SET007 Axioms: SET007+701.ax
%------------------------------------------------------------------------------
% File : SET007+701 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Upper and Lower Sequence of a Cage
% 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 : jordan1e [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 36 ( 0 unt; 0 def)
% Number of atoms : 273 ( 21 equ)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 301 ( 64 ~; 0 |; 151 &)
% ( 0 <=>; 86 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 24 ( 23 usr; 0 prp; 1-3 aty)
% Number of functors : 42 ( 42 usr; 6 con; 0-4 aty)
% Number of variables : 78 ( 78 !; 0 ?)
% 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_jordan1e,axiom,
! [A,B] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,k5_numbers) )
=> ( ~ v1_xboole_0(k1_jordan1e(A,B))
& v1_relat_1(k1_jordan1e(A,B))
& v1_funct_1(k1_jordan1e(A,B))
& v1_finset_1(k1_jordan1e(A,B))
& v1_finseq_1(k1_jordan1e(A,B)) ) ) ).
fof(fc2_jordan1e,axiom,
! [A,B] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,k5_numbers) )
=> ( ~ v1_xboole_0(k2_jordan1e(A,B))
& v1_relat_1(k2_jordan1e(A,B))
& v1_funct_1(k2_jordan1e(A,B))
& v1_finset_1(k2_jordan1e(A,B))
& v1_finseq_1(k2_jordan1e(A,B)) ) ) ).
fof(fc3_jordan1e,axiom,
! [A,B] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,k5_numbers) )
=> ( ~ v1_xboole_0(k1_jordan1e(A,B))
& v1_relat_1(k1_jordan1e(A,B))
& v1_funct_1(k1_jordan1e(A,B))
& v2_funct_1(k1_jordan1e(A,B))
& v1_finset_1(k1_jordan1e(A,B))
& v1_finseq_1(k1_jordan1e(A,B))
& v1_topreal1(k1_jordan1e(A,B))
& v2_topreal1(k1_jordan1e(A,B))
& v3_topreal1(k1_jordan1e(A,B)) ) ) ).
fof(fc4_jordan1e,axiom,
! [A,B] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,k5_numbers) )
=> ( ~ v1_xboole_0(k2_jordan1e(A,B))
& v1_relat_1(k2_jordan1e(A,B))
& v1_funct_1(k2_jordan1e(A,B))
& v2_funct_1(k2_jordan1e(A,B))
& v1_finset_1(k2_jordan1e(A,B))
& v1_finseq_1(k2_jordan1e(A,B))
& v1_topreal1(k2_jordan1e(A,B))
& v2_topreal1(k2_jordan1e(A,B))
& v3_topreal1(k2_jordan1e(A,B)) ) ) ).
fof(fc5_jordan1e,axiom,
! [A,B] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,k5_numbers) )
=> ( ~ v1_xboole_0(k1_jordan1e(A,B))
& v1_relat_1(k1_jordan1e(A,B))
& v1_funct_1(k1_jordan1e(A,B))
& v2_funct_1(k1_jordan1e(A,B))
& v1_finset_1(k1_jordan1e(A,B))
& v1_finseq_1(k1_jordan1e(A,B))
& ~ v1_realset1(k1_jordan1e(A,B))
& v1_topreal1(k1_jordan1e(A,B))
& v2_topreal1(k1_jordan1e(A,B))
& v3_topreal1(k1_jordan1e(A,B))
& v4_topreal1(k1_jordan1e(A,B)) ) ) ).
fof(fc6_jordan1e,axiom,
! [A,B] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,k5_numbers) )
=> ( ~ v1_xboole_0(k2_jordan1e(A,B))
& v1_relat_1(k2_jordan1e(A,B))
& v1_funct_1(k2_jordan1e(A,B))
& v2_funct_1(k2_jordan1e(A,B))
& v1_finset_1(k2_jordan1e(A,B))
& v1_finseq_1(k2_jordan1e(A,B))
& ~ v1_realset1(k2_jordan1e(A,B))
& v1_topreal1(k2_jordan1e(A,B))
& v2_topreal1(k2_jordan1e(A,B))
& v3_topreal1(k2_jordan1e(A,B))
& v4_topreal1(k2_jordan1e(A,B)) ) ) ).
fof(t1_jordan1e,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(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)))) )
=> ( r1_tarski(A,B)
=> r1_xreal_0(k19_pscomp_1(A),k19_pscomp_1(B)) ) ) ) ).
fof(t2_jordan1e,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(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)))) )
=> ( r1_tarski(A,B)
=> r1_xreal_0(k20_pscomp_1(A),k20_pscomp_1(B)) ) ) ) ).
fof(t3_jordan1e,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(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)))) )
=> ( r1_tarski(A,B)
=> r1_xreal_0(k21_pscomp_1(B),k21_pscomp_1(A)) ) ) ) ).
fof(t4_jordan1e,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k1_zfmisc_1(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)))) )
=> ( r1_tarski(A,B)
=> r1_xreal_0(k18_pscomp_1(B),k18_pscomp_1(A)) ) ) ) ).
fof(t5_jordan1e,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_sprect_2(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(C,k2_relat_1(A))
=> r1_sprect_2(B,k1_finseq_5(u1_struct_0(k15_euclid(np__2)),A,C)) ) ) ) ) ) ).
fof(t6_jordan1e,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m2_finseq_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( r1_sprect_2(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ( r2_hidden(C,k2_relat_1(A))
=> r1_sprect_2(B,k2_finseq_5(u1_struct_0(k15_euclid(np__2)),A,C)) ) ) ) ) ) ).
fof(t7_jordan1e,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(B,k5_topreal1(np__2,A))
& k3_jordan3(A,B) = k1_xboole_0 ) ) ) ).
fof(t8_jordan1e,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(B,k5_topreal1(np__2,A))
& r1_xreal_0(np__2,k3_finseq_1(k4_jordan3(A,B))) )
=> r2_hidden(k1_funct_1(A,np__1),k5_topreal1(np__2,k4_jordan3(A,B))) ) ) ) ).
fof(t9_jordan1e,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v4_topreal1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(B,k5_topreal1(np__2,A))
& r2_hidden(k1_funct_1(A,np__1),k5_topreal1(np__2,k1_jordan3(u1_struct_0(k15_euclid(np__2)),A,k1_nat_1(k2_jordan3(A,B),np__1),k3_finseq_1(A)))) ) ) ) ) ).
fof(t10_jordan1e,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)
=> ( ( k1_nat_1(A,B) = k1_nat_1(C,D)
& r1_xreal_0(A,C)
& r1_xreal_0(B,D) )
=> A = C ) ) ) ) ) ).
fof(t11_jordan1e,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v4_topreal1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( ( r2_hidden(B,k5_topreal1(np__2,A))
& r2_hidden(k1_funct_1(A,np__1),k5_topreal1(np__2,k3_jordan3(A,B))) )
=> k1_funct_1(A,np__1) = B ) ) ) ) ).
fof(d1_jordan1e,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_jordan1e(A,B) = k1_finseq_5(u1_struct_0(k15_euclid(np__2)),k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(A,B),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) ).
fof(t12_jordan1e,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k3_finseq_1(k1_jordan1e(A,B)) = k5_finseq_4(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(A,B),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) ).
fof(d2_jordan1e,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_jordan1e(A,B) = k2_finseq_5(u1_struct_0(k15_euclid(np__2)),k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(A,B),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) ).
fof(t13_jordan1e,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k3_finseq_1(k2_jordan1e(A,B)) = k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(A,B),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))))),k5_finseq_4(k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(A,B),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))))),np__1) ) ) ).
fof(t14_jordan1e,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_nat_1(k3_finseq_1(k1_jordan1e(A,B)),k3_finseq_1(k2_jordan1e(A,B))) = k1_nat_1(k3_finseq_1(k1_jordan9(A,B)),np__1) ) ) ).
fof(t15_jordan1e,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_finseq_6(u1_struct_0(k15_euclid(np__2)),k1_jordan9(A,B),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))) = k4_graph_2(u1_struct_0(k15_euclid(np__2)),k1_jordan1e(A,B),k2_jordan1e(A,B)) ) ) ).
fof(t16_jordan1e,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k5_topreal1(np__2,k1_jordan9(A,B)) = k5_topreal1(np__2,k4_graph_2(u1_struct_0(k15_euclid(np__2)),k1_jordan1e(A,B),k2_jordan1e(A,B))) ) ) ).
fof(t17_jordan1e,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k5_topreal1(np__2,k1_jordan9(A,B)) = k4_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_jordan1e(A,B)),k5_topreal1(np__2,k2_jordan1e(A,B))) ) ) ).
fof(t18_jordan1e,axiom,
! [A] :
( ( v1_topreal2(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k30_pscomp_1(A) != k35_pscomp_1(A) ) ).
fof(t19_jordan1e,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(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(np__3,k3_finseq_1(k1_jordan1e(A,B)))
& r1_xreal_0(np__3,k3_finseq_1(k2_jordan1e(A,B))) ) ) ) ).
fof(t20_jordan1e,axiom,
! [A] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k5_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_jordan1e(A,B)),k5_topreal1(np__2,k2_jordan1e(A,B))) = k2_struct_0(k15_euclid(np__2),k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B))),k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(A,B)))) ) ) ).
fof(t21_jordan1e,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_sprect_2(k1_jordan9(B,A),k1_jordan1e(B,A)) ) ) ).
fof(t22_jordan1e,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> r1_sprect_2(k1_jordan9(B,A),k2_jordan1e(B,A)) ) ) ).
fof(t23_jordan1e,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),np__2)) = k19_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) ) ) ).
fof(t24_jordan1e,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k1_jordan9(B,A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),C) = k34_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) )
=> k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k1_nat_1(C,np__1))) = k20_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) ) ) ) ) ).
fof(t25_jordan1e,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k1_jordan9(B,A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),C) = k36_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) )
=> k22_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k1_nat_1(C,np__1))) = k21_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) ) ) ) ) ).
fof(t26_jordan1e,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v2_connsp_1(B,k15_euclid(np__2))
& v6_compts_1(B,k15_euclid(np__2))
& ~ v1_sppol_1(B)
& ~ v2_sppol_1(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2)))) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(k1_nat_1(C,np__1),k3_finseq_1(k1_jordan9(B,A)))
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),C) = k30_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) )
=> k21_euclid(k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_jordan9(B,A),k1_nat_1(C,np__1))) = k18_pscomp_1(k5_topreal1(np__2,k1_jordan9(B,A))) ) ) ) ) ).
fof(dt_k1_jordan1e,axiom,
! [A,B] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,k5_numbers) )
=> m2_finseq_1(k1_jordan1e(A,B),u1_struct_0(k15_euclid(np__2))) ) ).
fof(dt_k2_jordan1e,axiom,
! [A,B] :
( ( v6_compts_1(A,k15_euclid(np__2))
& ~ v1_sppol_1(A)
& ~ v2_sppol_1(A)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& m1_subset_1(B,k5_numbers) )
=> m2_finseq_1(k2_jordan1e(A,B),u1_struct_0(k15_euclid(np__2))) ) ).
%------------------------------------------------------------------------------