SET007 Axioms: SET007+436.ax
%------------------------------------------------------------------------------
% File : SET007+436 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Associated Matrix of Linear Map
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : matrlin [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 82 ( 3 unt; 0 def)
% Number of atoms : 1672 ( 107 equ)
% Maximal formula atoms : 51 ( 20 avg)
% Number of connectives : 1783 ( 193 ~; 7 |;1215 &)
% ( 9 <=>; 359 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 15 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 47 ( 45 usr; 1 prp; 0-4 aty)
% Number of functors : 67 ( 67 usr; 5 con; 0-6 aty)
% Number of variables : 379 ( 369 !; 10 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_matrlin,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v1_matrlin(A) ) ).
fof(rc2_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ? [B] :
( l4_vectsp_1(B,A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v11_vectsp_1(B,A)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A) ) ) ).
fof(cc1_matrlin,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_finseq_1(B,k3_finseq_2(A))
=> ( v1_matrix_1(B)
=> ( v1_matrix_1(B)
& v1_matrlin(B) ) ) ) ) ).
fof(t1_matrlin,axiom,
$true ).
fof(t2_matrlin,axiom,
$true ).
fof(t3_matrlin,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( k3_finseq_1(B) = k1_nat_1(A,np__1)
=> k3_finseq_1(k2_finseq_3(k1_nat_1(A,np__1),B)) = A ) ) ) ).
fof(t4_matrlin,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_matrix_1(D,C,k1_nat_1(A,np__1),B)
=> ! [E] :
( ( v1_matrix_1(E)
& m2_finseq_1(E,k3_finseq_2(C)) )
=> ( ( ~ r1_xreal_0(A,np__0)
=> k1_matrix_1(D) = k1_matrix_1(k2_matrlin(C,k1_nat_1(A,np__1),D)) )
& ( E = k9_finseq_1(k1_funct_1(D,k1_nat_1(A,np__1)))
=> k1_matrix_1(D) = k1_matrix_1(E) ) ) ) ) ) ) ) ).
fof(t5_matrlin,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_matrix_1(D,C,k1_nat_1(A,np__1),B)
=> m1_matrix_1(k2_matrlin(C,k1_nat_1(A,np__1),D),C,A,B) ) ) ) ) ).
fof(t6_matrlin,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( k3_finseq_1(B) = k1_nat_1(A,np__1)
=> B = k7_finseq_1(k2_finseq_3(k3_finseq_1(B),B),k9_finseq_1(k1_funct_1(B,k3_finseq_1(B)))) ) ) ) ).
fof(t7_matrlin,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ( v1_funct_1(k8_finseq_1(k5_numbers,k14_finseq_1(k10_relat_1(B,A)),k14_finseq_1(k10_relat_1(B,k4_xboole_0(k2_relat_1(B),A)))))
& v1_funct_2(k8_finseq_1(k5_numbers,k14_finseq_1(k10_relat_1(B,A)),k14_finseq_1(k10_relat_1(B,k4_xboole_0(k2_relat_1(B),A)))),k1_relat_1(B),k1_relat_1(B))
& v3_funct_2(k8_finseq_1(k5_numbers,k14_finseq_1(k10_relat_1(B,A)),k14_finseq_1(k10_relat_1(B,k4_xboole_0(k2_relat_1(B),A)))),k1_relat_1(B),k1_relat_1(B))
& m2_relset_1(k8_finseq_1(k5_numbers,k14_finseq_1(k10_relat_1(B,A)),k14_finseq_1(k10_relat_1(B,k4_xboole_0(k2_relat_1(B),A)))),k1_relat_1(B),k1_relat_1(B)) ) ) ).
fof(t8_matrlin,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k2_relat_1(A)))
=> ~ ( v2_funct_1(A)
& ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_relat_1(A),k1_relat_1(A))
& v3_funct_2(C,k1_relat_1(A),k1_relat_1(A))
& m2_relset_1(C,k1_relat_1(A),k1_relat_1(A)) )
=> k7_finseq_1(k1_finseq_3(A,k3_subset_1(k2_relat_1(A),B)),k1_finseq_3(A,B)) != k5_relat_1(C,A) ) ) ) ) ).
fof(d1_matrlin,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ( v1_matrlin(A)
<=> ! [B] :
( r2_hidden(B,k1_relat_1(A))
=> ( v1_relat_1(k1_funct_1(A,B))
& v1_funct_1(k1_funct_1(A,B))
& v1_finseq_1(k1_funct_1(A,B)) ) ) ) ) ).
fof(d2_matrlin,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_matrlin(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_matrlin(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_matrlin(C) )
=> ( C = k4_matrlin(A,B)
<=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B))
& ! [D] :
( r2_hidden(D,k1_relat_1(C))
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v1_finseq_1(E) )
=> ! [F] :
( ( v1_relat_1(F)
& v1_funct_1(F)
& v1_finseq_1(F) )
=> ( ( E = k1_funct_1(A,D)
& F = k1_funct_1(B,D) )
=> k1_funct_1(C,D) = k7_finseq_1(E,F) ) ) ) ) ) ) ) ) ) ).
fof(t9_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_6(C,A,B)
=> ! [D] :
( m1_vectsp_6(D,A,B)
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( v1_vectsp_7(E,A,B)
& r1_tarski(k1_vectsp_6(A,B,C),E)
& r1_tarski(k1_vectsp_6(A,B,D),E)
& k4_vectsp_6(A,B,C) = k4_vectsp_6(A,B,D) )
=> r1_vectsp_6(A,B,C,D) ) ) ) ) ) ) ).
fof(t10_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_6(C,A,B)
=> ! [D] :
( m1_vectsp_6(D,A,B)
=> ! [E] :
( m1_vectsp_6(E,A,B)
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( v1_vectsp_7(F,A,B)
& r1_tarski(k1_vectsp_6(A,B,C),F)
& r1_tarski(k1_vectsp_6(A,B,D),F)
& r1_tarski(k1_vectsp_6(A,B,E),F)
& k4_vectsp_6(A,B,C) = k4_rlvect_1(B,k4_vectsp_6(A,B,D),k4_vectsp_6(A,B,E)) )
=> r1_vectsp_6(A,B,C,k5_vectsp_6(A,B,D,E)) ) ) ) ) ) ) ) ).
fof(t11_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_vectsp_6(D,A,B)
=> ! [E] :
( m1_vectsp_6(E,A,B)
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( v1_vectsp_7(F,A,B)
& r1_tarski(k1_vectsp_6(A,B,D),F)
& r1_tarski(k1_vectsp_6(A,B,E),F)
& k4_vectsp_6(A,B,D) = k6_vectsp_1(A,B,C,k4_vectsp_6(A,B,E)) )
=> ( C = k1_rlvect_1(A)
| r1_vectsp_6(A,B,D,k6_vectsp_6(A,B,C,E)) ) ) ) ) ) ) ) ) ).
fof(t12_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_vectsp_7(D,A,B)
=> ? [E] :
( m1_vectsp_6(E,A,B)
& C = k4_vectsp_6(A,B,E)
& r1_tarski(k1_vectsp_6(A,B,E),D) ) ) ) ) ) ).
fof(d3_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ( v2_matrlin(B,A)
<=> ? [C] :
( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& m1_vectsp_7(C,A,B) ) ) ) ) ).
fof(d4_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(B))
=> ( m1_matrlin(C,A,B)
<=> ( v2_funct_1(C)
& m1_vectsp_7(k2_relat_1(C),A,B) ) ) ) ) ) ).
fof(d5_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [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,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(C)) )
=> ( F = k5_matrlin(A,B,C,D,E)
<=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> k8_funct_2(u1_struct_0(B),u1_struct_0(C),F,G) = k4_rlvect_1(C,k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,G),k8_funct_2(u1_struct_0(B),u1_struct_0(C),E,G)) ) ) ) ) ) ) ) ) ).
fof(d6_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& v2_matrlin(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(F,u1_struct_0(B),u1_struct_0(C)) )
=> ( F = k6_matrlin(A,B,C,D,E)
<=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> k8_funct_2(u1_struct_0(B),u1_struct_0(C),F,G) = k6_vectsp_1(A,C,E,k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,G)) ) ) ) ) ) ) ) ) ).
fof(t13_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(B))
=> ! [E] :
( m2_finseq_1(E,u1_struct_0(A))
=> ( ( k3_finseq_1(D) = k3_finseq_1(E)
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( ( r2_hidden(F,k1_relat_1(D))
& G = k1_funct_1(E,F) )
=> k1_funct_1(D,F) = k6_vectsp_1(A,B,G,C) ) ) ) )
=> k9_rlvect_1(B,D) = k6_vectsp_1(A,B,k9_rlvect_1(A,E),C) ) ) ) ) ) ) ).
fof(t14_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(A))
=> ! [E] :
( m2_finseq_1(E,u1_struct_0(B))
=> ( ( k3_finseq_1(D) = k3_finseq_1(E)
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r2_hidden(F,k1_relat_1(D))
=> k1_funct_1(E,F) = k6_vectsp_1(A,B,k4_finseq_4(k5_numbers,u1_struct_0(A),D,F),C) ) ) )
=> k9_rlvect_1(B,E) = k6_vectsp_1(A,B,k9_rlvect_1(A,D),C) ) ) ) ) ) ) ).
fof(t15_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(A))
=> ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k1_relat_1(B))
=> k4_finseq_4(k5_numbers,u1_struct_0(A),B,C) = k1_rlvect_1(A) ) )
=> k9_rlvect_1(A,B) = k1_rlvect_1(A) ) ) ) ).
fof(d7_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(B))
=> k7_matrlin(A,B,C,D) = k1_finseqop(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u2_vectsp_1(A,B),C,D) ) ) ) ) ).
fof(t16_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(B))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(A))
=> ( k1_relat_1(D) = k1_relat_1(C)
=> k1_relat_1(k7_matrlin(A,B,D,C)) = k1_relat_1(D) ) ) ) ) ) ).
fof(d8_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m2_finseq_1(B,k3_finseq_2(u1_struct_0(A)))
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(A))
=> ( C = k8_matrlin(A,B)
<=> ( k3_finseq_1(C) = k3_finseq_1(B)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(D,k1_relat_1(C))
=> k4_finseq_4(k5_numbers,u1_struct_0(A),C,D) = k9_rlvect_1(A,k1_matrlin(u1_struct_0(A),k5_numbers,k3_finseq_2(u1_struct_0(A)),B,D)) ) ) ) ) ) ) ) ).
fof(t17_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) )
=> ( k3_finseq_1(C) = np__0
=> k9_rlvect_1(B,k8_matrlin(B,C)) = k1_rlvect_1(B) ) ) ) ) ).
fof(t18_matrlin,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v4_group_1(B)
& v7_group_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& v9_vectsp_1(B)
& ~ v10_vectsp_1(B)
& l3_vectsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,B)
& v2_matrlin(C,B)
& l4_vectsp_1(C,B) )
=> ! [D] :
( m1_matrix_1(D,u1_struct_0(C),k1_nat_1(A,np__1),np__0)
=> k9_rlvect_1(C,k8_matrlin(C,D)) = k1_rlvect_1(C) ) ) ) ) ).
fof(t19_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> k3_matrlin(u1_struct_0(B),k4_matrix_2(u1_struct_0(B),C)) = k4_matrix_1(u1_struct_0(B),k3_matrlin(u1_struct_0(B),k4_matrix_2(u1_struct_0(B),C))) ) ) ) ).
fof(t20_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& v2_matrlin(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) )
=> ! [E] :
( m2_finseq_1(E,u1_struct_0(C))
=> ( v1_mod_2(D,A,C,B)
=> k8_funct_2(u1_struct_0(C),u1_struct_0(B),D,k9_rlvect_1(C,E)) = k9_rlvect_1(B,k5_finseqop(u1_struct_0(C),u1_struct_0(B),E,D)) ) ) ) ) ) ) ).
fof(t21_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& v2_matrlin(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) )
=> ! [E] :
( m2_finseq_1(E,u1_struct_0(A))
=> ! [F] :
( m2_finseq_1(F,u1_struct_0(C))
=> ( ( k3_finseq_1(F) = k3_finseq_1(E)
& v1_mod_2(D,A,C,B) )
=> k5_finseqop(u1_struct_0(C),u1_struct_0(B),k7_matrlin(A,C,E,F),D) = k7_matrlin(A,B,E,k5_finseqop(u1_struct_0(C),u1_struct_0(B),F,D)) ) ) ) ) ) ) ) ).
fof(t22_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& v2_matrlin(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) )
=> ! [E] :
( m1_matrlin(E,A,C)
=> ! [F] :
( m2_finseq_1(F,u1_struct_0(A))
=> ( ( k3_finseq_1(F) = k3_finseq_1(E)
& v1_mod_2(D,A,C,B) )
=> k8_funct_2(u1_struct_0(C),u1_struct_0(B),D,k9_rlvect_1(C,k7_matrlin(A,C,F,E))) = k9_rlvect_1(B,k7_matrlin(A,B,F,k5_finseqop(u1_struct_0(C),u1_struct_0(B),E,D))) ) ) ) ) ) ) ) ).
fof(t23_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(B))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(B))
=> ! [E] :
( m1_vectsp_6(E,A,B)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k1_relat_1(C),k1_relat_1(C))
& v3_funct_2(F,k1_relat_1(C),k1_relat_1(C))
& m2_relset_1(F,k1_relat_1(C),k1_relat_1(C)) )
=> ( D = k1_partfun1(k1_relat_1(C),k1_relat_1(C),k5_numbers,u1_struct_0(B),F,C)
=> k3_vectsp_6(A,B,D,E) = k1_partfun1(k1_relat_1(C),k1_relat_1(C),k5_numbers,u1_struct_0(B),F,k3_vectsp_6(A,B,C,E)) ) ) ) ) ) ) ) ).
fof(t24_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(B))
=> ! [D] :
( m1_vectsp_6(D,A,B)
=> ( ( v2_funct_1(C)
& r1_tarski(k1_vectsp_6(A,B,D),k2_relat_1(C)) )
=> k9_rlvect_1(B,k3_vectsp_6(A,B,C,D)) = k4_vectsp_6(A,B,D) ) ) ) ) ) ).
fof(t25_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& v2_matrlin(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
=> ! [F,G] :
( m2_finseq_1(G,u1_struct_0(C))
=> ( ( r1_tarski(k2_relat_1(G),F)
& v1_mod_2(D,A,C,B)
& v1_mod_2(E,A,C,B)
& ! [H] :
( m1_subset_1(H,u1_struct_0(C))
=> ( r2_hidden(H,F)
=> k8_funct_2(u1_struct_0(C),u1_struct_0(B),D,H) = k8_funct_2(u1_struct_0(C),u1_struct_0(B),E,H) ) ) )
=> k8_funct_2(u1_struct_0(C),u1_struct_0(B),D,k9_rlvect_1(C,G)) = k8_funct_2(u1_struct_0(C),u1_struct_0(B),E,k9_rlvect_1(C,G)) ) ) ) ) ) ) ) ).
fof(t26_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& v2_matrlin(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(C),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(B)) )
=> ( ( v1_mod_2(D,A,C,B)
& v1_mod_2(E,A,C,B) )
=> ! [F] :
( m1_matrlin(F,A,C)
=> ( k5_finseqop(u1_struct_0(C),u1_struct_0(B),F,D) = k5_finseqop(u1_struct_0(C),u1_struct_0(B),F,E)
=> ( r1_xreal_0(k3_finseq_1(F),np__0)
| D = E ) ) ) ) ) ) ) ) ) ).
fof(t27_matrlin,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( ~ v1_xboole_0(E)
=> ! [F] :
( m1_matrix_1(F,E,A,B)
=> ! [G] :
( m1_matrix_1(G,E,C,B)
=> ( r2_hidden(D,k1_relat_1(F))
=> k7_matrix_1(E,k10_matrlin(E,A,C,B,F,G),D) = k7_matrix_1(E,F,D) ) ) ) ) ) ) ) ) ).
fof(t28_matrlin,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( m1_matrix_1(E,D,A,B)
=> ! [F] :
( m1_matrix_1(F,D,C,B)
=> ( k1_matrix_1(E) = k1_matrix_1(F)
=> k1_matrix_1(k10_matrlin(D,A,C,B,E,F)) = k1_matrix_1(E) ) ) ) ) ) ) ) ).
fof(t29_matrlin,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( ~ v1_xboole_0(F)
=> ! [G] :
( m1_matrix_1(G,F,A,B)
=> ! [H] :
( m1_matrix_1(H,F,C,B)
=> ( ( r2_hidden(D,k1_relat_1(H))
& E = k1_nat_1(k3_finseq_1(G),D) )
=> k7_matrix_1(F,k10_matrlin(F,A,C,B,G,H),E) = k7_matrix_1(F,H,D) ) ) ) ) ) ) ) ) ) ).
fof(t30_matrlin,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( m1_matrix_1(E,D,A,B)
=> ! [F] :
( m1_matrix_1(F,D,C,B)
=> ( k1_matrix_1(E) = k1_matrix_1(F)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( r2_hidden(G,k2_finseq_1(k1_matrix_1(E)))
=> k8_matrix_1(D,k10_matrlin(D,A,C,B,E,F),G) = k8_finseq_1(D,k8_matrix_1(D,E,G),k8_matrix_1(D,F,G)) ) ) ) ) ) ) ) ) ) ).
fof(t31_matrlin,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v4_group_1(D)
& v7_group_1(D)
& v7_vectsp_1(D)
& v8_vectsp_1(D)
& v9_vectsp_1(D)
& ~ v10_vectsp_1(D)
& l3_vectsp_1(D) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v3_rlvect_1(E)
& v4_rlvect_1(E)
& v5_rlvect_1(E)
& v6_rlvect_1(E)
& v12_vectsp_1(E,D)
& l4_vectsp_1(E,D) )
=> ! [F] :
( m1_matrix_1(F,u1_struct_0(E),A,B)
=> ! [G] :
( m1_matrix_1(G,u1_struct_0(E),C,B)
=> k8_matrlin(E,k10_matrlin(u1_struct_0(E),A,C,B,F,G)) = k8_finseq_1(u1_struct_0(E),k8_matrlin(E,F),k8_matrlin(E,G)) ) ) ) ) ) ) ) ).
fof(t32_matrlin,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ~ v1_xboole_0(D)
=> ! [E] :
( m1_matrix_1(E,D,A,B)
=> ! [F] :
( m1_matrix_1(F,D,C,B)
=> ( k1_matrix_1(E) = k1_matrix_1(F)
=> k4_matrix_1(D,k10_matrlin(D,A,C,B,E,F)) = k9_matrlin(D,k4_matrix_1(D,E),k4_matrix_1(D,F)) ) ) ) ) ) ) ) ).
fof(t33_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) )
=> ! [D] :
( ( v1_matrix_1(D)
& m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) )
=> k1_finseqop(u1_struct_0(B),u1_struct_0(B),u1_struct_0(B),u1_rlvect_1(B),k8_matrlin(B,C),k8_matrlin(B,D)) = k8_matrlin(B,k9_matrlin(u1_struct_0(B),C,D)) ) ) ) ) ).
fof(t34_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m2_finseq_1(C,u1_struct_0(B))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(B))
=> ( k3_finseq_1(C) = k3_finseq_1(D)
=> k9_rlvect_1(B,k11_matrlin(u1_struct_0(B),u1_rlvect_1(B),C,D)) = k4_rlvect_1(B,k9_rlvect_1(B,C),k9_rlvect_1(B,D)) ) ) ) ) ) ).
fof(t35_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) )
=> ! [D] :
( ( v1_matrix_1(D)
& m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) )
=> ( k3_finseq_1(C) = k3_finseq_1(D)
=> k4_rlvect_1(B,k9_rlvect_1(B,k8_matrlin(B,C)),k9_rlvect_1(B,k8_matrlin(B,D))) = k9_rlvect_1(B,k8_matrlin(B,k9_matrlin(u1_struct_0(B),C,D))) ) ) ) ) ) ).
fof(t36_matrlin,axiom,
$true ).
fof(t37_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( v1_matrix_1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) )
=> k9_rlvect_1(B,k8_matrlin(B,C)) = k9_rlvect_1(B,k8_matrlin(B,k4_matrix_1(u1_struct_0(B),C))) ) ) ) ).
fof(t38_matrlin,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v4_group_1(C)
& v7_group_1(C)
& v7_vectsp_1(C)
& v8_vectsp_1(C)
& v9_vectsp_1(C)
& ~ v10_vectsp_1(C)
& l3_vectsp_1(C) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v12_vectsp_1(D,C)
& v2_matrlin(D,C)
& l4_vectsp_1(D,C) )
=> ! [E] :
( m1_matrix_1(E,u1_struct_0(C),A,B)
=> ~ ( ~ r1_xreal_0(A,np__0)
& ~ r1_xreal_0(B,np__0)
& ? [F] :
( m2_finseq_1(F,u1_struct_0(C))
& ? [G] :
( m2_finseq_1(G,u1_struct_0(C))
& k3_finseq_1(F) = A
& k3_finseq_1(G) = B
& ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ( r2_hidden(H,k1_relat_1(G))
=> k4_finseq_4(k5_numbers,u1_struct_0(C),G,H) = k9_rlvect_1(C,k11_fvsum_1(C,F,k8_matrix_1(u1_struct_0(C),E,H))) ) )
& ? [H] :
( m2_finseq_1(H,u1_struct_0(D))
& ? [I] :
( m2_finseq_1(I,u1_struct_0(D))
& k3_finseq_1(H) = B
& k3_finseq_1(I) = A
& ! [J] :
( m2_subset_1(J,k1_numbers,k5_numbers)
=> ( r2_hidden(J,k1_relat_1(I))
=> k4_finseq_4(k5_numbers,u1_struct_0(D),I,J) = k9_rlvect_1(D,k7_matrlin(C,D,k7_matrix_1(u1_struct_0(C),E,J),H)) ) )
& k9_rlvect_1(D,k7_matrlin(C,D,F,I)) != k9_rlvect_1(D,k7_matrlin(C,D,G,H)) ) ) ) ) ) ) ) ) ) ) ).
fof(d9_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_matrlin(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m2_finseq_1(E,u1_struct_0(A))
=> ( E = k12_matrlin(A,B,C,D)
<=> ( k3_finseq_1(E) = k3_finseq_1(C)
& ? [F] :
( m1_vectsp_6(F,A,B)
& D = k4_vectsp_6(A,B,F)
& r1_tarski(k1_vectsp_6(A,B,F),k2_relat_1(C))
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,G)
& r1_xreal_0(G,k3_finseq_1(E)) )
=> k4_finseq_4(k5_numbers,u1_struct_0(A),E,G) = k8_funct_2(u1_struct_0(B),u1_struct_0(A),F,k4_finseq_4(k5_numbers,u1_struct_0(B),C,G)) ) ) ) ) ) ) ) ) ) ) ).
fof(t39_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_matrlin(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ( k12_matrlin(A,B,C,D) = k12_matrlin(A,B,C,E)
=> D = E ) ) ) ) ) ) ).
fof(t40_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_matrlin(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> D = k9_rlvect_1(B,k7_matrlin(A,B,k12_matrlin(A,B,C,D),C)) ) ) ) ) ).
fof(t41_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_matrlin(C,A,B)
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(A))
=> ( k3_finseq_1(D) = k3_finseq_1(C)
=> D = k12_matrlin(A,B,C,k9_rlvect_1(B,k7_matrlin(A,B,D,C))) ) ) ) ) ) ).
fof(t42_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& v2_matrlin(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ! [E] :
( m1_matrlin(E,A,B)
=> ! [F] :
( m1_matrlin(F,A,C)
=> ! [G] :
( m2_finseq_1(G,u1_struct_0(A))
=> ! [H] :
( m2_finseq_1(H,u1_struct_0(A))
=> ( k3_finseq_1(G) = k3_finseq_1(E)
=> ! [I] :
( m2_subset_1(I,k1_numbers,k5_numbers)
=> ( ( r2_hidden(I,k1_relat_1(F))
& k3_finseq_1(H) = k3_finseq_1(E)
& ! [J] :
( m2_subset_1(J,k1_numbers,k5_numbers)
=> ( r2_hidden(J,k1_relat_1(E))
=> k1_funct_1(H,J) = k4_finseq_4(k5_numbers,u1_struct_0(A),k12_matrlin(A,C,F,k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,k4_finseq_4(k5_numbers,u1_struct_0(B),E,J))),I) ) ) )
=> ( r1_xreal_0(k3_finseq_1(E),np__0)
| k4_finseq_4(k5_numbers,u1_struct_0(A),k12_matrlin(A,C,F,k9_rlvect_1(C,k7_matrlin(A,C,G,k5_finseqop(u1_struct_0(B),u1_struct_0(C),E,D)))),I) = k9_rlvect_1(A,k11_fvsum_1(A,G,H)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d10_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& v2_matrlin(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ! [E] :
( m2_finseq_1(E,u1_struct_0(B))
=> ! [F] :
( m1_matrlin(F,A,C)
=> ! [G] :
( ( v1_matrix_1(G)
& m2_finseq_1(G,k3_finseq_2(u1_struct_0(A))) )
=> ( G = k13_matrlin(A,B,C,D,E,F)
<=> ( k3_finseq_1(G) = k3_finseq_1(E)
& ! [H] :
( m2_subset_1(H,k1_numbers,k5_numbers)
=> ( r2_hidden(H,k1_relat_1(E))
=> k1_matrlin(u1_struct_0(A),k5_numbers,k3_finseq_2(u1_struct_0(A)),G,H) = k12_matrlin(A,C,F,k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,k4_finseq_4(k5_numbers,u1_struct_0(B),E,H))) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t43_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& v2_matrlin(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ! [E] :
( m1_matrlin(E,A,B)
=> ! [F] :
( m1_matrlin(F,A,C)
=> ( k3_finseq_1(E) = np__0
=> k13_matrlin(A,B,C,D,E,F) = k1_xboole_0 ) ) ) ) ) ) ) ).
fof(t44_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& v2_matrlin(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ! [E] :
( m1_matrlin(E,A,B)
=> ! [F] :
( m1_matrlin(F,A,C)
=> ( ~ r1_xreal_0(k3_finseq_1(E),np__0)
=> k1_matrix_1(k13_matrlin(A,B,C,D,E,F)) = k3_finseq_1(F) ) ) ) ) ) ) ) ).
fof(t45_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& v2_matrlin(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ! [F] :
( m1_matrlin(F,A,B)
=> ! [G] :
( m1_matrlin(G,A,C)
=> ( ( v1_mod_2(D,A,B,C)
& v1_mod_2(E,A,B,C)
& k13_matrlin(A,B,C,D,F,G) = k13_matrlin(A,B,C,E,F,G) )
=> ( r1_xreal_0(k3_finseq_1(F),np__0)
| D = E ) ) ) ) ) ) ) ) ) ).
fof(t46_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& v2_matrlin(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v12_vectsp_1(D,A)
& v2_matrlin(D,A)
& l4_vectsp_1(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
=> ! [G] :
( m1_matrlin(G,A,B)
=> ! [H] :
( m1_matrlin(H,A,C)
=> ! [I] :
( m1_matrlin(I,A,D)
=> ( ( v1_mod_2(E,A,B,C)
& v1_mod_2(F,A,C,D) )
=> ( r1_xreal_0(k3_finseq_1(G),np__0)
| r1_xreal_0(k3_finseq_1(H),np__0)
| r1_xreal_0(k3_finseq_1(I),np__0)
| k13_matrlin(A,B,D,k7_funct_2(u1_struct_0(B),u1_struct_0(C),u1_struct_0(D),E,F),G,I) = k4_matrix_3(A,k13_matrlin(A,B,C,E,G,H),k13_matrlin(A,C,D,F,H,I)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t47_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& v2_matrlin(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ! [F] :
( m1_matrlin(F,A,B)
=> ! [G] :
( m1_matrlin(G,A,C)
=> k13_matrlin(A,B,C,k5_matrlin(A,B,C,D,E),F,G) = k3_matrix_3(A,k13_matrlin(A,B,C,D,F,G),k13_matrlin(A,B,C,E,F,G)) ) ) ) ) ) ) ) ).
fof(t48_matrlin,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& v2_matrlin(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v12_vectsp_1(D,A)
& v2_matrlin(D,A)
& l4_vectsp_1(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(D))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(D)) )
=> ! [F] :
( m1_matrlin(F,A,C)
=> ! [G] :
( m1_matrlin(G,A,D)
=> ( B != k1_rlvect_1(A)
=> k13_matrlin(A,C,D,k6_matrlin(A,C,D,E,B),F,G) = k6_matrix_3(A,k13_matrlin(A,C,D,E,F,G),B) ) ) ) ) ) ) ) ) ).
fof(dt_m1_matrlin,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_matrlin(C,A,B)
=> m2_finseq_1(C,u1_struct_0(B)) ) ) ).
fof(existence_m1_matrlin,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A) )
=> ? [C] : m1_matrlin(C,A,B) ) ).
fof(dt_k1_matrlin,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(C)
& m1_finseq_2(C,A)
& v1_funct_1(D)
& m1_relset_1(D,B,C) )
=> m2_finseq_2(k1_matrlin(A,B,C,D,E),A,C) ) ).
fof(redefinition_k1_matrlin,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(C)
& m1_finseq_2(C,A)
& v1_funct_1(D)
& m1_relset_1(D,B,C) )
=> k1_matrlin(A,B,C,D,E) = k4_finseq_4(B,C,D,E) ) ).
fof(dt_k2_matrlin,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k5_numbers)
& v1_matrix_1(C)
& m1_finseq_1(C,k3_finseq_2(A)) )
=> ( v1_matrix_1(k2_matrlin(A,B,C))
& m2_finseq_1(k2_matrlin(A,B,C),k3_finseq_2(A)) ) ) ).
fof(redefinition_k2_matrlin,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k5_numbers)
& v1_matrix_1(C)
& m1_finseq_1(C,k3_finseq_2(A)) )
=> k2_matrlin(A,B,C) = k2_finseq_3(B,C) ) ).
fof(dt_k3_matrlin,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,A) )
=> m1_matrix_1(k3_matrlin(A,B),A,np__1,k3_finseq_1(B)) ) ).
fof(redefinition_k3_matrlin,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_finseq_1(B,A) )
=> k3_matrlin(A,B) = k5_finseq_1(B) ) ).
fof(dt_k4_matrlin,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_matrlin(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_matrlin(B) )
=> ( v1_relat_1(k4_matrlin(A,B))
& v1_funct_1(k4_matrlin(A,B))
& v1_matrlin(k4_matrlin(A,B)) ) ) ).
fof(dt_k5_matrlin,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(C))
& v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& m1_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( v1_funct_1(k5_matrlin(A,B,C,D,E))
& v1_funct_2(k5_matrlin(A,B,C,D,E),u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(k5_matrlin(A,B,C,D,E),u1_struct_0(B),u1_struct_0(C)) ) ) ).
fof(dt_k6_matrlin,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& v2_matrlin(C,A)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(C))
& m1_subset_1(E,u1_struct_0(A)) )
=> ( v1_funct_1(k6_matrlin(A,B,C,D,E))
& v1_funct_2(k6_matrlin(A,B,C,D,E),u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(k6_matrlin(A,B,C,D,E),u1_struct_0(B),u1_struct_0(C)) ) ) ).
fof(dt_k7_matrlin,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A)
& m1_finseq_1(C,u1_struct_0(A))
& m1_finseq_1(D,u1_struct_0(B)) )
=> m2_finseq_1(k7_matrlin(A,B,C,D),u1_struct_0(B)) ) ).
fof(dt_k8_matrlin,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A)
& m1_finseq_1(B,k3_finseq_2(u1_struct_0(A))) )
=> m2_finseq_1(k8_matrlin(A,B),u1_struct_0(A)) ) ).
fof(dt_k9_matrlin,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_matrix_1(B)
& m1_finseq_1(B,k3_finseq_2(A))
& v1_matrix_1(C)
& m1_finseq_1(C,k3_finseq_2(A)) )
=> ( v1_matrix_1(k9_matrlin(A,B,C))
& m2_finseq_1(k9_matrlin(A,B,C),k3_finseq_2(A)) ) ) ).
fof(redefinition_k9_matrlin,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& v1_matrix_1(B)
& m1_finseq_1(B,k3_finseq_2(A))
& v1_matrix_1(C)
& m1_finseq_1(C,k3_finseq_2(A)) )
=> k9_matrlin(A,B,C) = k4_matrlin(B,C) ) ).
fof(dt_k10_matrlin,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers)
& m1_matrix_1(E,A,B,D)
& m1_matrix_1(F,A,C,D) )
=> m1_matrix_1(k10_matrlin(A,B,C,D,E,F),A,k1_nat_1(B,C),D) ) ).
fof(redefinition_k10_matrlin,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers)
& m1_matrix_1(E,A,B,D)
& m1_matrix_1(F,A,C,D) )
=> k10_matrlin(A,B,C,D,E,F) = k7_finseq_1(E,F) ) ).
fof(dt_k11_matrlin,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& m1_finseq_1(C,A)
& m1_finseq_1(D,A) )
=> m2_finseq_1(k11_matrlin(A,B,C,D),A) ) ).
fof(redefinition_k11_matrlin,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& m1_finseq_1(C,A)
& m1_finseq_1(D,A) )
=> k11_matrlin(A,B,C,D) = k3_funcop_1(B,C,D) ) ).
fof(dt_k12_matrlin,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A)
& m1_matrlin(C,A,B)
& m1_subset_1(D,u1_struct_0(B)) )
=> m2_finseq_1(k12_matrlin(A,B,C,D),u1_struct_0(A)) ) ).
fof(dt_k13_matrlin,axiom,
! [A,B,C,D,E,F] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& v2_matrlin(B,A)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& v2_matrlin(C,A)
& l4_vectsp_1(C,A)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(C))
& m1_finseq_1(E,u1_struct_0(B))
& m1_matrlin(F,A,C) )
=> ( v1_matrix_1(k13_matrlin(A,B,C,D,E,F))
& m2_finseq_1(k13_matrlin(A,B,C,D,E,F),k3_finseq_2(u1_struct_0(A))) ) ) ).
%------------------------------------------------------------------------------