SET007 Axioms: SET007+670.ax
%------------------------------------------------------------------------------
% File : SET007+670 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Gauges and Cages. Part I
% 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 : jordan1a [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 139 ( 3 unt; 0 def)
% Number of atoms : 1171 ( 81 equ)
% Maximal formula atoms : 20 ( 8 avg)
% Number of connectives : 1241 ( 209 ~; 29 |; 554 &)
% ( 19 <=>; 430 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 10 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 47 ( 45 usr; 1 prp; 0-3 aty)
% Number of functors : 70 ( 70 usr; 10 con; 0-4 aty)
% Number of variables : 390 ( 372 !; 18 ?)
% 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_jordan1a,axiom,
? [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& ~ v1_xboole_0(A)
& v4_pre_topc(A,k15_euclid(np__2))
& v2_connsp_1(A,k15_euclid(np__2))
& v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& v1_jordan2c(A,np__2)
& v1_topreal2(A) ) ).
fof(rc2_jordan1a,axiom,
? [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& ~ v1_xboole_0(A)
& v4_pre_topc(A,k15_euclid(np__2))
& v6_compts_1(A,k15_euclid(np__2))
& v1_sppol_1(A)
& v1_jordan2c(A,np__2) ) ).
fof(rc3_jordan1a,axiom,
? [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& ~ v1_xboole_0(A)
& v4_pre_topc(A,k15_euclid(np__2))
& v6_compts_1(A,k15_euclid(np__2))
& v2_sppol_1(A)
& v1_jordan2c(A,np__2) ) ).
fof(fc1_jordan1a,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ~ v1_xboole_0(k9_jordan6(A))
& v4_pre_topc(k9_jordan6(A),k15_euclid(np__2))
& v6_compts_1(k9_jordan6(A),k15_euclid(np__2))
& v1_jordan2c(k9_jordan6(A),np__2) ) ) ).
fof(fc2_jordan1a,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ~ v1_xboole_0(k8_jordan6(A))
& v4_pre_topc(k8_jordan6(A),k15_euclid(np__2))
& v6_compts_1(k8_jordan6(A),k15_euclid(np__2))
& v1_jordan2c(k8_jordan6(A),np__2) ) ) ).
fof(fc3_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( ~ v1_xboole_0(k2_jordan1a(A))
& v2_connsp_1(k2_jordan1a(A),k15_euclid(np__2))
& v1_jordan1(k2_jordan1a(A),np__2) ) ) ).
fof(fc4_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( ~ v1_xboole_0(k3_jordan1a(A))
& v2_connsp_1(k3_jordan1a(A),k15_euclid(np__2))
& v1_jordan1(k3_jordan1a(A),np__2) ) ) ).
fof(fc5_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( ~ v1_xboole_0(k4_jordan1a(A))
& v2_connsp_1(k4_jordan1a(A),k15_euclid(np__2))
& v1_jordan1(k4_jordan1a(A),np__2) ) ) ).
fof(fc6_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( ~ v1_xboole_0(k5_jordan1a(A))
& v2_connsp_1(k5_jordan1a(A),k15_euclid(np__2))
& v1_jordan1(k5_jordan1a(A),np__2) ) ) ).
fof(t1_jordan1a,axiom,
$true ).
fof(t2_jordan1a,axiom,
$true ).
fof(t3_jordan1a,axiom,
$true ).
fof(t4_jordan1a,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v4_ordinal2(B)
=> ( k4_nat_1(A,B) = np__0
=> ( r1_xreal_0(B,np__0)
| k3_nat_1(A,B) = k7_xcmplx_0(A,B) ) ) ) ) ).
fof(t5_jordan1a,axiom,
! [A] :
( v4_ordinal2(A)
=> ! [B] :
( v4_ordinal2(B)
=> ( ~ r1_xreal_0(B,np__0)
=> k3_nat_1(k2_newton(A,B),A) = k7_xcmplx_0(k2_newton(A,B),A) ) ) ) ).
fof(t6_jordan1a,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v4_ordinal2(B)
=> ~ ( ~ r1_xreal_0(B,np__0)
& ~ r1_xreal_0(A,np__1)
& r1_xreal_0(k2_newton(A,B),np__1) ) ) ) ).
fof(t7_jordan1a,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v4_ordinal2(B)
=> ! [C] :
( v4_ordinal2(C)
=> ~ ( ~ r1_xreal_0(A,np__1)
& ~ r1_xreal_0(B,C)
& r1_xreal_0(k2_newton(A,B),k2_newton(A,C)) ) ) ) ) ).
fof(t8_jordan1a,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v2_connsp_1(B,A)
& r4_connsp_1(A,C,D)
& r1_tarski(B,C) )
=> ( r1_xboole_0(B,D)
| r1_tarski(B,D) ) ) ) ) ) ) ).
fof(d1_jordan1a,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> k1_jordan1a(A) = k1_nat_1(k3_nat_1(k3_finseq_1(A),np__2),np__1) ) ).
fof(t9_jordan1a,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( ~ v1_abian(k3_finseq_1(A))
=> k3_finseq_1(A) = k5_real_1(k2_nat_1(np__2,k1_jordan1a(A)),np__1) ) ) ).
fof(t10_jordan1a,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ( v1_abian(k3_finseq_1(A))
=> k3_finseq_1(A) = k5_real_1(k2_nat_1(np__2,k1_jordan1a(A)),np__2) ) ) ).
fof(t11_jordan1a,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(B,k27_pscomp_1(A))
=> k22_euclid(B) = k19_pscomp_1(A) ) ) ) ).
fof(t12_jordan1a,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(B,k28_pscomp_1(A))
=> k21_euclid(B) = k20_pscomp_1(A) ) ) ) ).
fof(t13_jordan1a,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(B,k29_pscomp_1(A))
=> k22_euclid(B) = k21_pscomp_1(A) ) ) ) ).
fof(t14_jordan1a,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(B,k26_pscomp_1(A))
=> k21_euclid(B) = k18_pscomp_1(A) ) ) ) ).
fof(t15_jordan1a,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> r1_xboole_0(k1_jordan2c(np__2,A),A) ) ).
fof(t16_jordan1a,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_tarski(k9_jordan6(A),A)
& r1_tarski(k8_jordan6(A),A) ) ) ).
fof(t17_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> r2_hidden(A,k6_jordan6(k21_euclid(A))) ) ).
fof(t18_jordan1a,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> r2_hidden(k23_euclid(A,B),k6_jordan6(A)) ) ) ).
fof(t19_jordan1a,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( r1_tarski(B,k6_jordan6(A))
=> v2_sppol_1(B) ) ) ) ).
fof(t20_jordan1a,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( k8_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k23_euclid(A,B)) = B
& k8_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,k23_euclid(A,B)) = A ) ) ) ).
fof(t21_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( v1_xreal_0(C)
=> ( ( k21_euclid(A) = k21_euclid(B)
& r2_hidden(C,k1_rcomp_1(k8_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,A),k8_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,B))) )
=> r2_hidden(k23_euclid(k21_euclid(A),C),k3_topreal1(np__2,A,B)) ) ) ) ) ).
fof(t22_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( v1_xreal_0(C)
=> ( ( k22_euclid(A) = k22_euclid(B)
& r2_hidden(C,k1_rcomp_1(k8_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,A),k8_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k16_pscomp_1,B))) )
=> r2_hidden(k23_euclid(C,k22_euclid(A)),k3_topreal1(np__2,A,B)) ) ) ) ) ).
fof(t23_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( v1_xreal_0(C)
=> ( ( r2_hidden(A,k6_jordan6(C))
& r2_hidden(B,k6_jordan6(C)) )
=> r1_tarski(k3_topreal1(np__2,A,B),k6_jordan6(C)) ) ) ) ) ).
fof(t24_jordan1a,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ~ ( ~ r1_xboole_0(A,B)
& r1_xboole_0(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,A),k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,B)) ) ) ) ).
fof(t25_jordan1a,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( r1_xboole_0(B,C)
& r1_tarski(B,k6_jordan6(A))
& r1_tarski(C,k6_jordan6(A)) )
=> r1_xboole_0(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,B),k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,C)) ) ) ) ) ).
fof(t26_jordan1a,axiom,
! [A] :
( ( v4_pre_topc(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( v1_jordan2c(A,np__2)
=> v2_rcomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,A)) ) ) ).
fof(t27_jordan1a,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( v1_jordan2c(A,np__2)
=> v3_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,A)) ) ) ).
fof(t28_jordan1a,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> v1_rcomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,A)) ) ).
fof(d2_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( B = k2_jordan1a(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(C,B)
<=> ( k21_euclid(C) = k21_euclid(A)
& r1_xreal_0(k22_euclid(A),k22_euclid(C)) ) ) ) ) ) ) ).
fof(d3_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( B = k3_jordan1a(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(C,B)
<=> ( r1_xreal_0(k21_euclid(A),k21_euclid(C))
& k22_euclid(C) = k22_euclid(A) ) ) ) ) ) ) ).
fof(d4_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( B = k4_jordan1a(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(C,B)
<=> ( k21_euclid(C) = k21_euclid(A)
& r1_xreal_0(k22_euclid(C),k22_euclid(A)) ) ) ) ) ) ) ).
fof(d5_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( B = k5_jordan1a(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(C,B)
<=> ( r1_xreal_0(k21_euclid(C),k21_euclid(A))
& k22_euclid(C) = k22_euclid(A) ) ) ) ) ) ) ).
fof(t37_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_relat_1(C)
& v1_matrix_1(C)
& v3_goboard1(C)
& v4_goboard1(C)
& v5_goboard1(C)
& v6_goboard1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(C))
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k1_matrix_1(C)) )
=> r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,B),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,k1_matrix_1(C)))) ) ) ) ) ).
fof(t38_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_relat_1(C)
& v1_matrix_1(C)
& v3_goboard1(C)
& v4_goboard1(C)
& v5_goboard1(C)
& v6_goboard1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(C))
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k1_matrix_1(C)) )
=> r2_hidden(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,A,B),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,np__1,B),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),C,k3_finseq_1(C),B))) ) ) ) ) ).
fof(t39_jordan1a,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] :
( ( ~ v3_relat_1(E)
& v1_matrix_1(E)
& v3_goboard1(E)
& v4_goboard1(E)
& v5_goboard1(E)
& v6_goboard1(E)
& m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k1_matrix_1(E))
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k1_matrix_1(E))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(E)) )
=> r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,C,A)),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,D,B))) ) ) ) ) ) ) ).
fof(t40_jordan1a,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] :
( ( ~ v3_relat_1(E)
& v1_matrix_1(E)
& v3_goboard1(E)
& v4_goboard1(E)
& v5_goboard1(E)
& v6_goboard1(E)
& m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(E))
& r1_xreal_0(np__1,B)
& r1_xreal_0(B,k3_finseq_1(E))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,D)
& r1_xreal_0(D,k1_matrix_1(E)) )
=> r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,A,C)),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),E,B,D))) ) ) ) ) ) ) ).
fof(t41_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& ~ v5_seqm_3(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(B)) )
=> r1_xreal_0(k19_pscomp_1(k5_topreal1(np__2,C)),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,A,k1_matrix_1(B)))) ) ) ) ) ).
fof(t42_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& ~ v5_seqm_3(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k1_matrix_1(B)) )
=> r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,np__1,A)),k18_pscomp_1(k5_topreal1(np__2,C))) ) ) ) ) ).
fof(t43_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& ~ v5_seqm_3(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(B)) )
=> r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,A,np__1)),k21_pscomp_1(k5_topreal1(np__2,C))) ) ) ) ) ).
fof(t44_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& ~ v5_seqm_3(C)
& v1_topreal1(C)
& v2_topreal1(C)
& v1_finseq_6(C,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(C)
& v2_goboard5(C)
& m2_finseq_1(C,u1_struct_0(k15_euclid(np__2))) )
=> ( ( r1_goboard1(u1_struct_0(k15_euclid(np__2)),C,B)
& r1_xreal_0(np__1,A)
& r1_xreal_0(A,k1_matrix_1(B)) )
=> r1_xreal_0(k20_pscomp_1(k5_topreal1(np__2,C)),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),B,k3_finseq_1(B),A))) ) ) ) ) ).
fof(t45_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_relat_1(C)
& v1_matrix_1(C)
& v3_goboard1(C)
& v4_goboard1(C)
& v5_goboard1(C)
& v6_goboard1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( r1_xreal_0(A,k3_finseq_1(C))
& r1_xreal_0(B,k1_matrix_1(C))
& v1_xboole_0(k3_goboard5(C,A,B)) ) ) ) ) ).
fof(t46_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v3_relat_1(C)
& v1_matrix_1(C)
& v3_goboard1(C)
& v4_goboard1(C)
& v5_goboard1(C)
& v6_goboard1(C)
& m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(A,k3_finseq_1(C))
& r1_xreal_0(B,k1_matrix_1(C)) )
=> v2_connsp_1(k3_goboard5(C,A,B),k15_euclid(np__2)) ) ) ) ) ).
fof(t47_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( r1_xreal_0(A,k3_finseq_1(B))
& v1_jordan2c(k3_goboard5(B,A,np__0),np__2) ) ) ) ).
fof(t48_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v3_relat_1(B)
& v1_matrix_1(B)
& v3_goboard1(B)
& v4_goboard1(B)
& v5_goboard1(B)
& v6_goboard1(B)
& m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( r1_xreal_0(A,k3_finseq_1(B))
& v1_jordan2c(k3_goboard5(B,A,k1_matrix_1(B)),np__2) ) ) ) ).
fof(t49_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k1_matrix_1(k1_jordan8(B,A)) = k1_nat_1(k2_wsierp_1(np__2,A),np__3) ) ) ).
fof(t50_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( ~ r1_xreal_0(B,A)
& r1_xreal_0(k3_finseq_1(k1_jordan8(C,B)),k3_finseq_1(k1_jordan8(C,A))) ) ) ) ) ).
fof(t51_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_xreal_0(A,B)
=> r1_xreal_0(k3_finseq_1(k1_jordan8(C,A)),k3_finseq_1(k1_jordan8(C,B))) ) ) ) ) ).
fof(t52_jordan1a,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)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_xreal_0(A,B)
=> ( r1_xreal_0(C,np__1)
| r1_xreal_0(k3_finseq_1(k1_jordan8(D,A)),C)
| ( ~ r1_xreal_0(k3_real_1(k4_real_1(k2_wsierp_1(np__2,k5_binarith(B,A)),k5_real_1(C,np__2)),np__2),np__1)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan8(D,B)),k3_real_1(k4_real_1(k2_wsierp_1(np__2,k5_binarith(B,A)),k5_real_1(C,np__2)),np__2)) ) ) ) ) ) ) ) ).
fof(t53_jordan1a,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)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_xreal_0(A,B)
=> ( r1_xreal_0(C,np__1)
| r1_xreal_0(k1_matrix_1(k1_jordan8(D,A)),C)
| ( ~ r1_xreal_0(k3_real_1(k4_real_1(k2_wsierp_1(np__2,k5_binarith(B,A)),k5_real_1(C,np__2)),np__2),np__1)
& ~ r1_xreal_0(k1_matrix_1(k1_jordan8(D,B)),k3_real_1(k4_real_1(k2_wsierp_1(np__2,k5_binarith(B,A)),k5_real_1(C,np__2)),np__2)) ) ) ) ) ) ) ) ).
fof(t54_jordan1a,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)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_xreal_0(A,B)
=> ( r1_xreal_0(C,np__1)
| r1_xreal_0(k3_finseq_1(k1_jordan8(E,A)),C)
| r1_xreal_0(D,np__1)
| r1_xreal_0(k1_matrix_1(k1_jordan8(E,A)),D)
| ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ( F = k3_real_1(k4_real_1(k2_wsierp_1(np__2,k5_binarith(B,A)),k5_real_1(C,np__2)),np__2)
& G = k3_real_1(k4_real_1(k2_wsierp_1(np__2,k5_binarith(B,A)),k5_real_1(D,np__2)),np__2) )
=> k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,A),C,D) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,B),F,G) ) ) ) ) ) ) ) ) ) ) ).
fof(t55_jordan1a,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)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_xreal_0(A,B)
=> ( r1_xreal_0(C,np__1)
| r1_xreal_0(k3_finseq_1(k1_jordan8(D,A)),k1_nat_1(C,np__1))
| ( ~ r1_xreal_0(k3_real_1(k4_real_1(k2_wsierp_1(np__2,k5_binarith(B,A)),k5_real_1(C,np__1)),np__2),np__1)
& r1_xreal_0(k3_real_1(k4_real_1(k2_wsierp_1(np__2,k5_binarith(B,A)),k5_real_1(C,np__1)),np__2),k3_finseq_1(k1_jordan8(D,B))) ) ) ) ) ) ) ) ).
fof(t56_jordan1a,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)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_xreal_0(A,B)
=> ( r1_xreal_0(C,np__1)
| r1_xreal_0(k1_matrix_1(k1_jordan8(D,A)),k1_nat_1(C,np__1))
| ( ~ r1_xreal_0(k3_real_1(k4_real_1(k2_wsierp_1(np__2,k5_binarith(B,A)),k5_real_1(C,np__1)),np__2),np__1)
& r1_xreal_0(k3_real_1(k4_real_1(k2_wsierp_1(np__2,k5_binarith(B,A)),k5_real_1(C,np__1)),np__2),k1_matrix_1(k1_jordan8(D,B))) ) ) ) ) ) ) ) ).
fof(t57_jordan1a,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)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(k1_jordan8(E,B)))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(E,D))) )
=> ( ( ~ ( ~ r1_xreal_0(B,np__0)
& ~ r1_xreal_0(D,np__0) )
& ~ ( B = np__0
& D = np__0 ) )
| k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,B),k1_jordan1a(k1_jordan8(E,B)),A)) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,D),k1_jordan1a(k1_jordan8(E,D)),C)) ) ) ) ) ) ) ) ).
fof(t58_jordan1a,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)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(k1_jordan8(E,B)))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(E,D))) )
=> ( ( ~ ( ~ r1_xreal_0(B,np__0)
& ~ r1_xreal_0(D,np__0) )
& ~ ( B = np__0
& D = np__0 ) )
| k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,B),A,k1_jordan1a(k1_jordan8(E,B)))) = k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,D),C,k1_jordan1a(k1_jordan8(E,D)))) ) ) ) ) ) ) ) ).
fof(t59_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(k1_jordan8(B,np__1))) )
=> k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,np__1),k1_jordan1a(k1_jordan8(B,np__1)),A)) = k6_real_1(k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B)),np__2) ) ) ) ).
fof(t60_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(k1_jordan8(B,np__1))) )
=> k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,np__1),A,k1_jordan1a(k1_jordan8(B,np__1)))) = k6_real_1(k3_real_1(k21_pscomp_1(B),k19_pscomp_1(B)),np__2) ) ) ) ).
fof(t61_jordan1a,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] :
( ( v6_compts_1(E,k15_euclid(np__2))
& ~ v1_sppol_1(E)
& ~ v2_sppol_1(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(k1_jordan8(E,B)))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(E,D)))
& r1_xreal_0(D,B) )
=> r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,B),A,k3_finseq_1(k1_jordan8(E,B)))),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,D),C,k3_finseq_1(k1_jordan8(E,D))))) ) ) ) ) ) ) ).
fof(t62_jordan1a,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] :
( ( v6_compts_1(E,k15_euclid(np__2))
& ~ v1_sppol_1(E)
& ~ v2_sppol_1(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(k1_jordan8(E,B)))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(E,D)))
& r1_xreal_0(D,B) )
=> r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,B),k3_finseq_1(k1_jordan8(E,B)),A)),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,D),k3_finseq_1(k1_jordan8(E,D)),C))) ) ) ) ) ) ) ).
fof(t63_jordan1a,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] :
( ( v6_compts_1(E,k15_euclid(np__2))
& ~ v1_sppol_1(E)
& ~ v2_sppol_1(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(k1_jordan8(E,B)))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(E,D)))
& r1_xreal_0(D,B) )
=> r1_xreal_0(k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,D),np__1,C)),k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,B),np__1,A))) ) ) ) ) ) ) ).
fof(t64_jordan1a,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] :
( ( v6_compts_1(E,k15_euclid(np__2))
& ~ v1_sppol_1(E)
& ~ v2_sppol_1(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(k1_jordan8(E,B)))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(E,D)))
& r1_xreal_0(D,B) )
=> r1_xreal_0(k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,D),C,np__1)),k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,B),A,np__1))) ) ) ) ) ) ) ).
fof(t65_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v6_compts_1(C,k15_euclid(np__2))
& ~ v1_sppol_1(C)
& ~ v2_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,B) )
=> r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,B),k1_jordan1a(k1_jordan8(C,B)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,B),k1_jordan1a(k1_jordan8(C,B)),k3_finseq_1(k1_jordan8(C,B)))),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,A),k1_jordan1a(k1_jordan8(C,A)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,A),k1_jordan1a(k1_jordan8(C,A)),k3_finseq_1(k1_jordan8(C,A))))) ) ) ) ) ).
fof(t66_jordan1a,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] :
( ( v6_compts_1(D,k15_euclid(np__2))
& ~ v1_sppol_1(D)
& ~ v2_sppol_1(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,B)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(D,B))) )
=> r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(D,B),k1_jordan1a(k1_jordan8(D,B)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(D,B),k1_jordan1a(k1_jordan8(D,B)),C)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(D,A),k1_jordan1a(k1_jordan8(D,A)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(D,B),k1_jordan1a(k1_jordan8(D,B)),C))) ) ) ) ) ) ).
fof(t67_jordan1a,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] :
( ( v6_compts_1(D,k15_euclid(np__2))
& ~ v1_sppol_1(D)
& ~ v2_sppol_1(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,B)
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(D,B))) )
=> r1_tarski(k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(D,A),k1_jordan1a(k1_jordan8(D,A)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(D,B),k1_jordan1a(k1_jordan8(D,B)),C)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(D,A),k1_jordan1a(k1_jordan8(D,A)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(D,A),k1_jordan1a(k1_jordan8(D,A)),k3_finseq_1(k1_jordan8(D,A))))) ) ) ) ) ) ).
fof(t68_jordan1a,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] :
( ( v6_compts_1(E,k15_euclid(np__2))
& ~ v1_sppol_1(E)
& ~ v2_sppol_1(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_xreal_0(A,B)
=> ( r1_xreal_0(C,np__1)
| r1_xreal_0(k3_finseq_1(k1_jordan8(E,A)),k1_nat_1(C,np__1))
| r1_xreal_0(D,np__1)
| r1_xreal_0(k1_matrix_1(k1_jordan8(E,A)),k1_nat_1(D,np__1))
| ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(k3_real_1(k4_real_1(k2_wsierp_1(np__2,k5_binarith(B,A)),k5_real_1(C,np__2)),np__2),F)
& r1_xreal_0(k3_real_1(k4_real_1(k2_wsierp_1(np__2,k5_binarith(B,A)),k5_real_1(D,np__2)),np__2),G) )
=> ( r1_xreal_0(k3_real_1(k4_real_1(k2_wsierp_1(np__2,k5_binarith(B,A)),k5_real_1(C,np__1)),np__2),F)
| r1_xreal_0(k3_real_1(k4_real_1(k2_wsierp_1(np__2,k5_binarith(B,A)),k5_real_1(D,np__1)),np__2),G)
| r1_tarski(k3_goboard5(k1_jordan8(E,B),F,G),k3_goboard5(k1_jordan8(E,A),C,D)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t69_jordan1a,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] :
( ( v6_compts_1(E,k15_euclid(np__2))
& ~ v1_sppol_1(E)
& ~ v2_sppol_1(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(np__3,C) )
=> ( r1_xreal_0(k3_finseq_1(k1_jordan8(E,A)),C)
| r1_xreal_0(D,np__1)
| r1_xreal_0(k1_matrix_1(k1_jordan8(E,A)),k1_nat_1(D,np__1))
| ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( ( F = k3_real_1(k4_real_1(k2_wsierp_1(np__2,k5_binarith(B,A)),k5_real_1(C,np__2)),np__2)
& G = k3_real_1(k4_real_1(k2_wsierp_1(np__2,k5_binarith(B,A)),k5_real_1(D,np__2)),np__2) )
=> r1_tarski(k3_goboard5(k1_jordan8(E,B),k5_binarith(F,np__1),G),k3_goboard5(k1_jordan8(E,A),k5_binarith(C,np__1),D)) ) ) ) ) ) ) ) ) ) ) ).
fof(t70_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v6_compts_1(C,k15_euclid(np__2))
& ~ v1_sppol_1(C)
& ~ v2_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_xreal_0(A,k3_finseq_1(k1_jordan8(C,B)))
=> r1_tarski(k3_goboard5(k1_jordan8(C,B),A,np__0),k2_jordan2c(np__2,C)) ) ) ) ) ).
fof(t71_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v6_compts_1(C,k15_euclid(np__2))
& ~ v1_sppol_1(C)
& ~ v2_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [D] :
( ( v6_compts_1(D,k15_euclid(np__2))
& ~ v1_sppol_1(D)
& ~ v2_sppol_1(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_xreal_0(A,k3_finseq_1(k1_jordan8(C,B)))
=> r1_tarski(k3_goboard5(k1_jordan8(C,B),A,k1_matrix_1(k1_jordan8(C,B))),k2_jordan2c(np__2,C)) ) ) ) ) ) ).
fof(t72_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,B)
& r2_subset_1(k2_jordan1a(C),k5_topreal1(np__2,k1_jordan9(B,A))) ) ) ) ) ).
fof(t73_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,B)
& r2_subset_1(k3_jordan1a(C),k5_topreal1(np__2,k1_jordan9(B,A))) ) ) ) ) ).
fof(t74_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,B)
& r2_subset_1(k4_jordan1a(C),k5_topreal1(np__2,k1_jordan9(B,A))) ) ) ) ) ).
fof(t75_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,B)
& r2_subset_1(k5_jordan1a(C),k5_topreal1(np__2,k1_jordan9(B,A))) ) ) ) ) ).
fof(t76_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k1_matrix_1(k1_jordan8(B,A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),np__1,D) ) ) ) ) ).
fof(t77_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(k1_jordan8(B,A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),D,np__1) ) ) ) ) ).
fof(t78_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ? [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
& ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(k1_jordan9(B,A)),C)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k1_matrix_1(k1_jordan8(B,A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),C) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(B,A),k3_finseq_1(k1_jordan8(B,A)),D) ) ) ) ) ).
fof(t79_jordan1a,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] :
( ( v2_connsp_1(D,k15_euclid(np__2))
& v6_compts_1(D,k15_euclid(np__2))
& ~ v1_sppol_1(D)
& ~ v2_sppol_1(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(k1_jordan9(D,B)))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(D,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(D,B),A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(D,B),C,k1_matrix_1(k1_jordan8(D,B))) )
=> r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(D,B),A),k27_pscomp_1(k5_topreal1(np__2,k1_jordan9(D,B)))) ) ) ) ) ) ).
fof(t80_jordan1a,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] :
( ( v2_connsp_1(D,k15_euclid(np__2))
& v6_compts_1(D,k15_euclid(np__2))
& ~ v1_sppol_1(D)
& ~ v2_sppol_1(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(k1_jordan9(D,B)))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(D,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(D,B),A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(D,B),np__1,C) )
=> r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(D,B),A),k26_pscomp_1(k5_topreal1(np__2,k1_jordan9(D,B)))) ) ) ) ) ) ).
fof(t81_jordan1a,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] :
( ( v2_connsp_1(D,k15_euclid(np__2))
& v6_compts_1(D,k15_euclid(np__2))
& ~ v1_sppol_1(D)
& ~ v2_sppol_1(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(k1_jordan9(D,B)))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(D,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(D,B),A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(D,B),C,np__1) )
=> r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(D,B),A),k29_pscomp_1(k5_topreal1(np__2,k1_jordan9(D,B)))) ) ) ) ) ) ).
fof(t82_jordan1a,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] :
( ( v2_connsp_1(D,k15_euclid(np__2))
& v6_compts_1(D,k15_euclid(np__2))
& ~ v1_sppol_1(D)
& ~ v2_sppol_1(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(k1_jordan9(D,B)))
& r1_xreal_0(np__1,C)
& r1_xreal_0(C,k1_matrix_1(k1_jordan8(D,B)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(D,B),A) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(D,B),k3_finseq_1(k1_jordan8(D,B)),C) )
=> r2_hidden(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(D,B),A),k28_pscomp_1(k5_topreal1(np__2,k1_jordan9(D,B)))) ) ) ) ) ) ).
fof(t83_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) = k5_real_1(k18_pscomp_1(B),k6_real_1(k5_real_1(k20_pscomp_1(B),k18_pscomp_1(B)),k2_wsierp_1(np__2,A))) ) ) ).
fof(t84_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k21_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) = k5_real_1(k21_pscomp_1(B),k6_real_1(k5_real_1(k19_pscomp_1(B),k21_pscomp_1(B)),k2_wsierp_1(np__2,A))) ) ) ).
fof(t85_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) = k3_real_1(k20_pscomp_1(B),k6_real_1(k5_real_1(k20_pscomp_1(B),k18_pscomp_1(B)),k2_wsierp_1(np__2,A))) ) ) ).
fof(t86_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v2_connsp_1(C,k15_euclid(np__2))
& v6_compts_1(C,k15_euclid(np__2))
& ~ v1_sppol_1(C)
& ~ v2_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k3_real_1(k19_pscomp_1(k5_topreal1(np__2,k1_jordan9(C,A))),k21_pscomp_1(k5_topreal1(np__2,k1_jordan9(C,A)))) = k3_real_1(k19_pscomp_1(k5_topreal1(np__2,k1_jordan9(C,B))),k21_pscomp_1(k5_topreal1(np__2,k1_jordan9(C,B)))) ) ) ) ).
fof(t87_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v2_connsp_1(C,k15_euclid(np__2))
& v6_compts_1(C,k15_euclid(np__2))
& ~ v1_sppol_1(C)
& ~ v2_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k3_real_1(k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(C,A))),k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(C,A)))) = k3_real_1(k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(C,B))),k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(C,B)))) ) ) ) ).
fof(t88_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v2_connsp_1(C,k15_euclid(np__2))
& v6_compts_1(C,k15_euclid(np__2))
& ~ v1_sppol_1(C)
& ~ v2_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( ~ r1_xreal_0(B,A)
& r1_xreal_0(k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(C,A))),k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(C,B)))) ) ) ) ) ).
fof(t89_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v2_connsp_1(C,k15_euclid(np__2))
& v6_compts_1(C,k15_euclid(np__2))
& ~ v1_sppol_1(C)
& ~ v2_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( ~ r1_xreal_0(B,A)
& r1_xreal_0(k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(C,B))),k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(C,A)))) ) ) ) ) ).
fof(t90_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v2_connsp_1(C,k15_euclid(np__2))
& v6_compts_1(C,k15_euclid(np__2))
& ~ v1_sppol_1(C)
& ~ v2_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( ~ r1_xreal_0(B,A)
& r1_xreal_0(k21_pscomp_1(k5_topreal1(np__2,k1_jordan9(C,B))),k21_pscomp_1(k5_topreal1(np__2,k1_jordan9(C,A)))) ) ) ) ) ).
fof(t91_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v2_connsp_1(C,k15_euclid(np__2))
& v6_compts_1(C,k15_euclid(np__2))
& ~ v1_sppol_1(C)
& ~ v2_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(k1_jordan8(C,B))) )
=> k19_pscomp_1(k5_topreal1(np__2,k1_jordan9(C,B))) = k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,B),A,k3_finseq_1(k1_jordan8(C,B)))) ) ) ) ) ).
fof(t92_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v2_connsp_1(C,k15_euclid(np__2))
& v6_compts_1(C,k15_euclid(np__2))
& ~ v1_sppol_1(C)
& ~ v2_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(k1_jordan8(C,B))) )
=> k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(C,B))) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,B),k3_finseq_1(k1_jordan8(C,B)),A)) ) ) ) ) ).
fof(t93_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v2_connsp_1(C,k15_euclid(np__2))
& v6_compts_1(C,k15_euclid(np__2))
& ~ v1_sppol_1(C)
& ~ v2_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(k1_jordan8(C,B))) )
=> k21_pscomp_1(k5_topreal1(np__2,k1_jordan9(C,B))) = k22_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,B),A,np__1)) ) ) ) ) ).
fof(t94_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v2_connsp_1(C,k15_euclid(np__2))
& v6_compts_1(C,k15_euclid(np__2))
& ~ v1_sppol_1(C)
& ~ v2_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(A,k3_finseq_1(k1_jordan8(C,B))) )
=> k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(C,B))) = k21_euclid(k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,B),np__1,A)) ) ) ) ) ).
fof(t95_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,B)
& r2_hidden(D,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k2_jordan1a(C),k5_topreal1(np__2,k1_jordan9(B,A))))
& r1_xreal_0(k22_euclid(D),k22_euclid(C)) ) ) ) ) ) ).
fof(t96_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,B)
& r2_hidden(D,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_jordan1a(C),k5_topreal1(np__2,k1_jordan9(B,A))))
& r1_xreal_0(k21_euclid(D),k21_euclid(C)) ) ) ) ) ) ).
fof(t97_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,B)
& r2_hidden(D,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_jordan1a(C),k5_topreal1(np__2,k1_jordan9(B,A))))
& r1_xreal_0(k22_euclid(C),k22_euclid(D)) ) ) ) ) ) ).
fof(t98_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,B)
& r2_hidden(D,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_jordan1a(C),k5_topreal1(np__2,k1_jordan9(B,A))))
& r1_xreal_0(k21_euclid(C),k21_euclid(D)) ) ) ) ) ) ).
fof(t99_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v2_connsp_1(C,k15_euclid(np__2))
& v6_compts_1(C,k15_euclid(np__2))
& ~ v1_sppol_1(C)
& ~ v2_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(D,k27_pscomp_1(C))
& r2_hidden(E,k2_jordan1a(D))
& r1_xreal_0(np__1,A)
& r2_hidden(E,k4_topreal1(np__2,k1_jordan9(C,B),A)) )
=> ( r1_xreal_0(k3_finseq_1(k1_jordan9(C,B)),A)
| v1_sppol_1(k4_topreal1(np__2,k1_jordan9(C,B),A)) ) ) ) ) ) ) ) ).
fof(t100_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v2_connsp_1(C,k15_euclid(np__2))
& v6_compts_1(C,k15_euclid(np__2))
& ~ v1_sppol_1(C)
& ~ v2_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(D,k28_pscomp_1(C))
& r2_hidden(E,k3_jordan1a(D))
& r1_xreal_0(np__1,A)
& r2_hidden(E,k4_topreal1(np__2,k1_jordan9(C,B),A)) )
=> ( r1_xreal_0(k3_finseq_1(k1_jordan9(C,B)),A)
| v2_sppol_1(k4_topreal1(np__2,k1_jordan9(C,B),A)) ) ) ) ) ) ) ) ).
fof(t101_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v2_connsp_1(C,k15_euclid(np__2))
& v6_compts_1(C,k15_euclid(np__2))
& ~ v1_sppol_1(C)
& ~ v2_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(D,k29_pscomp_1(C))
& r2_hidden(E,k4_jordan1a(D))
& r1_xreal_0(np__1,A)
& r2_hidden(E,k4_topreal1(np__2,k1_jordan9(C,B),A)) )
=> ( r1_xreal_0(k3_finseq_1(k1_jordan9(C,B)),A)
| v1_sppol_1(k4_topreal1(np__2,k1_jordan9(C,B),A)) ) ) ) ) ) ) ) ).
fof(t102_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v2_connsp_1(C,k15_euclid(np__2))
& v6_compts_1(C,k15_euclid(np__2))
& ~ v1_sppol_1(C)
& ~ v2_sppol_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(D,k26_pscomp_1(C))
& r2_hidden(E,k5_jordan1a(D))
& r1_xreal_0(np__1,A)
& r2_hidden(E,k4_topreal1(np__2,k1_jordan9(C,B),A)) )
=> ( r1_xreal_0(k3_finseq_1(k1_jordan9(C,B)),A)
| v2_sppol_1(k4_topreal1(np__2,k1_jordan9(C,B),A)) ) ) ) ) ) ) ) ).
fof(t103_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(C,k27_pscomp_1(B))
& r2_hidden(D,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k2_jordan1a(C),k5_topreal1(np__2,k1_jordan9(B,A)))) )
=> k22_euclid(D) = k19_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) ) ) ) ) ) ).
fof(t104_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(C,k28_pscomp_1(B))
& r2_hidden(D,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_jordan1a(C),k5_topreal1(np__2,k1_jordan9(B,A)))) )
=> k21_euclid(D) = k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) ) ) ) ) ) ).
fof(t105_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(C,k29_pscomp_1(B))
& r2_hidden(D,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_jordan1a(C),k5_topreal1(np__2,k1_jordan9(B,A)))) )
=> k22_euclid(D) = k21_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) ) ) ) ) ) ).
fof(t106_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(C,k26_pscomp_1(B))
& r2_hidden(D,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_jordan1a(C),k5_topreal1(np__2,k1_jordan9(B,A)))) )
=> k21_euclid(D) = k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) ) ) ) ) ) ).
fof(t107_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,k27_pscomp_1(B))
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k2_jordan1a(C),k5_topreal1(np__2,k1_jordan9(B,A))) != k1_struct_0(k15_euclid(np__2),D) ) ) ) ) ) ).
fof(t108_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,k28_pscomp_1(B))
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_jordan1a(C),k5_topreal1(np__2,k1_jordan9(B,A))) != k1_struct_0(k15_euclid(np__2),D) ) ) ) ) ) ).
fof(t109_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,k29_pscomp_1(B))
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k4_jordan1a(C),k5_topreal1(np__2,k1_jordan9(B,A))) != k1_struct_0(k15_euclid(np__2),D) ) ) ) ) ) ).
fof(t110_jordan1a,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(C,k26_pscomp_1(B))
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_jordan1a(C),k5_topreal1(np__2,k1_jordan9(B,A))) != k1_struct_0(k15_euclid(np__2),D) ) ) ) ) ) ).
fof(s1_jordan1a,axiom,
? [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(f1_s1_jordan1a))))
& ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(f1_s1_jordan1a)))
=> ( r2_hidden(B,A)
<=> p1_s1_jordan1a(B) ) ) ) ).
fof(s2_jordan1a,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(f1_s2_jordan1a))))
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(f1_s2_jordan1a))))
=> ( ( ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(f1_s2_jordan1a)))
=> ( r2_hidden(C,A)
<=> p1_s2_jordan1a(C) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(f1_s2_jordan1a)))
=> ( r2_hidden(C,B)
<=> p1_s2_jordan1a(C) ) ) )
=> A = B ) ) ) ).
fof(dt_k1_jordan1a,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> m2_subset_1(k1_jordan1a(A),k1_numbers,k5_numbers) ) ).
fof(dt_k2_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> m1_subset_1(k2_jordan1a(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k3_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> m1_subset_1(k3_jordan1a(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k4_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> m1_subset_1(k4_jordan1a(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(dt_k5_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> m1_subset_1(k5_jordan1a(A),k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) ) ).
fof(t29_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> k2_jordan1a(A) = a_1_0_jordan1a(A) ) ).
fof(t30_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> k2_jordan1a(A) = a_1_1_jordan1a(A) ) ).
fof(t31_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> k3_jordan1a(A) = a_1_2_jordan1a(A) ) ).
fof(t32_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> k3_jordan1a(A) = a_1_3_jordan1a(A) ) ).
fof(t33_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> k4_jordan1a(A) = a_1_4_jordan1a(A) ) ).
fof(t34_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> k4_jordan1a(A) = a_1_5_jordan1a(A) ) ).
fof(t35_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> k5_jordan1a(A) = a_1_6_jordan1a(A) ) ).
fof(t36_jordan1a,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> k5_jordan1a(A) = a_1_7_jordan1a(A) ) ).
fof(fraenkel_a_1_0_jordan1a,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(A,a_1_0_jordan1a(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& k21_euclid(C) = k21_euclid(B)
& r1_xreal_0(k22_euclid(B),k22_euclid(C)) ) ) ) ).
fof(fraenkel_a_1_1_jordan1a,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(A,a_1_1_jordan1a(B))
<=> ? [C] :
( m1_subset_1(C,k1_numbers)
& A = k23_euclid(k21_euclid(B),C)
& r1_xreal_0(k22_euclid(B),C) ) ) ) ).
fof(fraenkel_a_1_2_jordan1a,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(A,a_1_2_jordan1a(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(k21_euclid(B),k21_euclid(C))
& k22_euclid(C) = k22_euclid(B) ) ) ) ).
fof(fraenkel_a_1_3_jordan1a,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(A,a_1_3_jordan1a(B))
<=> ? [C] :
( m1_subset_1(C,k1_numbers)
& A = k23_euclid(C,k22_euclid(B))
& r1_xreal_0(k21_euclid(B),C) ) ) ) ).
fof(fraenkel_a_1_4_jordan1a,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(A,a_1_4_jordan1a(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& k21_euclid(C) = k21_euclid(B)
& r1_xreal_0(k22_euclid(C),k22_euclid(B)) ) ) ) ).
fof(fraenkel_a_1_5_jordan1a,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(A,a_1_5_jordan1a(B))
<=> ? [C] :
( m1_subset_1(C,k1_numbers)
& A = k23_euclid(k21_euclid(B),C)
& r1_xreal_0(C,k22_euclid(B)) ) ) ) ).
fof(fraenkel_a_1_6_jordan1a,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(A,a_1_6_jordan1a(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
& A = C
& r1_xreal_0(k21_euclid(C),k21_euclid(B))
& k22_euclid(C) = k22_euclid(B) ) ) ) ).
fof(fraenkel_a_1_7_jordan1a,axiom,
! [A,B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(A,a_1_7_jordan1a(B))
<=> ? [C] :
( m1_subset_1(C,k1_numbers)
& A = k23_euclid(C,k22_euclid(B))
& r1_xreal_0(C,k21_euclid(B)) ) ) ) ).
%------------------------------------------------------------------------------