SET007 Axioms: SET007+920.ax
%------------------------------------------------------------------------------
% File : SET007+920 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Jordan Curve Theorem
% 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 : jordan [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 157 ( 0 unt; 0 def)
% Number of atoms : 1058 ( 93 equ)
% Maximal formula atoms : 23 ( 6 avg)
% Number of connectives : 1013 ( 112 ~; 8 |; 444 &)
% ( 8 <=>; 441 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 9 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 59 ( 58 usr; 0 prp; 1-4 aty)
% Number of functors : 99 ( 99 usr; 12 con; 0-6 aty)
% Number of variables : 411 ( 401 !; 10 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_jordan,axiom,
! [A,B,C] :
( ( v6_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( v1_xreal_0(k2_metric_1(A,B,C))
& ~ v3_xreal_0(k2_metric_1(A,B,C))
& v1_xcmplx_0(k2_metric_1(A,B,C)) ) ) ).
fof(fc2_jordan,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,u1_struct_0(k15_euclid(A)))
& m1_subset_1(C,u1_struct_0(k15_euclid(A))) )
=> ( v1_xreal_0(k1_gobrd14(A,B,C))
& ~ v3_xreal_0(k1_gobrd14(A,B,C))
& v1_xcmplx_0(k1_gobrd14(A,B,C)) ) ) ).
fof(fc3_jordan,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,u1_struct_0(k15_euclid(A)))
& m1_subset_1(C,u1_struct_0(k15_euclid(A))) )
=> ( v1_xreal_0(k5_toprns_1(A,k20_euclid(A,B,C)))
& ~ v3_xreal_0(k5_toprns_1(A,k20_euclid(A,B,C)))
& v1_xcmplx_0(k5_toprns_1(A,k20_euclid(A,B,C))) ) ) ).
fof(fc4_jordan,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ~ v1_xboole_0(k1_topreal1(np__2,k22_pscomp_1(A),k25_pscomp_1(A)))
& v4_pre_topc(k1_topreal1(np__2,k22_pscomp_1(A),k25_pscomp_1(A)),k15_euclid(np__2))
& v6_compts_1(k1_topreal1(np__2,k22_pscomp_1(A),k25_pscomp_1(A)),k15_euclid(np__2))
& v1_jordan2c(k1_topreal1(np__2,k22_pscomp_1(A),k25_pscomp_1(A)),np__2)
& v2_connsp_1(k1_topreal1(np__2,k22_pscomp_1(A),k25_pscomp_1(A)),k15_euclid(np__2))
& v2_tops_1(k1_topreal1(np__2,k22_pscomp_1(A),k25_pscomp_1(A)),k15_euclid(np__2))
& v3_tops_1(k1_topreal1(np__2,k22_pscomp_1(A),k25_pscomp_1(A)),k15_euclid(np__2))
& v1_jordan1(k1_topreal1(np__2,k22_pscomp_1(A),k25_pscomp_1(A)),np__2)
& v1_sppol_1(k1_topreal1(np__2,k22_pscomp_1(A),k25_pscomp_1(A))) ) ) ).
fof(fc5_jordan,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ~ v1_xboole_0(k1_topreal1(np__2,k23_pscomp_1(A),k22_pscomp_1(A)))
& v4_pre_topc(k1_topreal1(np__2,k23_pscomp_1(A),k22_pscomp_1(A)),k15_euclid(np__2))
& v6_compts_1(k1_topreal1(np__2,k23_pscomp_1(A),k22_pscomp_1(A)),k15_euclid(np__2))
& v1_jordan2c(k1_topreal1(np__2,k23_pscomp_1(A),k22_pscomp_1(A)),np__2)
& v2_connsp_1(k1_topreal1(np__2,k23_pscomp_1(A),k22_pscomp_1(A)),k15_euclid(np__2))
& v2_tops_1(k1_topreal1(np__2,k23_pscomp_1(A),k22_pscomp_1(A)),k15_euclid(np__2))
& v3_tops_1(k1_topreal1(np__2,k23_pscomp_1(A),k22_pscomp_1(A)),k15_euclid(np__2))
& v1_jordan1(k1_topreal1(np__2,k23_pscomp_1(A),k22_pscomp_1(A)),np__2)
& v2_sppol_1(k1_topreal1(np__2,k23_pscomp_1(A),k22_pscomp_1(A))) ) ) ).
fof(fc6_jordan,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ~ v1_xboole_0(k1_topreal1(np__2,k24_pscomp_1(A),k25_pscomp_1(A)))
& v4_pre_topc(k1_topreal1(np__2,k24_pscomp_1(A),k25_pscomp_1(A)),k15_euclid(np__2))
& v6_compts_1(k1_topreal1(np__2,k24_pscomp_1(A),k25_pscomp_1(A)),k15_euclid(np__2))
& v1_jordan2c(k1_topreal1(np__2,k24_pscomp_1(A),k25_pscomp_1(A)),np__2)
& v2_connsp_1(k1_topreal1(np__2,k24_pscomp_1(A),k25_pscomp_1(A)),k15_euclid(np__2))
& v2_tops_1(k1_topreal1(np__2,k24_pscomp_1(A),k25_pscomp_1(A)),k15_euclid(np__2))
& v3_tops_1(k1_topreal1(np__2,k24_pscomp_1(A),k25_pscomp_1(A)),k15_euclid(np__2))
& v1_jordan1(k1_topreal1(np__2,k24_pscomp_1(A),k25_pscomp_1(A)),np__2)
& v2_sppol_1(k1_topreal1(np__2,k24_pscomp_1(A),k25_pscomp_1(A))) ) ) ).
fof(fc7_jordan,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ~ v1_xboole_0(k1_topreal1(np__2,k25_pscomp_1(A),k22_pscomp_1(A)))
& v4_pre_topc(k1_topreal1(np__2,k25_pscomp_1(A),k22_pscomp_1(A)),k15_euclid(np__2))
& v6_compts_1(k1_topreal1(np__2,k25_pscomp_1(A),k22_pscomp_1(A)),k15_euclid(np__2))
& v1_jordan2c(k1_topreal1(np__2,k25_pscomp_1(A),k22_pscomp_1(A)),np__2)
& v2_connsp_1(k1_topreal1(np__2,k25_pscomp_1(A),k22_pscomp_1(A)),k15_euclid(np__2))
& v2_tops_1(k1_topreal1(np__2,k25_pscomp_1(A),k22_pscomp_1(A)),k15_euclid(np__2))
& v3_tops_1(k1_topreal1(np__2,k25_pscomp_1(A),k22_pscomp_1(A)),k15_euclid(np__2))
& v1_jordan1(k1_topreal1(np__2,k25_pscomp_1(A),k22_pscomp_1(A)),np__2)
& v1_sppol_1(k1_topreal1(np__2,k25_pscomp_1(A),k22_pscomp_1(A))) ) ) ).
fof(fc8_jordan,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ~ v1_xboole_0(k1_topreal1(np__2,k22_pscomp_1(A),k23_pscomp_1(A)))
& v4_pre_topc(k1_topreal1(np__2,k22_pscomp_1(A),k23_pscomp_1(A)),k15_euclid(np__2))
& v6_compts_1(k1_topreal1(np__2,k22_pscomp_1(A),k23_pscomp_1(A)),k15_euclid(np__2))
& v1_jordan2c(k1_topreal1(np__2,k22_pscomp_1(A),k23_pscomp_1(A)),np__2)
& v2_connsp_1(k1_topreal1(np__2,k22_pscomp_1(A),k23_pscomp_1(A)),k15_euclid(np__2))
& v2_tops_1(k1_topreal1(np__2,k22_pscomp_1(A),k23_pscomp_1(A)),k15_euclid(np__2))
& v3_tops_1(k1_topreal1(np__2,k22_pscomp_1(A),k23_pscomp_1(A)),k15_euclid(np__2))
& v1_jordan1(k1_topreal1(np__2,k22_pscomp_1(A),k23_pscomp_1(A)),np__2)
& v2_sppol_1(k1_topreal1(np__2,k22_pscomp_1(A),k23_pscomp_1(A))) ) ) ).
fof(fc9_jordan,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ~ v1_xboole_0(k1_topreal1(np__2,k25_pscomp_1(A),k24_pscomp_1(A)))
& v4_pre_topc(k1_topreal1(np__2,k25_pscomp_1(A),k24_pscomp_1(A)),k15_euclid(np__2))
& v6_compts_1(k1_topreal1(np__2,k25_pscomp_1(A),k24_pscomp_1(A)),k15_euclid(np__2))
& v1_jordan2c(k1_topreal1(np__2,k25_pscomp_1(A),k24_pscomp_1(A)),np__2)
& v2_connsp_1(k1_topreal1(np__2,k25_pscomp_1(A),k24_pscomp_1(A)),k15_euclid(np__2))
& v2_tops_1(k1_topreal1(np__2,k25_pscomp_1(A),k24_pscomp_1(A)),k15_euclid(np__2))
& v3_tops_1(k1_topreal1(np__2,k25_pscomp_1(A),k24_pscomp_1(A)),k15_euclid(np__2))
& v1_jordan1(k1_topreal1(np__2,k25_pscomp_1(A),k24_pscomp_1(A)),np__2)
& v2_sppol_1(k1_topreal1(np__2,k25_pscomp_1(A),k24_pscomp_1(A))) ) ) ).
fof(cc1_jordan,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& v2_sppol_1(A) )
=> ( ~ v1_xboole_0(A)
& v1_jordan21(A) ) ) ) ).
fof(cc2_jordan,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( v1_xboole_0(B)
=> v1_jordan2c(B,A) ) ) ) ).
fof(cc3_jordan,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( ~ v1_jordan2c(B,A)
=> ~ v1_xboole_0(B) ) ) ) ).
fof(rc1_jordan,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k5_numbers) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
& ~ v1_xboole_0(B)
& v3_pre_topc(B,k15_euclid(A))
& v4_pre_topc(B,k15_euclid(A))
& ~ v1_jordan2c(B,A)
& v1_jordan1(B,A) ) ) ).
fof(fc10_jordan,axiom,
! [A,B,C,D] :
( ( v1_xreal_0(A)
& v2_xreal_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,u1_struct_0(k15_euclid(B)))
& m1_subset_1(D,u1_struct_0(k15_euclid(B))) )
=> ~ v1_xboole_0(k4_xboole_0(k2_topreal9(B,C,A),k1_struct_0(k15_euclid(B),D))) ) ).
fof(cc4_jordan,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k5_numbers) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( v1_jordan2c(B,A)
=> v1_tex_2(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ) ) ).
fof(rc2_jordan,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
& ~ v1_xboole_0(B)
& v4_pre_topc(B,k15_euclid(A))
& v1_jordan2c(B,A)
& v1_jordan1(B,A) ) ) ).
fof(rc3_jordan,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
& ~ v1_xboole_0(B)
& v3_pre_topc(B,k15_euclid(A))
& v1_jordan2c(B,A)
& v1_jordan1(B,A) ) ) ).
fof(fc11_jordan,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& v1_jordan2c(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
=> ( v4_pre_topc(k6_pre_topc(k15_euclid(A),B),k15_euclid(A))
& v1_jordan2c(k6_pre_topc(k15_euclid(A),B),A) ) ) ).
fof(fc12_jordan,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& v1_jordan2c(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
=> ( v4_pre_topc(k2_tops_1(k15_euclid(A),B),k15_euclid(A))
& v1_jordan2c(k2_tops_1(k15_euclid(A),B),A) ) ) ).
fof(cc5_jordan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v3_compts_1(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ( ~ v3_struct_0(B)
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v3_compts_1(B) ) ) ) ) ).
fof(fc13_jordan,axiom,
! [A,B] :
( ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
& v1_xreal_0(B) )
=> ( v2_pre_topc(k2_brouwer(np__2,A,B))
& v1_borsuk_1(k2_brouwer(np__2,A,B),k15_euclid(np__2))
& v1_topalg_2(k2_brouwer(np__2,A,B),np__2) ) ) ).
fof(fc14_jordan,axiom,
! [A,B] :
( ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
& v1_xreal_0(B) )
=> ( v2_pre_topc(k2_brouwer(np__2,A,B))
& v2_compts_1(k2_brouwer(np__2,A,B))
& v1_borsuk_1(k2_brouwer(np__2,A,B),k15_euclid(np__2))
& v1_topalg_2(k2_brouwer(np__2,A,B),np__2) ) ) ).
fof(fc15_jordan,axiom,
! [A,B,C,D] :
( ( v1_xreal_0(A)
& v1_xreal_0(B)
& v1_xreal_0(C)
& v1_xreal_0(D) )
=> ( v4_pre_topc(k2_jgraph_6(A,B,C,D),k15_euclid(np__2))
& v1_jordan1(k2_jgraph_6(A,B,C,D),np__2) ) ) ).
fof(fc16_jordan,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( ~ v1_xboole_0(k3_jordan(A))
& v1_relat_1(k3_jordan(A))
& v1_funct_1(k3_jordan(A))
& v1_funct_2(k3_jordan(A),u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& v1_partfun1(k3_jordan(A),u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& v1_seq_1(k3_jordan(A))
& v9_pscomp_1(k3_jordan(A),k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))) ) ) ).
fof(fc17_jordan,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( ~ v1_xboole_0(k4_jordan(A))
& v1_relat_1(k4_jordan(A))
& v1_funct_1(k4_jordan(A))
& v1_funct_2(k4_jordan(A),u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& v1_partfun1(k4_jordan(A),u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& v1_seq_1(k4_jordan(A))
& v9_pscomp_1(k4_jordan(A),k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))) ) ) ).
fof(fc18_jordan,axiom,
( ~ v1_xboole_0(k5_jordan)
& v1_relat_1(k5_jordan)
& v1_funct_1(k5_jordan)
& v1_funct_2(k5_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& v1_partfun1(k5_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& v1_seq_1(k5_jordan)
& v9_pscomp_1(k5_jordan,k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))) ) ).
fof(fc19_jordan,axiom,
( ~ v1_xboole_0(k6_jordan)
& v1_relat_1(k6_jordan)
& v1_funct_1(k6_jordan)
& v1_funct_2(k6_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& v1_partfun1(k6_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& v1_seq_1(k6_jordan)
& v9_pscomp_1(k6_jordan,k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))) ) ).
fof(fc20_jordan,axiom,
( ~ v1_xboole_0(k7_jordan)
& v1_relat_1(k7_jordan)
& v1_funct_1(k7_jordan)
& v1_funct_2(k7_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& v1_partfun1(k7_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& v1_seq_1(k7_jordan)
& v9_pscomp_1(k7_jordan,k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))) ) ).
fof(fc21_jordan,axiom,
( ~ v1_xboole_0(k8_jordan)
& v1_relat_1(k8_jordan)
& v1_funct_1(k8_jordan)
& v1_funct_2(k8_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& v1_partfun1(k8_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& v1_seq_1(k8_jordan)
& v9_pscomp_1(k8_jordan,k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))) ) ).
fof(t1_jordan,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ~ ( B != C
& k18_euclid(k6_real_1(np__1,np__2),A,k17_euclid(A,B,C)) = B ) ) ) ) ).
fof(t2_jordan,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)))
=> ~ ( ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& r1_xreal_0(k22_euclid(k18_euclid(k6_real_1(np__1,np__2),np__2,k17_euclid(np__2,A,B))),k22_euclid(A)) ) ) ) ).
fof(t3_jordan,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)))
=> ~ ( ~ r1_xreal_0(k22_euclid(B),k22_euclid(A))
& r1_xreal_0(k22_euclid(B),k22_euclid(k18_euclid(k6_real_1(np__1,np__2),np__2,k17_euclid(np__2,A,B)))) ) ) ) ).
fof(t4_jordan,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( ( v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> v2_sppol_1(k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,A)) ) ) ).
fof(t5_jordan,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ! [B] :
( ( v1_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> v1_sppol_1(k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,A)) ) ) ).
fof(t6_jordan,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] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(A,k3_topreal1(np__2,B,C))
& v2_sppol_1(k3_topreal1(np__2,B,C)) )
=> v2_sppol_1(k3_topreal1(np__2,A,C)) ) ) ) ) ).
fof(t7_jordan,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] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(A,k3_topreal1(np__2,B,C))
& v1_sppol_1(k3_topreal1(np__2,B,C)) )
=> v1_sppol_1(k3_topreal1(np__2,A,C)) ) ) ) ) ).
fof(t8_jordan,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_tarski(A,B)
=> ( ( ~ r2_hidden(k30_pscomp_1(B),A)
& ~ r2_hidden(k31_pscomp_1(B),A) )
| k18_pscomp_1(A) = k18_pscomp_1(B) ) ) ) ) ).
fof(t9_jordan,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_tarski(A,B)
=> ( ( ~ r2_hidden(k35_pscomp_1(B),A)
& ~ r2_hidden(k34_pscomp_1(B),A) )
| k20_pscomp_1(A) = k20_pscomp_1(B) ) ) ) ) ).
fof(t10_jordan,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_tarski(A,B)
=> ( ( ~ r2_hidden(k32_pscomp_1(B),A)
& ~ r2_hidden(k33_pscomp_1(B),A) )
| k19_pscomp_1(A) = k19_pscomp_1(B) ) ) ) ) ).
fof(t11_jordan,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v6_compts_1(B,k15_euclid(np__2))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_tarski(A,B)
=> ( ( ~ r2_hidden(k37_pscomp_1(B),A)
& ~ r2_hidden(k36_pscomp_1(B),A) )
| k21_pscomp_1(A) = k21_pscomp_1(B) ) ) ) ) ).
fof(t12_jordan,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(k3_jordan19(A)) ) ).
fof(t13_jordan,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(k3_jordan19(A)) ) ).
fof(t14_jordan,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(k4_jordan19(A)) ) ).
fof(t15_jordan,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(k4_jordan19(A)) ) ).
fof(t16_jordan,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r1_xreal_0(k21_euclid(B),A)
& r1_xreal_0(A,k21_euclid(C))
& r1_xboole_0(k3_topreal1(np__2,B,C),k6_jordan6(A)) ) ) ) ) ).
fof(t17_jordan,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r1_xreal_0(k22_euclid(B),A)
& r1_xreal_0(A,k22_euclid(C))
& r1_xboole_0(k3_topreal1(np__2,B,C),k7_jordan6(A)) ) ) ) ) ).
fof(t18_jordan,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_xboole_0(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k2_jordan1a(k1_jordan21(A)),k1_struct_0(k15_euclid(np__2),k1_jordan21(A))),A) ) ).
fof(t19_jordan,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_xboole_0(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k4_jordan1a(k2_jordan21(A)),k1_struct_0(k15_euclid(np__2),k2_jordan21(A))),A) ) ).
fof(t20_jordan,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_tarski(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k2_jordan1a(k1_jordan21(A)),k1_struct_0(k15_euclid(np__2),k1_jordan21(A))),k2_jordan2c(np__2,A)) ) ).
fof(t21_jordan,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_tarski(k6_subset_1(u1_struct_0(k15_euclid(np__2)),k4_jordan1a(k2_jordan21(A)),k1_struct_0(k15_euclid(np__2),k2_jordan21(A))),k2_jordan2c(np__2,A)) ) ).
fof(t22_jordan,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_jordan2c(np__2,B,A)
=> r1_xboole_0(k2_jordan2c(np__2,B),A) ) ) ) ).
fof(t23_jordan,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))))
=> ( r2_jordan2c(np__2,B,A)
=> r1_xboole_0(k1_jordan2c(np__2,B),A) ) ) ) ).
fof(t24_jordan,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_xreal_0(B)
& v2_xreal_0(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> r2_hidden(C,k1_topreal9(A,C,B)) ) ) ) ).
fof(t25_jordan,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_xreal_0(B)
& ~ v3_xreal_0(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> m1_subset_1(C,u1_struct_0(k2_brouwer(A,C,B))) ) ) ) ).
fof(t26_jordan,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(C)))
=> ( r1_xreal_0(A,B)
=> r1_tarski(k1_topreal9(C,D,A),k1_topreal9(C,D,B)) ) ) ) ) ) ).
fof(t27_jordan,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(B)))
=> k6_subset_1(u1_struct_0(k15_euclid(B)),k2_topreal9(B,C,A),k1_topreal9(B,C,A)) = k3_topreal9(B,C,A) ) ) ) ).
fof(t28_jordan,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(B)))
=> ( r2_hidden(C,k3_topreal9(B,D,A))
=> r1_tarski(k6_subset_1(u1_struct_0(k15_euclid(B)),k3_topreal1(B,D,C),k2_struct_0(k15_euclid(B),D,C)),k1_topreal9(B,D,A)) ) ) ) ) ) ).
fof(t29_jordan,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(C)))
=> ( ~ r1_xreal_0(B,A)
=> r1_tarski(k2_topreal9(C,D,A),k1_topreal9(C,D,B)) ) ) ) ) ) ).
fof(t30_jordan,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(C)))
=> ( ~ r1_xreal_0(B,A)
=> r1_tarski(k3_topreal9(C,D,A),k1_topreal9(C,D,B)) ) ) ) ) ) ).
fof(t31_jordan,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_xreal_0(C) )
=> k6_pre_topc(k15_euclid(A),k1_topreal9(A,B,C)) = k2_topreal9(A,B,C) ) ) ) ).
fof(t32_jordan,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_xreal_0(C) )
=> k2_tops_1(k15_euclid(A),k1_topreal9(A,B,C)) = k3_topreal9(A,B,C) ) ) ) ).
fof(t33_jordan,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v4_pre_topc(B,k15_euclid(A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ~ ( ~ r2_hidden(C,B)
& ! [D] :
( ( v1_xreal_0(D)
& v2_xreal_0(D) )
=> ~ r1_xboole_0(k1_topreal9(A,C,D),B) ) ) ) ) ) ).
fof(t34_jordan,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_jordan2c(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ? [D] :
( v1_xreal_0(D)
& v2_xreal_0(D)
& r1_tarski(B,k1_topreal9(A,C,D)) ) ) ) ) ).
fof(t35_jordan,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v3_tops_2(C,A,B)
=> v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ).
fof(t36_jordan,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( C = D
=> k3_pre_topc(A,C) = k3_pre_topc(B,D) ) ) ) ) ) ).
fof(t37_jordan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> ( r1_borsuk_6(A,B,C)
=> v2_connsp_1(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),D),A) ) ) ) ) ) ).
fof(t38_jordan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_borsuk_2(G,A,C,D)
=> ( ( C = E
& D = F
& r1_borsuk_6(A,C,D)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),G),u1_struct_0(B)) )
=> ( r1_borsuk_6(B,E,F)
& m1_borsuk_2(G,B,E,F) ) ) ) ) ) ) ) ) ) ).
fof(t39_jordan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_pre_topc(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( m1_borsuk_2(G,A,C,D)
=> ( ( C = E
& D = F
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),G),u1_struct_0(B)) )
=> ( r1_borsuk_6(B,E,F)
& m1_borsuk_2(G,B,E,F) ) ) ) ) ) ) ) ) ) ).
fof(t40_jordan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> ( r1_borsuk_6(A,B,C)
=> k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),D) = k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),k2_borsuk_2(A,B,C,D)) ) ) ) ) ) ).
fof(t41_jordan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_borsuk_2(D,A,B,C)
=> k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),D) = k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),k2_borsuk_2(A,B,C,D)) ) ) ) ) ).
fof(t42_jordan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ! [F] :
( m1_borsuk_2(F,A,C,D)
=> ( ( r1_borsuk_6(A,B,C)
& r1_borsuk_6(A,C,D) )
=> r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),E),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),k1_borsuk_2(A,B,C,D,E,F))) ) ) ) ) ) ) ) ).
fof(t43_jordan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ! [F] :
( m1_borsuk_2(F,A,C,D)
=> r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),E),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),k1_borsuk_2(A,B,C,D,E,F))) ) ) ) ) ) ) ).
fof(t44_jordan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_borsuk_2(E,A,C,D)
=> ! [F] :
( m1_borsuk_2(F,A,B,C)
=> ( ( r1_borsuk_6(A,B,C)
& r1_borsuk_6(A,C,D) )
=> r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),E),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),k1_borsuk_2(A,B,C,D,F,E))) ) ) ) ) ) ) ) ).
fof(t45_jordan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_borsuk_2(E,A,C,D)
=> ! [F] :
( m1_borsuk_2(F,A,B,C)
=> r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),E),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),k1_borsuk_2(A,B,C,D,F,E))) ) ) ) ) ) ) ).
fof(t46_jordan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ! [F] :
( m1_borsuk_2(F,A,C,D)
=> ( ( r1_borsuk_6(A,B,C)
& r1_borsuk_6(A,C,D) )
=> k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),k1_borsuk_2(A,B,C,D,E,F)) = k4_subset_1(u1_struct_0(A),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),E),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),F)) ) ) ) ) ) ) ) ).
fof(t47_jordan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_borsuk_2(E,A,B,C)
=> ! [F] :
( m1_borsuk_2(F,A,C,D)
=> k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),k1_borsuk_2(A,B,C,D,E,F)) = k4_subset_1(u1_struct_0(A),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),E),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),F)) ) ) ) ) ) ) ).
fof(t48_jordan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_borsuk_2(F,A,B,C)
=> ! [G] :
( m1_borsuk_2(G,A,C,D)
=> ! [H] :
( m1_borsuk_2(H,A,D,E)
=> ( ( r1_borsuk_6(A,B,C)
& r1_borsuk_6(A,C,D)
& r1_borsuk_6(A,D,E) )
=> k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,C,D,F,G),H)) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),F),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),G)),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),H)) ) ) ) ) ) ) ) ) ) ).
fof(t49_jordan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& v1_borsuk_2(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_borsuk_2(F,A,B,C)
=> ! [G] :
( m1_borsuk_2(G,A,C,D)
=> ! [H] :
( m1_borsuk_2(H,A,D,E)
=> k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,C,D,F,G),H)) = k4_subset_1(u1_struct_0(A),k4_subset_1(u1_struct_0(A),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),F),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),G)),k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),H)) ) ) ) ) ) ) ) ) ).
fof(t50_jordan,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> m1_borsuk_2(k3_borsuk_1(k5_topmetr,A,B),A,B,B) ) ) ).
fof(t51_jordan,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ~ ( r1_topreal1(k15_euclid(A),B,C,D)
& ! [E] :
( m1_borsuk_2(E,k15_euclid(A),B,C)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),D)))
& m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),D))) )
=> ~ ( k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),D)),F) = D
& E = F ) ) ) ) ) ) ) ) ).
fof(t52_jordan,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ? [D] :
( m1_borsuk_2(D,k15_euclid(A),B,C)
& ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),k3_topreal1(A,B,C))))
& m2_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),k3_topreal1(A,B,C))))
& k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),k3_topreal1(A,B,C))),E) = k3_topreal1(A,B,C)
& D = E ) ) ) ) ) ).
fof(t53_jordan,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)
& r2_hidden(D,A)
& r2_hidden(E,A)
& D != B
& D != C
& E != B
& E != C
& ! [F] :
( m1_borsuk_2(F,k15_euclid(np__2),D,E)
=> ~ ( r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F),A)
& r1_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(np__2)),F),k2_struct_0(k15_euclid(np__2),B,C)) ) ) ) ) ) ) ) ) ).
fof(t54_jordan,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> r1_tarski(k1_sppol_2(A,B,C,D),k2_jgraph_6(A,B,C,D)) ) ) ) ) ) ).
fof(t55_jordan,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> r1_tarski(k1_jgraph_6(A,B,C,D),k2_jgraph_6(A,B,C,D)) ) ) ) ) ).
fof(t56_jordan,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> k2_jgraph_6(A,B,C,D) = k3_subset_1(u1_struct_0(k15_euclid(np__2)),k3_jgraph_6(A,B,C,D)) ) ) ) ) ).
fof(t57_jordan,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> r1_xboole_0(k2_jgraph_6(A,B,C,D),k3_jgraph_6(A,B,C,D)) ) ) ) ) ).
fof(t58_jordan,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k2_jgraph_6(A,B,C,D),k1_jgraph_6(A,B,C,D)) = k1_jgraph_6(A,B,C,D) ) ) ) ) ).
fof(t59_jordan,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ~ ( ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(D,C)
& k1_tops_1(k15_euclid(np__2),k2_jgraph_6(A,B,C,D)) != k1_jgraph_6(A,B,C,D) ) ) ) ) ) ).
fof(t60_jordan,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> k6_subset_1(u1_struct_0(k15_euclid(np__2)),k2_jgraph_6(A,B,C,D),k1_jgraph_6(A,B,C,D)) = k1_sppol_2(A,B,C,D) ) ) ) ) ) ).
fof(t61_jordan,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ~ ( ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(D,C)
& k2_tops_1(k15_euclid(np__2),k2_jgraph_6(A,B,C,D)) != k1_sppol_2(A,B,C,D) ) ) ) ) ) ).
fof(t62_jordan,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> k18_pscomp_1(k2_jgraph_6(A,B,C,D)) = A ) ) ) ) ) ).
fof(t63_jordan,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> k21_pscomp_1(k2_jgraph_6(A,B,C,D)) = C ) ) ) ) ) ).
fof(t64_jordan,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> k20_pscomp_1(k2_jgraph_6(A,B,C,D)) = B ) ) ) ) ) ).
fof(t65_jordan,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ( ( r1_xreal_0(A,B)
& r1_xreal_0(C,D) )
=> k19_pscomp_1(k2_jgraph_6(A,B,C,D)) = D ) ) ) ) ) ).
fof(t66_jordan,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_xreal_0(C)
=> ! [D] :
( v1_xreal_0(D)
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(np__2)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(np__2)))
=> ! [G] :
( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( r2_hidden(E,k2_jgraph_6(A,B,C,D))
& r1_topreal1(k15_euclid(np__2),E,F,G) )
=> ( r1_xreal_0(B,A)
| r1_xreal_0(D,C)
| r2_hidden(F,k2_jgraph_6(A,B,C,D))
| r1_tarski(k5_jordan6(G,E,F,E,k1_jordan5c(G,k1_sppol_2(A,B,C,D),E,F)),k2_jgraph_6(A,B,C,D)) ) ) ) ) ) ) ) ) ) ).
fof(d1_jordan,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& m2_relset_1(B,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers) )
=> ( B = k3_jordan(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))))
=> k8_funct_2(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers,B,C) = k5_real_1(k21_euclid(k2_jordan(k15_euclid(np__2),k15_euclid(np__2),C)),k21_euclid(A)) ) ) ) ) ).
fof(d2_jordan,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& m2_relset_1(B,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers) )
=> ( B = k4_jordan(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))))
=> k8_funct_2(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers,B,C) = k5_real_1(k22_euclid(k2_jordan(k15_euclid(np__2),k15_euclid(np__2),C)),k22_euclid(A)) ) ) ) ) ).
fof(d3_jordan,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& m2_relset_1(A,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers) )
=> ( A = k5_jordan
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))))
=> k8_funct_2(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers,A,B) = k5_real_1(k21_euclid(k1_jordan(k15_euclid(np__2),k15_euclid(np__2),B)),k21_euclid(k2_jordan(k15_euclid(np__2),k15_euclid(np__2),B))) ) ) ) ).
fof(d4_jordan,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& m2_relset_1(A,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers) )
=> ( A = k6_jordan
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))))
=> k8_funct_2(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers,A,B) = k5_real_1(k22_euclid(k1_jordan(k15_euclid(np__2),k15_euclid(np__2),B)),k22_euclid(k2_jordan(k15_euclid(np__2),k15_euclid(np__2),B))) ) ) ) ).
fof(d5_jordan,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& m2_relset_1(A,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers) )
=> ( A = k7_jordan
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))))
=> k8_funct_2(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers,A,B) = k21_euclid(k2_jordan(k15_euclid(np__2),k15_euclid(np__2),B)) ) ) ) ).
fof(d6_jordan,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& m2_relset_1(A,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers) )
=> ( A = k8_jordan
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))))
=> k8_funct_2(u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers,A,B) = k22_euclid(k2_jordan(k15_euclid(np__2),k15_euclid(np__2),B)) ) ) ) ).
fof(t67_jordan,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v1_funct_1(k3_jordan(A))
& v1_funct_2(k3_jordan(A),u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),u1_struct_0(k3_topmetr))
& v5_pre_topc(k3_jordan(A),k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2)),k3_topmetr)
& m2_relset_1(k3_jordan(A),u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),u1_struct_0(k3_topmetr)) ) ) ).
fof(t68_jordan,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v1_funct_1(k4_jordan(A))
& v1_funct_2(k4_jordan(A),u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),u1_struct_0(k3_topmetr))
& v5_pre_topc(k4_jordan(A),k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2)),k3_topmetr)
& m2_relset_1(k4_jordan(A),u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),u1_struct_0(k3_topmetr)) ) ) ).
fof(t69_jordan,axiom,
( v1_funct_1(k5_jordan)
& v1_funct_2(k5_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),u1_struct_0(k3_topmetr))
& v5_pre_topc(k5_jordan,k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2)),k3_topmetr)
& m2_relset_1(k5_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),u1_struct_0(k3_topmetr)) ) ).
fof(t70_jordan,axiom,
( v1_funct_1(k6_jordan)
& v1_funct_2(k6_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),u1_struct_0(k3_topmetr))
& v5_pre_topc(k6_jordan,k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2)),k3_topmetr)
& m2_relset_1(k6_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),u1_struct_0(k3_topmetr)) ) ).
fof(t71_jordan,axiom,
( v1_funct_1(k7_jordan)
& v1_funct_2(k7_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),u1_struct_0(k3_topmetr))
& v5_pre_topc(k7_jordan,k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2)),k3_topmetr)
& m2_relset_1(k7_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),u1_struct_0(k3_topmetr)) ) ).
fof(t72_jordan,axiom,
( v1_funct_1(k8_jordan)
& v1_funct_2(k8_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),u1_struct_0(k3_topmetr))
& v5_pre_topc(k8_jordan,k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2)),k3_topmetr)
& m2_relset_1(k8_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),u1_struct_0(k3_topmetr)) ) ).
fof(d7_jordan,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( ( v1_xreal_0(D)
& v2_xreal_0(D) )
=> ( m1_subset_1(C,u1_struct_0(k2_brouwer(A,B,D)))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k3_pre_topc(k15_euclid(A),k6_subset_1(u1_struct_0(k15_euclid(A)),k2_topreal9(A,B,D),k1_struct_0(k15_euclid(A),C)))),u1_struct_0(k7_toprealb(A,B,D)))
& m2_relset_1(E,u1_struct_0(k3_pre_topc(k15_euclid(A),k6_subset_1(u1_struct_0(k15_euclid(A)),k2_topreal9(A,B,D),k1_struct_0(k15_euclid(A),C)))),u1_struct_0(k7_toprealb(A,B,D))) )
=> ( E = k9_jordan(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(k3_pre_topc(k15_euclid(A),k6_subset_1(u1_struct_0(k15_euclid(A)),k2_topreal9(A,B,D),k1_struct_0(k15_euclid(A),C)))))
=> ? [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(A)))
& F = G
& k8_funct_2(u1_struct_0(k3_pre_topc(k15_euclid(A),k6_subset_1(u1_struct_0(k15_euclid(A)),k2_topreal9(A,B,D),k1_struct_0(k15_euclid(A),C)))),u1_struct_0(k7_toprealb(A,B,D)),E,F) = k3_brouwer(A,B,C,G,D) ) ) ) ) ) ) ) ) ) ).
fof(t73_jordan,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)
& v2_xreal_0(C) )
=> ( m1_subset_1(B,u1_struct_0(k2_brouwer(np__2,A,C)))
=> v5_pre_topc(k9_jordan(np__2,A,B,C),k3_pre_topc(k15_euclid(np__2),k6_subset_1(u1_struct_0(k15_euclid(np__2)),k2_topreal9(np__2,A,C),k1_struct_0(k15_euclid(np__2),B))),k7_toprealb(np__2,A,C)) ) ) ) ) ).
fof(t74_jordan,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( ( v1_xreal_0(D)
& v2_xreal_0(D) )
=> ( r2_hidden(C,k1_topreal9(A,B,D))
=> k2_partfun1(u1_struct_0(k3_pre_topc(k15_euclid(A),k6_subset_1(u1_struct_0(k15_euclid(A)),k2_topreal9(A,B,D),k1_struct_0(k15_euclid(A),C)))),u1_struct_0(k7_toprealb(A,B,D)),k9_jordan(A,B,C,D),k3_topreal9(A,B,D)) = k6_partfun1(k3_topreal9(A,B,D)) ) ) ) ) ) ).
fof(d8_jordan,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( ( v1_xreal_0(D)
& v2_xreal_0(D) )
=> ( r2_hidden(C,k1_topreal9(A,B,D))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k7_toprealb(A,B,D)),u1_struct_0(k7_toprealb(A,B,D)))
& m2_relset_1(E,u1_struct_0(k7_toprealb(A,B,D)),u1_struct_0(k7_toprealb(A,B,D))) )
=> ( E = k10_jordan(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(k7_toprealb(A,B,D)))
=> ? [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(A)))
& F = G
& k8_funct_2(u1_struct_0(k7_toprealb(A,B,D)),u1_struct_0(k7_toprealb(A,B,D)),E,F) = k3_brouwer(A,B,G,C,D) ) ) ) ) ) ) ) ) ) ).
fof(t75_jordan,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)
& v2_xreal_0(C) )
=> ( r2_hidden(B,k1_topreal9(np__2,A,C))
=> v5_pre_topc(k10_jordan(np__2,A,B,C),k7_toprealb(np__2,A,C),k7_toprealb(np__2,A,C)) ) ) ) ) ).
fof(t76_jordan,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( ( v1_xreal_0(D)
& v2_xreal_0(D) )
=> ~ ( r2_hidden(C,k1_topreal9(A,B,D))
& r3_abian(k10_jordan(A,B,C,D)) ) ) ) ) ) ).
fof(t77_jordan,axiom,
! [A] :
( ( v1_topreal2(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))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)))))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)))))
=> ( ( C = B
& r3_connsp_1(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)),C)
& r3_connsp_1(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)),D) )
=> ( C = D
| r1_xboole_0(k6_pre_topc(k15_euclid(np__2),B),D) ) ) ) ) ) ) ).
fof(t78_jordan,axiom,
! [A] :
( ( v1_topreal2(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(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)))))
=> ( r3_connsp_1(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)),B)
=> v1_borsuk_2(k3_pre_topc(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)),B)) ) ) ) ).
fof(t79_jordan,axiom,
! [A] :
( ( v1_topreal2(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))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)))))
=> ( ( C = B
& r3_connsp_1(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)),C) )
=> A = k2_tops_1(k15_euclid(np__2),B) ) ) ) ) ).
fof(t80_jordan,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m1_topgrp_1(B,k15_euclid(np__2))
=> v1_topreal2(k4_pre_topc(k15_euclid(np__2),k15_euclid(np__2),B,A)) ) ) ).
fof(t81_jordan,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( r1_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
=> r1_tarski(A,k2_jgraph_6(k1_real_1(np__1),np__1,k1_real_1(np__3),np__3)) ) ) ).
fof(t82_jordan,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( r1_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
=> r1_xboole_0(A,k3_topreal1(np__2,k23_euclid(k1_real_1(np__1),np__3),k23_euclid(np__1,np__3))) ) ) ).
fof(t83_jordan,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( r1_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
=> r1_xboole_0(A,k3_topreal1(np__2,k23_euclid(k1_real_1(np__1),k1_real_1(np__3)),k23_euclid(np__1,k1_real_1(np__3)))) ) ) ).
fof(t84_jordan,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( r1_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),A,k1_sppol_2(k1_real_1(np__1),np__1,k1_real_1(np__3),np__3)) = k2_struct_0(k15_euclid(np__2),k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0)) ) ) ).
fof(t85_jordan,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( r1_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
=> k18_pscomp_1(A) = k1_real_1(np__1) ) ) ).
fof(t86_jordan,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( r1_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
=> k20_pscomp_1(A) = np__1 ) ) ).
fof(t87_jordan,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
=> k26_pscomp_1(A) = k1_struct_0(k15_euclid(np__2),k23_euclid(k1_real_1(np__1),np__0)) ) ) ).
fof(t88_jordan,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
=> k28_pscomp_1(A) = k1_struct_0(k15_euclid(np__2),k23_euclid(np__1,np__0)) ) ) ).
fof(t89_jordan,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
=> ( k30_pscomp_1(A) = k23_euclid(k1_real_1(np__1),np__0)
& k31_pscomp_1(A) = k23_euclid(k1_real_1(np__1),np__0) ) ) ) ).
fof(t90_jordan,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
=> ( k35_pscomp_1(A) = k23_euclid(np__1,np__0)
& k34_pscomp_1(A) = k23_euclid(np__1,np__0) ) ) ) ).
fof(t91_jordan,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( r1_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
=> v2_sppol_1(k3_topreal1(np__2,k23_euclid(np__0,np__3),k1_jordan21(A))) ) ) ).
fof(t92_jordan,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( r1_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
=> v2_sppol_1(k3_topreal1(np__2,k2_jordan21(A),k23_euclid(np__0,k1_real_1(np__3)))) ) ) ).
fof(t93_jordan,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))))
=> ~ ( r1_jordan24(np__2,B,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
& r2_hidden(A,B)
& r1_xreal_0(np__3,k22_euclid(A)) ) ) ) ).
fof(t94_jordan,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))))
=> ~ ( r1_jordan24(np__2,B,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
& r2_hidden(A,B)
& r1_xreal_0(k22_euclid(A),k1_real_1(np__3)) ) ) ) ).
fof(t95_jordan,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( v6_compts_1(B,k15_euclid(np__2))
& v1_jordan21(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_jordan24(np__2,B,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
& r2_hidden(A,k3_topreal1(np__2,k23_euclid(np__0,np__3),k1_jordan21(B))) )
=> r1_xreal_0(k22_euclid(k1_jordan21(B)),k22_euclid(A)) ) ) ) ).
fof(t96_jordan,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( ( v6_compts_1(B,k15_euclid(np__2))
& v1_jordan21(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_jordan24(np__2,B,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
& r2_hidden(A,k3_topreal1(np__2,k2_jordan21(B),k23_euclid(np__0,k1_real_1(np__3)))) )
=> r1_xreal_0(k22_euclid(A),k22_euclid(k2_jordan21(B))) ) ) ) ).
fof(t97_jordan,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)))) )
=> ( r1_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
=> r1_tarski(k3_topreal1(np__2,k23_euclid(np__0,np__3),k1_jordan21(A)),k2_jordan1a(k1_jordan21(A))) ) ) ).
fof(t98_jordan,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)))) )
=> ( r1_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
=> r1_tarski(k3_topreal1(np__2,k2_jordan21(A),k23_euclid(np__0,k1_real_1(np__3))),k4_jordan1a(k2_jordan21(A))) ) ) ).
fof(t99_jordan,axiom,
! [A] :
( ( v1_topreal2(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_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
& r1_jordan2c(np__2,A,B) )
=> r1_xboole_0(k3_topreal1(np__2,k23_euclid(np__0,np__3),k1_jordan21(A)),B) ) ) ) ).
fof(t100_jordan,axiom,
! [A] :
( ( v1_topreal2(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_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
& r1_jordan2c(np__2,A,B) )
=> r1_xboole_0(k3_topreal1(np__2,k2_jordan21(A),k23_euclid(np__0,k1_real_1(np__3))),B) ) ) ) ).
fof(t101_jordan,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)))) )
=> ( r1_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(np__0,np__3),k1_jordan21(A)),A) = k1_struct_0(k15_euclid(np__2),k1_jordan21(A)) ) ) ).
fof(t102_jordan,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)))) )
=> ( r1_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k23_euclid(np__0,k1_real_1(np__3)),k2_jordan21(A)),A) = k1_struct_0(k15_euclid(np__2),k2_jordan21(A)) ) ) ).
fof(t103_jordan,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))))
=> ( ( v6_compts_1(A,k15_euclid(np__2))
& r1_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
& r1_jordan2c(np__2,A,B) )
=> r1_tarski(B,k2_jgraph_6(k1_real_1(np__1),np__1,k1_real_1(np__3),np__3)) ) ) ) ).
fof(t104_jordan,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ~ ( r1_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
& r2_subset_1(k3_topreal1(np__2,k23_euclid(np__0,np__3),k23_euclid(np__0,k1_real_1(np__3))),A) ) ) ).
fof(t105_jordan,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
=> ! [B] :
( ( v6_compts_1(B,k15_euclid(np__2))
& v1_jordan21(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( ( v6_compts_1(C,k15_euclid(np__2))
& v1_jordan21(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_topreal1(k15_euclid(np__2),k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0),B)
& r1_topreal1(k15_euclid(np__2),k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0),C)
& A = k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,C)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,C) = k2_struct_0(k15_euclid(np__2),k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
& r2_hidden(k1_jordan21(A),B)
& r2_hidden(k2_jordan21(A),C)
& k18_pscomp_1(A) = k18_pscomp_1(B)
& k20_pscomp_1(A) = k20_pscomp_1(B) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( D = k1_connsp_1(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)),k2_connsp_3(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A),k18_euclid(k6_real_1(np__1,np__2),np__2,k17_euclid(np__2,k1_jordan21(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k2_jordan21(B),k23_euclid(np__0,k1_real_1(np__3))),C)),k2_jordan21(B)))))
=> ( r1_jordan2c(np__2,A,D)
& ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( r1_jordan2c(np__2,A,E)
=> E = D ) ) ) ) ) ) ) ) ) ) ).
fof(t106_jordan,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( r1_jordan24(np__2,A,k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
=> ! [B] :
( ( v6_compts_1(B,k15_euclid(np__2))
& v1_jordan21(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( ( v6_compts_1(C,k15_euclid(np__2))
& v1_jordan21(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ( ( r1_topreal1(k15_euclid(np__2),k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0),B)
& r1_topreal1(k15_euclid(np__2),k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0),C)
& A = k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,C)
& k5_subset_1(u1_struct_0(k15_euclid(np__2)),B,C) = k2_struct_0(k15_euclid(np__2),k23_euclid(k1_real_1(np__1),np__0),k23_euclid(np__1,np__0))
& r2_hidden(k1_jordan21(A),B)
& r2_hidden(k2_jordan21(A),C)
& k18_pscomp_1(A) = k18_pscomp_1(B)
& k20_pscomp_1(A) = k20_pscomp_1(B) )
=> k1_jordan2c(np__2,A) = k1_connsp_1(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)),k2_connsp_3(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A),k18_euclid(k6_real_1(np__1,np__2),np__2,k17_euclid(np__2,k1_jordan21(k5_subset_1(u1_struct_0(k15_euclid(np__2)),k3_topreal1(np__2,k2_jordan21(B),k23_euclid(np__0,k1_real_1(np__3))),C)),k2_jordan21(B))))) ) ) ) ) ) ).
fof(t107_jordan,axiom,
! [A] :
( ( v1_topreal2(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))))
& ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& k3_subset_1(u1_struct_0(k15_euclid(np__2)),A) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),B,C)
& r1_xboole_0(B,C)
& k6_subset_1(u1_struct_0(k15_euclid(np__2)),k6_pre_topc(k15_euclid(np__2),B),B) = k6_subset_1(u1_struct_0(k15_euclid(np__2)),k6_pre_topc(k15_euclid(np__2),C),C)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)))))
=> ( ( D = B
& E = C )
=> ( r3_connsp_1(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)),D)
& r3_connsp_1(k3_pre_topc(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),A)),E) ) ) ) ) ) ) ) ).
fof(t108_jordan,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> v2_jordan1(A) ) ).
fof(dt_k1_jordan,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(k6_borsuk_1(A,B))) )
=> m1_subset_1(k1_jordan(A,B,C),u1_struct_0(A)) ) ).
fof(redefinition_k1_jordan,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(k6_borsuk_1(A,B))) )
=> k1_jordan(A,B,C) = k1_mcart_1(C) ) ).
fof(dt_k2_jordan,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(k6_borsuk_1(A,B))) )
=> m1_subset_1(k2_jordan(A,B,C),u1_struct_0(B)) ) ).
fof(redefinition_k2_jordan,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(B)
& m1_subset_1(C,u1_struct_0(k6_borsuk_1(A,B))) )
=> k2_jordan(A,B,C) = k2_mcart_1(C) ) ).
fof(dt_k3_jordan,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v1_funct_1(k3_jordan(A))
& v1_funct_2(k3_jordan(A),u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& m2_relset_1(k3_jordan(A),u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers) ) ) ).
fof(dt_k4_jordan,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v1_funct_1(k4_jordan(A))
& v1_funct_2(k4_jordan(A),u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& m2_relset_1(k4_jordan(A),u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers) ) ) ).
fof(dt_k5_jordan,axiom,
( v1_funct_1(k5_jordan)
& v1_funct_2(k5_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& m2_relset_1(k5_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers) ) ).
fof(dt_k6_jordan,axiom,
( v1_funct_1(k6_jordan)
& v1_funct_2(k6_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& m2_relset_1(k6_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers) ) ).
fof(dt_k7_jordan,axiom,
( v1_funct_1(k7_jordan)
& v1_funct_2(k7_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& m2_relset_1(k7_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers) ) ).
fof(dt_k8_jordan,axiom,
( v1_funct_1(k8_jordan)
& v1_funct_2(k8_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers)
& m2_relset_1(k8_jordan,u1_struct_0(k6_borsuk_1(k15_euclid(np__2),k15_euclid(np__2))),k1_numbers) ) ).
fof(dt_k9_jordan,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k5_numbers)
& m1_subset_1(B,u1_struct_0(k15_euclid(A)))
& m1_subset_1(C,u1_struct_0(k15_euclid(A)))
& v1_xreal_0(D)
& v2_xreal_0(D) )
=> ( v1_funct_1(k9_jordan(A,B,C,D))
& v1_funct_2(k9_jordan(A,B,C,D),u1_struct_0(k3_pre_topc(k15_euclid(A),k6_subset_1(u1_struct_0(k15_euclid(A)),k2_topreal9(A,B,D),k1_struct_0(k15_euclid(A),C)))),u1_struct_0(k7_toprealb(A,B,D)))
& m2_relset_1(k9_jordan(A,B,C,D),u1_struct_0(k3_pre_topc(k15_euclid(A),k6_subset_1(u1_struct_0(k15_euclid(A)),k2_topreal9(A,B,D),k1_struct_0(k15_euclid(A),C)))),u1_struct_0(k7_toprealb(A,B,D))) ) ) ).
fof(dt_k10_jordan,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k5_numbers)
& m1_subset_1(B,u1_struct_0(k15_euclid(A)))
& m1_subset_1(C,u1_struct_0(k15_euclid(A)))
& v1_xreal_0(D)
& v2_xreal_0(D) )
=> ( v1_funct_1(k10_jordan(A,B,C,D))
& v1_funct_2(k10_jordan(A,B,C,D),u1_struct_0(k7_toprealb(A,B,D)),u1_struct_0(k7_toprealb(A,B,D)))
& m2_relset_1(k10_jordan(A,B,C,D),u1_struct_0(k7_toprealb(A,B,D)),u1_struct_0(k7_toprealb(A,B,D))) ) ) ).
%------------------------------------------------------------------------------