_4(k14_bilinear(k1_complfld,A,B),k1_complfld,A) ) ) ).
fof(t55_hermitan,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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(B,k1_complfld,A,A)
& v4_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A)
& v5_hermitan(B,A)
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> k14_bilinear(k1_complfld,A,B) = k12_bilinear(k1_complfld,A,A,B) ) ) ).
fof(t56_hermitan,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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(B,k1_complfld,A,A)
& v4_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A)
& v5_hermitan(B,A)
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> k14_bilinear(k1_complfld,A,B) = k13_bilinear(k1_complfld,A,A,B) ) ) ).
fof(t57_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> k14_bilinear(k1_complfld,A,B) = k14_bilinear(k1_complfld,A,k3_hermitan(A,A,B)) ) ) ).
fof(t58_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( k12_bilinear(k1_complfld,A,B,C) = k12_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))
& k13_bilinear(k1_complfld,A,B,C) = k13_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C)) ) ) ) ) ).
fof(t59_hermitan,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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(B,k1_complfld,A,A)
& v4_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A)
& v5_hermitan(B,A)
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> k15_bilinear(k1_complfld,A,A,B) = k16_bilinear(k1_complfld,A,A,k3_hermitan(A,A,B)) ) ) ).
fof(t60_hermitan,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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v4_hermitan(B,A)
& v5_hermitan(B,A)
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k3_complex1(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,C))) = np__0
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,C)) = k1_rlvect_1(k1_complfld) ) ) ) ) ).
fof(t61_hermitan,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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(B,k1_complfld,A,A)
& v4_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A)
& v5_hermitan(B,A)
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k3_complex1(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,C))) = np__0
=> ( ( v5_bilinear(B,k1_complfld,A,A)
& v6_bilinear(B,k1_complfld,A,A) )
| C = k1_rlvect_1(A) ) ) ) ) ) ).
fof(d11_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& l4_vectsp_1(B,k1_complfld) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(C,k1_complfld,A,B)
& v2_hermitan(C,A,B)
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> k7_hermitan(A,B,C) = k3_hermitan(A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k18_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))) ) ) ) ).
fof(t62_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& l4_vectsp_1(B,k1_complfld) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(C,k1_complfld,A,B)
& v2_hermitan(C,A,B)
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k1_funct_1(k7_hermitan(A,B,C),k1_domain_1(u1_struct_0(A),k1_zfmisc_1(u1_struct_0(B)),D,k3_vectsp_4(k1_complfld,B,E,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),C,k1_domain_1(u1_struct_0(A),u1_struct_0(B),D,E)) ) ) ) ) ) ).
fof(d12_hermitan,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] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& l4_vectsp_1(B,k1_complfld) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(C,k1_complfld,A,B)
& v2_bilinear(C,k1_complfld,A,B)
& v4_bilinear(C,k1_complfld,A,B)
& v2_hermitan(C,A,B)
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C))),u1_struct_0(k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))),u1_struct_0(k1_complfld))
& v1_bilinear(D,k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& v2_bilinear(D,k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& v4_bilinear(D,k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& v2_hermitan(D,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C))),u1_struct_0(k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))),u1_struct_0(k1_complfld)) )
=> ( D = k8_hermitan(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C))))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C)))))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> ( ( E = k3_vectsp_4(k1_complfld,A,G,k15_bilinear(k1_complfld,A,B,C))
& F = k3_vectsp_4(k1_complfld,B,H,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))) )
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C))),u1_struct_0(k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))),u1_struct_0(k1_complfld),D,k1_domain_1(u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C))),u1_struct_0(k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C)))),E,F)) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld),C,k1_domain_1(u1_struct_0(A),u1_struct_0(B),G,H)) ) ) ) ) ) ) ) ) ) ) ).
fof(t63_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& l4_vectsp_1(B,k1_complfld) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(C,k1_complfld,A,B)
& v2_hermitan(C,A,B)
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> k12_bilinear(k1_complfld,A,B,C) = k12_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C)) ) ) ) ).
fof(t64_hermitan,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] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& l4_vectsp_1(B,k1_complfld) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(C,k1_complfld,A,B)
& v2_bilinear(C,k1_complfld,A,B)
& v4_bilinear(C,k1_complfld,A,B)
& v2_hermitan(C,A,B)
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C)) = k16_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k3_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C))) ) ) ) ).
fof(t65_hermitan,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] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& l4_vectsp_1(B,k1_complfld) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(C,k1_complfld,A,B)
& v2_bilinear(C,k1_complfld,A,B)
& v4_bilinear(C,k1_complfld,A,B)
& v2_hermitan(C,A,B)
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> k15_bilinear(k1_complfld,A,B,C) = k15_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C)) ) ) ) ).
fof(t66_hermitan,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] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& l4_vectsp_1(B,k1_complfld) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(C,k1_complfld,A,B)
& v2_bilinear(C,k1_complfld,A,B)
& v4_bilinear(C,k1_complfld,A,B)
& v2_hermitan(C,A,B)
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( k8_hermitan(A,B,C) = k7_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C))
& k8_hermitan(A,B,C) = k17_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C)) ) ) ) ) ).
fof(t67_hermitan,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] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& l4_vectsp_1(B,k1_complfld) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(C,k1_complfld,A,B)
& v2_bilinear(C,k1_complfld,A,B)
& v4_bilinear(C,k1_complfld,A,B)
& v2_hermitan(C,A,B)
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( k12_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k8_hermitan(A,B,C)) = k12_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k3_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C)))),k7_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C)))
& k13_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k8_hermitan(A,B,C)) = k13_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k3_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C)))),k7_hermitan(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),B,k17_bilinear(k1_complfld,A,B,C)))
& k12_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k8_hermitan(A,B,C)) = k12_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C))),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k17_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C)))
& k13_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k8_hermitan(A,B,C)) = k13_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C))),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k17_bilinear(k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))),k7_hermitan(A,B,C))) ) ) ) ) ).
fof(d13_hermitan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ( v6_hermitan(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( C != k1_rlvect_1(A)
& r1_xreal_0(k3_complex1(k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,C))),np__0) ) ) ) ) ) ).
fof(d14_hermitan,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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(B,k1_complfld,A,A)
& v4_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A)
& v5_hermitan(B,A)
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> k9_hermitan(A,B) = k8_hermitan(A,A,B) ) ) ).
fof(t68_hermitan,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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(B,k1_complfld,A,A)
& v4_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A)
& v5_hermitan(B,A)
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B))))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B))))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( C = k3_vectsp_4(k1_complfld,A,E,k15_bilinear(k1_complfld,A,A,B))
& D = k3_vectsp_4(k1_complfld,A,F,k15_bilinear(k1_complfld,A,A,B)) )
=> k8_funct_2(k2_zfmisc_1(u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B))),u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))),u1_struct_0(k1_complfld),k9_hermitan(A,B),k1_domain_1(u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B))),u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B))),C,D)) = k8_funct_2(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld),B,k1_domain_1(u1_struct_0(A),u1_struct_0(A),E,F)) ) ) ) ) ) ) ) ).
fof(t69_hermitan,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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(B,k1_complfld,A,A)
& v4_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A)
& v5_hermitan(B,A)
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> k12_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)),k9_hermitan(A,B)) = k12_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)),k6_vectsp10(k1_complfld,A,k16_bilinear(k1_complfld,A,A,k3_hermitan(A,A,B))),k8_hermitan(A,A,B)) ) ) ).
fof(t70_hermitan,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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(B,k1_complfld,A,A)
& v4_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A)
& v5_hermitan(B,A)
& m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> k13_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)),k9_hermitan(A,B)) = k13_bilinear(k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)),k6_vectsp10(k1_complfld,A,k16_bilinear(k1_complfld,A,A,k3_hermitan(A,A,B))),k8_hermitan(A,A,B)) ) ) ).
fof(dt_k1_hermitan,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(k1_hermitan(A,B))
& v1_funct_2(k1_hermitan(A,B),u1_struct_0(A),u1_struct_0(k1_complfld))
& m2_relset_1(k1_hermitan(A,B),u1_struct_0(A),u1_struct_0(k1_complfld)) ) ) ).
fof(dt_k2_hermitan,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),u1_struct_0(k1_complfld))
& v1_hahnban1(B,k1_complfld,A)
& v1_hermitan(B,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(k1_complfld)) )
=> ( v1_funct_1(k2_hermitan(A,B))
& v1_funct_2(k2_hermitan(A,B),u1_struct_0(k6_vectsp10(k1_complfld,A,k9_vectsp10(k1_complfld,A,k1_hermitan(A,B)))),u1_struct_0(k1_complfld))
& v1_hahnban1(k2_hermitan(A,B),k1_complfld,k6_vectsp10(k1_complfld,A,k9_vectsp10(k1_complfld,A,k1_hermitan(A,B))))
& v1_hermitan(k2_hermitan(A,B),k6_vectsp10(k1_complfld,A,k9_vectsp10(k1_complfld,A,k1_hermitan(A,B))))
& m2_relset_1(k2_hermitan(A,B),u1_struct_0(k6_vectsp10(k1_complfld,A,k9_vectsp10(k1_complfld,A,k1_hermitan(A,B)))),u1_struct_0(k1_complfld)) ) ) ).
fof(dt_k3_hermitan,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& ~ v3_struct_0(B)
& l4_vectsp_1(B,k1_complfld)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( v1_funct_1(k3_hermitan(A,B,C))
& v1_funct_2(k3_hermitan(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& m2_relset_1(k3_hermitan(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) ) ) ).
fof(dt_k4_hermitan,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& m1_subset_1(C,u1_struct_0(A)) )
=> v1_xreal_0(k4_hermitan(A,B,C)) ) ).
fof(dt_k5_hermitan,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ( v1_funct_1(k5_hermitan(A,B))
& v1_funct_2(k5_hermitan(A,B),u1_struct_0(A),k1_numbers)
& m2_relset_1(k5_hermitan(A,B),u1_struct_0(A),k1_numbers) ) ) ).
fof(dt_k6_hermitan,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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(B,k1_complfld,A,A)
& v4_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A)
& v5_hermitan(B,A)
& m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ( v1_funct_1(k6_hermitan(A,B))
& v1_funct_2(k6_hermitan(A,B),u1_struct_0(A),k1_numbers)
& v4_hahnban1(k6_hermitan(A,B),k1_complfld,A)
& v7_hahnban1(k6_hermitan(A,B),A)
& m2_relset_1(k6_hermitan(A,B),u1_struct_0(A),k1_numbers) ) ) ).
fof(redefinition_k6_hermitan,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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(B,k1_complfld,A,A)
& v4_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A)
& v5_hermitan(B,A)
& m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> k6_hermitan(A,B) = k5_hermitan(A,B) ) ).
fof(dt_k7_hermitan,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l4_vectsp_1(A,k1_complfld)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& l4_vectsp_1(B,k1_complfld)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(C,k1_complfld,A,B)
& v2_hermitan(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( v1_funct_1(k7_hermitan(A,B,C))
& v1_funct_2(k7_hermitan(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))),u1_struct_0(k1_complfld))
& v1_bilinear(k7_hermitan(A,B,C),k1_complfld,A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& v2_hermitan(k7_hermitan(A,B,C),A,k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& m2_relset_1(k7_hermitan(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))),u1_struct_0(k1_complfld)) ) ) ).
fof(dt_k8_hermitan,axiom,
! [A,B,C] :
( ( ~ 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)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,k1_complfld)
& l4_vectsp_1(B,k1_complfld)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld))
& v1_bilinear(C,k1_complfld,A,B)
& v2_bilinear(C,k1_complfld,A,B)
& v4_bilinear(C,k1_complfld,A,B)
& v2_hermitan(C,A,B)
& m1_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),u1_struct_0(k1_complfld)) )
=> ( v1_funct_1(k8_hermitan(A,B,C))
& v1_funct_2(k8_hermitan(A,B,C),k2_zfmisc_1(u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C))),u1_struct_0(k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))),u1_struct_0(k1_complfld))
& v1_bilinear(k8_hermitan(A,B,C),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& v2_bilinear(k8_hermitan(A,B,C),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& v4_bilinear(k8_hermitan(A,B,C),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& v2_hermitan(k8_hermitan(A,B,C),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C)),k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))
& m2_relset_1(k8_hermitan(A,B,C),k2_zfmisc_1(u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,B,C))),u1_struct_0(k6_vectsp10(k1_complfld,B,k16_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))),u1_struct_0(k1_complfld)) ) ) ).
fof(dt_k9_hermitan,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,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld))
& v2_bilinear(B,k1_complfld,A,A)
& v4_bilinear(B,k1_complfld,A,A)
& v3_hermitan(B,A)
& v5_hermitan(B,A)
& m1_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(k1_complfld)) )
=> ( v1_funct_1(k9_hermitan(A,B))
& v1_funct_2(k9_hermitan(A,B),k2_zfmisc_1(u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B))),u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))),u1_struct_0(k1_complfld))
& v2_bilinear(k9_hermitan(A,B),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& v4_bilinear(k9_hermitan(A,B),k1_complfld,k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& v3_hermitan(k9_hermitan(A,B),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& v5_hermitan(k9_hermitan(A,B),k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))
& m2_relset_1(k9_hermitan(A,B),k2_zfmisc_1(u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B))),u1_struct_0(k6_vectsp10(k1_complfld,A,k15_bilinear(k1_complfld,A,A,B)))),u1_struct_0(k1_complfld)) ) ) ).
%------------------------------------------------------------------------------