SET007 Axioms: SET007+871.ax
%------------------------------------------------------------------------------
% File : SET007+871 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On Some Points of a Simple Closed Curve
% 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 : jordan21 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 95 ( 0 unt; 0 def)
% Number of atoms : 446 ( 43 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 437 ( 86 ~; 8 |; 158 &)
% ( 5 <=>; 180 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 24 ( 23 usr; 0 prp; 1-4 aty)
% Number of functors : 54 ( 54 usr; 6 con; 0-5 aty)
% Number of variables : 170 ( 165 !; 5 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_jordan21,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( v1_jordan21(A)
=> ~ v1_xboole_0(A) ) ) ).
fof(cc2_jordan21,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( v1_topreal2(A)
=> ( ~ 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_realset1(A)
& v1_topreal2(A)
& v1_jordan21(A) ) ) ) ).
fof(rc1_jordan21,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_realset1(A)
& v1_topreal2(A)
& v1_jordan21(A) ) ).
fof(fc1_jordan21,axiom,
! [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))
& v1_jordan2c(k9_jordan6(A),np__2)
& v6_compts_1(k9_jordan6(A),k15_euclid(np__2))
& v1_jordan21(k9_jordan6(A)) ) ) ).
fof(fc2_jordan21,axiom,
! [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))
& v1_jordan2c(k8_jordan6(A),np__2)
& v6_compts_1(k8_jordan6(A),k15_euclid(np__2))
& v1_jordan21(k8_jordan6(A)) ) ) ).
fof(t1_jordan21,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> v1_jordan2c(k1_struct_0(k15_euclid(A),B),A) ) ) ).
fof(t6_jordan21,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> v1_jordan1(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k2_jordan1a(A),k1_struct_0(k15_euclid(np__2),A)),np__2) ) ).
fof(t7_jordan21,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> v1_jordan1(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k4_jordan1a(A),k1_struct_0(k15_euclid(np__2),A)),np__2) ) ).
fof(t8_jordan21,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> v1_jordan1(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k5_jordan1a(A),k1_struct_0(k15_euclid(np__2),A)),np__2) ) ).
fof(t9_jordan21,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> v1_jordan1(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k3_jordan1a(A),k1_struct_0(k15_euclid(np__2),A)),np__2) ) ).
fof(t10_jordan21,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> r1_xboole_0(k2_jordan2c(np__2,A),A) ) ).
fof(t11_jordan21,axiom,
! [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)))
=> ! [C] :
( m1_subset_1(C,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)))
=> ( r1_topreal1(k15_euclid(np__2),B,C,A)
=> ( B = D
| C = E
| ( ~ r2_hidden(B,k5_jordan6(A,B,C,D,E))
& ~ r2_hidden(C,k5_jordan6(A,B,C,D,E)) ) ) ) ) ) ) ) ) ).
fof(d1_jordan21,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( v1_jordan21(A)
<=> ~ r1_xboole_0(A,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))) ) ) ).
fof(t12_jordan21,axiom,
! [A] :
( ( v1_jordan21(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ v1_xboole_0(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))) ) ).
fof(t13_jordan21,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( v2_rcomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)))))
& v2_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2)))))
& v1_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))) ) ) ).
fof(t14_jordan21,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r2_hidden(k4_tarski(np__1,np__1),k2_matrix_1(k1_jordan8(A,B))) ) ) ).
fof(t15_jordan21,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r2_hidden(k4_tarski(np__1,np__2),k2_matrix_1(k1_jordan8(A,B))) ) ) ).
fof(t16_jordan21,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r2_hidden(k4_tarski(np__2,np__1),k2_matrix_1(k1_jordan8(A,B))) ) ) ).
fof(t17_jordan21,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)
& r2_hidden(k4_tarski(C,D),k2_matrix_1(k1_jordan8(E,B)))
& r2_hidden(k4_tarski(C,k1_nat_1(D,np__1)),k2_matrix_1(k1_jordan8(E,B)))
& r1_xreal_0(k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,B),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,B),C,k1_nat_1(D,np__1))),k1_gobrd14(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,A),C,k1_nat_1(D,np__1)))) ) ) ) ) ) ) ).
fof(t18_jordan21,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,B)
& r1_xreal_0(k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,B),np__1,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,B),np__1,np__2)),k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,A),np__1,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,A),np__1,np__2))) ) ) ) ) ).
fof(t19_jordan21,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)
& r2_hidden(k4_tarski(C,D),k2_matrix_1(k1_jordan8(E,B)))
& r2_hidden(k4_tarski(k1_nat_1(C,np__1),D),k2_matrix_1(k1_jordan8(E,B)))
& r1_xreal_0(k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,B),C,D),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(E,B),k1_nat_1(C,np__1),D)),k1_gobrd14(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,A),k1_nat_1(C,np__1),D))) ) ) ) ) ) ) ).
fof(t20_jordan21,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,B)
& r1_xreal_0(k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,B),np__1,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,B),np__2,np__1)),k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,A),np__1,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(C,A),np__2,np__1))) ) ) ) ) ).
fof(t21_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ~ ( ~ r1_xreal_0(C,np__0)
& ~ r1_xreal_0(D,np__0)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(E,B)
& ~ r1_xreal_0(C,k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,E),np__1,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,E),np__1,np__2)))
& ~ r1_xreal_0(D,k1_gobrd14(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,E),np__1,np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,E),np__2,np__1))) ) ) ) ) ) ) ) ).
fof(t22_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r2_hidden(k7_jordan1k(A),A) ) ).
fof(t23_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r2_hidden(k6_jordan1k(A),A) ) ).
fof(t24_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k22_euclid(k6_jordan1k(A)) != k22_euclid(k7_jordan1k(A)) ) ).
fof(t25_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k6_jordan1k(A) != k7_jordan1k(A) ) ).
fof(t26_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k18_pscomp_1(A) = k18_pscomp_1(k8_jordan6(A)) ) ).
fof(t27_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k20_pscomp_1(A) = k20_pscomp_1(k8_jordan6(A)) ) ).
fof(t28_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k18_pscomp_1(A) = k18_pscomp_1(k9_jordan6(A)) ) ).
fof(t29_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k20_pscomp_1(A) = k20_pscomp_1(k9_jordan6(A)) ) ).
fof(t30_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ~ v1_xboole_0(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k8_jordan6(A),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))
& ~ v1_xboole_0(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k8_jordan6(A),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))) ) ) ).
fof(t31_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ~ v1_xboole_0(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k9_jordan6(A),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))
& ~ v1_xboole_0(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k9_jordan6(A),k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))) ) ) ).
fof(t32_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( r1_tarski(B,A)
& r2_hidden(k30_pscomp_1(A),B)
& r2_hidden(k34_pscomp_1(A),B)
& ~ r1_tarski(k8_jordan6(A),B)
& ~ r1_tarski(k9_jordan6(A),B) ) ) ) ).
fof(d2_jordan21,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k1_jordan21(A) = k23_euclid(k6_real_1(k3_real_1(k20_pscomp_1(A),k18_pscomp_1(A)),np__2),k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k20_pscomp_1(A),k18_pscomp_1(A)),np__2)))))) ) ).
fof(d3_jordan21,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k2_jordan21(A) = k23_euclid(k6_real_1(k3_real_1(k20_pscomp_1(A),k18_pscomp_1(A)),np__2),k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k20_pscomp_1(A),k18_pscomp_1(A)),np__2)))))) ) ).
fof(t33_jordan21,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k21_euclid(k1_jordan21(A)) = k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2) ) ).
fof(t34_jordan21,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k22_euclid(k1_jordan21(A)) = k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k20_pscomp_1(A),k18_pscomp_1(A)),np__2))))) ) ).
fof(t35_jordan21,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k21_euclid(k2_jordan21(A)) = k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2) ) ).
fof(t36_jordan21,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> k22_euclid(k2_jordan21(A)) = k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k20_pscomp_1(A),k18_pscomp_1(A)),np__2))))) ) ).
fof(t37_jordan21,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k1_jordan21(A) != k30_pscomp_1(A) ) ).
fof(t38_jordan21,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k1_jordan21(A) != k34_pscomp_1(A) ) ).
fof(t39_jordan21,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k2_jordan21(A) != k30_pscomp_1(A) ) ).
fof(t40_jordan21,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k2_jordan21(A) != k34_pscomp_1(A) ) ).
fof(t41_jordan21,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(A,k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B)),np__2))))
=> r1_xreal_0(k22_euclid(A),k22_euclid(k1_jordan21(B))) ) ) ) ).
fof(t42_jordan21,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r2_hidden(A,k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B)),np__2))))
=> r1_xreal_0(k22_euclid(k2_jordan21(B)),k22_euclid(A)) ) ) ) ).
fof(t43_jordan21,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& v1_jordan21(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r2_hidden(k1_jordan21(A),A) ) ).
fof(t44_jordan21,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& v1_jordan21(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r2_hidden(k2_jordan21(A),A) ) ).
fof(t45_jordan21,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> v2_sppol_1(k3_topreal1(np__2,k1_jordan21(A),k23_euclid(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2),k19_pscomp_1(A)))) ) ).
fof(t46_jordan21,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> v2_sppol_1(k3_topreal1(np__2,k2_jordan21(A),k23_euclid(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2),k21_pscomp_1(A)))) ) ).
fof(t47_jordan21,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& v1_jordan21(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k1_jordan21(A),k23_euclid(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2),k19_pscomp_1(A))),A) = k1_struct_0(k15_euclid(np__2),k1_jordan21(A)) ) ).
fof(t48_jordan21,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& v1_jordan21(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k2_jordan21(A),k23_euclid(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2),k21_pscomp_1(A))),A) = k1_struct_0(k15_euclid(np__2),k2_jordan21(A)) ) ).
fof(t49_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ r1_xreal_0(k22_euclid(k1_jordan21(A)),k22_euclid(k2_jordan21(A))) ) ).
fof(t50_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k1_jordan21(A) != k2_jordan21(A) ) ).
fof(t51_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ r1_xreal_0(k22_euclid(k1_jordan21(A)),k21_pscomp_1(A)) ) ).
fof(t52_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_xreal_0(k22_euclid(k1_jordan21(A)),k19_pscomp_1(A)) ) ).
fof(t53_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_xreal_0(k21_pscomp_1(A),k22_euclid(k2_jordan21(A))) ) ).
fof(t54_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ r1_xreal_0(k19_pscomp_1(A),k22_euclid(k2_jordan21(A))) ) ).
fof(t55_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_subset_1(k3_topreal1(np__2,k1_jordan21(A),k23_euclid(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2),k19_pscomp_1(A))),k3_topreal1(np__2,k2_jordan21(A),k23_euclid(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2),k21_pscomp_1(A)))) ) ).
fof(t56_jordan21,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_tarski(A,B)
& k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)) = k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B))
& v1_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))) )
=> ( v1_xboole_0(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))
| r1_xreal_0(k22_euclid(k1_jordan21(A)),k22_euclid(k1_jordan21(B))) ) ) ) ) ).
fof(t57_jordan21,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_tarski(A,B)
& k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)) = k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B))
& v2_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))) )
=> ( v1_xboole_0(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))
| r1_xreal_0(k22_euclid(k2_jordan21(B)),k22_euclid(k2_jordan21(A))) ) ) ) ) ).
fof(t58_jordan21,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_tarski(A,B)
& r2_hidden(k1_jordan21(B),A)
& v1_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B)),np__2)))))
& k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)) = k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B)) )
=> ( v1_xboole_0(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))
| k1_jordan21(A) = k1_jordan21(B) ) ) ) ) ).
fof(t59_jordan21,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_tarski(A,B)
& r2_hidden(k2_jordan21(B),A)
& v2_seq_4(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B)),np__2)))))
& k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)) = k3_real_1(k18_pscomp_1(B),k20_pscomp_1(B)) )
=> ( v1_xboole_0(k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k6_jordan6(k6_real_1(k3_real_1(k18_pscomp_1(A),k20_pscomp_1(A)),np__2))))
| k2_jordan21(A) = k2_jordan21(B) ) ) ) ) ).
fof(t60_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_xreal_0(k22_euclid(k1_jordan21(k8_jordan6(A))),k19_pscomp_1(A)) ) ).
fof(t61_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_xreal_0(k21_pscomp_1(A),k22_euclid(k2_jordan21(k9_jordan6(A)))) ) ).
fof(t62_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( r2_hidden(k2_jordan21(A),k9_jordan6(A))
& r2_hidden(k1_jordan21(A),k9_jordan6(A)) ) ) ).
fof(t63_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( r2_hidden(k2_jordan21(A),k8_jordan6(A))
& r2_hidden(k1_jordan21(A),k8_jordan6(A)) ) ) ).
fof(t64_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(B,np__0)
=> k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_jordan9(A,B)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),k3_finseq_1(k1_jordan8(A,B))))))) = k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_jordan9(A,B)),k6_jordan6(k6_real_1(k3_real_1(k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2))))) ) ) ) ).
fof(t65_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(B,np__0)
=> k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_jordan9(A,B)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),k3_finseq_1(k1_jordan8(A,B))))))) = k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_jordan9(A,B)),k6_jordan6(k6_real_1(k3_real_1(k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2))))) ) ) ) ).
fof(t66_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(B,np__0)
=> k1_jordan21(k5_topreal1(np__2,k1_jordan9(A,B))) = k23_euclid(k6_real_1(k3_real_1(k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2),k3_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_jordan9(A,B)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),k3_finseq_1(k1_jordan8(A,B)))))))) ) ) ) ).
fof(t67_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(B,np__0)
=> k2_jordan21(k5_topreal1(np__2,k1_jordan9(A,B))) = k23_euclid(k6_real_1(k3_real_1(k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),np__2),k4_pscomp_1(k2_funct_2(u1_struct_0(k15_euclid(np__2)),k1_numbers,k17_pscomp_1,k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_jordan9(A,B)),k3_topreal1(np__2,k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),np__1),k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),k3_finseq_1(k1_jordan8(A,B)))))))) ) ) ) ).
fof(t68_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ r1_xreal_0(k22_euclid(k1_jordan21(k5_topreal1(np__2,k1_jordan9(A,B)))),k22_euclid(k1_jordan21(A))) ) ) ).
fof(t69_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ r1_xreal_0(k22_euclid(k2_jordan21(A)),k22_euclid(k2_jordan21(k5_topreal1(np__2,k1_jordan9(A,B))))) ) ) ).
fof(t70_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r2_hidden(k1_jordan21(k8_jordan6(k5_topreal1(np__2,k1_jordan9(A,B)))),k8_jordan6(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) ).
fof(t71_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r2_hidden(k2_jordan21(k9_jordan6(k5_topreal1(np__2,k1_jordan9(A,B)))),k9_jordan6(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) ).
fof(t72_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(B,np__0)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(A,B)))
& k1_jordan21(k5_topreal1(np__2,k1_jordan9(A,B))) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),C) ) ) ) ) ) ).
fof(t73_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(B,np__0)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(k1_jordan8(A,B)))
& k2_jordan21(k5_topreal1(np__2,k1_jordan9(A,B))) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),C) ) ) ) ) ) ).
fof(t74_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(B,np__0)
=> k1_jordan21(k5_topreal1(np__2,k1_jordan9(A,B))) = k1_jordan21(k8_jordan6(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) ) ).
fof(t75_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(B,np__0)
=> k2_jordan21(k5_topreal1(np__2,k1_jordan9(A,B))) = k2_jordan21(k9_jordan6(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) ) ).
fof(t76_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(B,np__0)
& r1_xreal_0(k22_euclid(k1_jordan21(k8_jordan6(k5_topreal1(np__2,k1_jordan9(A,B))))),k22_euclid(k1_jordan21(A))) ) ) ) ).
fof(t77_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(B,np__0)
& r1_xreal_0(k22_euclid(k2_jordan21(A)),k22_euclid(k2_jordan21(k9_jordan6(k5_topreal1(np__2,k1_jordan9(A,B)))))) ) ) ) ).
fof(t78_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(B,C)
=> r1_xreal_0(k22_euclid(k1_jordan21(k5_topreal1(np__2,k1_jordan9(A,C)))),k22_euclid(k1_jordan21(k5_topreal1(np__2,k1_jordan9(A,B))))) ) ) ) ) ).
fof(t79_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(B,C)
=> r1_xreal_0(k22_euclid(k2_jordan21(k5_topreal1(np__2,k1_jordan9(A,B)))),k22_euclid(k2_jordan21(k5_topreal1(np__2,k1_jordan9(A,C))))) ) ) ) ) ).
fof(t80_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(B,C)
=> ( r1_xreal_0(B,np__0)
| r1_xreal_0(k22_euclid(k1_jordan21(k8_jordan6(k5_topreal1(np__2,k1_jordan9(A,C))))),k22_euclid(k1_jordan21(k8_jordan6(k5_topreal1(np__2,k1_jordan9(A,B)))))) ) ) ) ) ) ).
fof(t81_jordan21,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r1_xreal_0(B,C)
=> ( r1_xreal_0(B,np__0)
| r1_xreal_0(k22_euclid(k2_jordan21(k9_jordan6(k5_topreal1(np__2,k1_jordan9(A,B))))),k22_euclid(k2_jordan21(k9_jordan6(k5_topreal1(np__2,k1_jordan9(A,C)))))) ) ) ) ) ) ).
fof(dt_k1_jordan21,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k1_jordan21(A),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k2_jordan21,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> m1_subset_1(k2_jordan21(A),u1_struct_0(k15_euclid(np__2))) ) ).
fof(t2_jordan21,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( C = a_2_0_jordan21(A,B)
=> v1_jordan1(C,np__2) ) ) ) ) ).
fof(t3_jordan21,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( C = a_2_1_jordan21(A,B)
=> v1_jordan1(C,np__2) ) ) ) ) ).
fof(t4_jordan21,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( C = a_2_2_jordan21(A,B)
=> v1_jordan1(C,np__2) ) ) ) ) ).
fof(t5_jordan21,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( C = a_2_3_jordan21(A,B)
=> v1_jordan1(C,np__2) ) ) ) ) ).
fof(fraenkel_a_2_0_jordan21,axiom,
! [A,B,C] :
( ( v1_xreal_0(B)
& v1_xreal_0(C) )
=> ( r2_hidden(A,a_2_0_jordan21(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_numbers)
& A = k23_euclid(D,C)
& ~ r1_xreal_0(D,B) ) ) ) ).
fof(fraenkel_a_2_1_jordan21,axiom,
! [A,B,C] :
( ( v1_xreal_0(B)
& v1_xreal_0(C) )
=> ( r2_hidden(A,a_2_1_jordan21(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_numbers)
& A = k23_euclid(D,C)
& ~ r1_xreal_0(B,D) ) ) ) ).
fof(fraenkel_a_2_2_jordan21,axiom,
! [A,B,C] :
( ( v1_xreal_0(B)
& v1_xreal_0(C) )
=> ( r2_hidden(A,a_2_2_jordan21(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_numbers)
& A = k23_euclid(B,D)
& ~ r1_xreal_0(D,C) ) ) ) ).
fof(fraenkel_a_2_3_jordan21,axiom,
! [A,B,C] :
( ( v1_xreal_0(B)
& v1_xreal_0(C) )
=> ( r2_hidden(A,a_2_3_jordan21(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_numbers)
& A = k23_euclid(B,D)
& ~ r1_xreal_0(C,D) ) ) ) ).
%------------------------------------------------------------------------------