SET007 Axioms: SET007+581.ax
%------------------------------------------------------------------------------
% File : SET007+581 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Bounded Domains and Unbounded Domains
% 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 : jordan2c [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 155 ( 7 unt; 0 def)
% Number of atoms : 1146 ( 205 equ)
% Maximal formula atoms : 28 ( 7 avg)
% Number of connectives : 1166 ( 175 ~; 8 |; 489 &)
% ( 20 <=>; 474 =>; 0 <=; 0 <~>)
% Maximal formula depth : 38 ( 10 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 50 ( 48 usr; 1 prp; 0-3 aty)
% Number of functors : 94 ( 94 usr; 11 con; 0-4 aty)
% Number of variables : 474 ( 452 !; 22 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_jordan2c,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_metric_1(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v6_tbsp_1(B,A) ) ) ).
fof(fc1_jordan2c,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( ~ v1_xboole_0(k2_pre_topc(k15_euclid(A)))
& v4_pre_topc(k2_pre_topc(k15_euclid(A)),k15_euclid(A))
& v2_connsp_1(k2_pre_topc(k15_euclid(A)),k15_euclid(A)) ) ) ).
fof(cc1_jordan2c,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( v6_compts_1(B,k15_euclid(A))
=> v1_jordan2c(B,A) ) ) ) ).
fof(fc2_jordan2c,axiom,
! [A,B] :
( ( m1_subset_1(A,u1_struct_0(k15_euclid(np__2)))
& m1_subset_1(B,u1_struct_0(k15_euclid(np__2))) )
=> ( ~ v1_xboole_0(k1_topreal1(np__2,A,B))
& v2_tops_1(k1_topreal1(np__2,A,B),k15_euclid(np__2)) ) ) ).
fof(fc3_jordan2c,axiom,
! [A] :
( m1_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> ( v2_tops_1(k5_topreal1(np__2,A),k15_euclid(np__2))
& v6_compts_1(k5_topreal1(np__2,A),k15_euclid(np__2))
& v1_jordan2c(k5_topreal1(np__2,A),np__2) ) ) ).
fof(t1_jordan2c,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ( r1_xreal_0(A,np__0)
=> k18_complex1(A) = k7_binop_2(A) ) ) ).
fof(t2_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(A,B)
& r1_xreal_0(B,k23_binop_2(A,np__2))
& B != A
& B != k23_binop_2(A,np__1)
& B != k23_binop_2(A,np__2) ) ) ) ).
fof(t3_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(A,B)
& r1_xreal_0(B,k23_binop_2(A,np__3))
& B != A
& B != k23_binop_2(A,np__1)
& B != k23_binop_2(A,np__2)
& B != k23_binop_2(A,np__3) ) ) ) ).
fof(t4_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(A,B)
& r1_xreal_0(B,k23_binop_2(A,np__4))
& B != A
& B != k23_binop_2(A,np__1)
& B != k23_binop_2(A,np__2)
& B != k23_binop_2(A,np__3)
& B != k23_binop_2(A,np__4) ) ) ) ).
fof(t5_jordan2c,axiom,
$true ).
fof(t6_jordan2c,axiom,
$true ).
fof(t7_jordan2c,axiom,
! [A,B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ~ ( k2_relat_1(C) = k2_tarski(A,B)
& k3_finseq_1(C) = np__2
& ~ ( k1_funct_1(C,np__1) = A
& k1_funct_1(C,np__2) = B )
& ~ ( k1_funct_1(C,np__1) = B
& k1_funct_1(C,np__2) = A ) ) ) ).
fof(t8_jordan2c,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( ( v1_goboard1(C)
& m2_finseq_1(C,k1_numbers) )
=> ( ( k2_relat_1(C) = k2_tarski(A,B)
& k3_finseq_1(C) = np__2
& r1_xreal_0(A,B) )
=> ( k1_goboard1(C,np__1) = A
& k1_goboard1(C,np__2) = B ) ) ) ) ) ).
fof(t9_jordan2c,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,u1_struct_0(k15_euclid(A)))
=> k20_euclid(A,k17_euclid(A,B,C),D) = k17_euclid(A,k20_euclid(A,B,D),C) ) ) ) ) ).
fof(t10_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> k18_complex1(k5_toprns_1(A,B)) = k5_toprns_1(A,B) ) ) ).
fof(t11_jordan2c,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)))
=> r1_xreal_0(k18_complex1(k10_binop_2(k5_toprns_1(A,B),k5_toprns_1(A,C))),k5_toprns_1(A,k20_euclid(A,B,C))) ) ) ) ).
fof(t12_jordan2c,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> k5_toprns_1(np__1,k2_jordan2b(A)) = k18_complex1(A) ) ).
fof(t13_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(A)))
=> ( k20_euclid(A,B,k16_euclid(A)) = B
& k20_euclid(A,k16_euclid(A),B) = k19_euclid(A,B) ) ) ) ).
fof(t14_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( v1_jordan1(B,A)
=> v2_connsp_1(B,k15_euclid(A)) ) ) ) ).
fof(t15_jordan2c,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(A,C))))
=> ( ( B = D
& v2_connsp_1(B,A) )
=> v2_connsp_1(D,k3_pre_topc(A,C)) ) ) ) ) ) ).
fof(d1_jordan2c,axiom,
$true ).
fof(d2_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( v1_jordan2c(B,A)
<=> ( v6_tbsp_1(B,k14_euclid(A))
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k14_euclid(A)))) ) ) ) ) ).
fof(t16_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( ( v1_jordan2c(C,A)
& r1_tarski(B,C) )
=> v1_jordan2c(B,A) ) ) ) ) ).
fof(d3_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( r1_jordan2c(A,B,C)
<=> ( r4_connsp_1(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B),C)
& v1_jordan2c(C,A) ) ) ) ) ) ).
fof(t17_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( r1_jordan2c(A,B,C)
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B)))))
& D = C
& r3_connsp_1(k3_pre_topc(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B)),D)
& v6_tbsp_1(D,k14_euclid(A))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k14_euclid(A)))) ) ) ) ) ) ).
fof(d4_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( r2_jordan2c(A,B,C)
<=> ( r4_connsp_1(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B),C)
& ~ v1_jordan2c(C,A) ) ) ) ) ) ).
fof(t18_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( r2_jordan2c(A,B,C)
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pre_topc(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B)))))
& D = C
& r3_connsp_1(k3_pre_topc(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B)),D)
& ~ ( v6_tbsp_1(D,k14_euclid(A))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k14_euclid(A)))) ) ) ) ) ) ) ).
fof(t19_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( r1_jordan2c(A,B,C)
=> r1_tarski(C,k3_subset_1(u1_struct_0(k15_euclid(A)),B)) ) ) ) ) ).
fof(t20_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( r2_jordan2c(A,B,C)
=> r1_tarski(C,k3_subset_1(u1_struct_0(k15_euclid(A)),B)) ) ) ) ) ).
fof(t21_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> v1_jordan1(k2_pre_topc(k15_euclid(A)),A) ) ).
fof(t22_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> v2_connsp_1(k2_pre_topc(k15_euclid(A)),k15_euclid(A)) ) ).
fof(t23_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> r3_connsp_1(k15_euclid(A),k2_pre_topc(k15_euclid(A))) ) ).
fof(t24_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> m1_connsp_3(k1_jordan2c(A,B),k3_pre_topc(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B))) ) ) ).
fof(t25_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> m1_connsp_3(k2_jordan2c(A,B),k3_pre_topc(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B))) ) ) ).
fof(t26_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( r1_jordan2c(A,B,C)
=> r1_tarski(C,k1_jordan2c(A,B)) ) ) ) ) ).
fof(t27_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( r2_jordan2c(A,B,C)
=> r1_tarski(C,k2_jordan2c(A,B)) ) ) ) ) ).
fof(t28_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> r1_xboole_0(k1_jordan2c(A,B),k2_jordan2c(A,B)) ) ) ).
fof(t29_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> r1_tarski(k1_jordan2c(A,B),k3_subset_1(u1_struct_0(k15_euclid(A)),B)) ) ) ).
fof(t30_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> r1_tarski(k2_jordan2c(A,B),k3_subset_1(u1_struct_0(k15_euclid(A)),B)) ) ) ).
fof(t31_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> k4_subset_1(u1_struct_0(k15_euclid(A)),k1_jordan2c(A,B),k2_jordan2c(A,B)) = k3_subset_1(u1_struct_0(k15_euclid(A)),B) ) ) ).
fof(t32_jordan2c,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] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(A)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(A))
& m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(A)) )
=> ~ ( v5_pre_topc(E,k5_topmetr,A)
& B = k1_funct_1(E,np__0)
& C = k1_funct_1(E,np__1)
& v5_pre_topc(F,k5_topmetr,A)
& C = k1_funct_1(F,np__0)
& D = k1_funct_1(F,np__1)
& ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(A))
& m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(A)) )
=> ~ ( v5_pre_topc(G,k5_topmetr,A)
& B = k1_funct_1(G,np__0)
& D = k1_funct_1(G,np__1)
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(A),G),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(t33_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( B = k1_euclid(A)
=> v2_connsp_1(B,k15_euclid(A)) ) ) ) ).
fof(d7_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k3_jordan2c(A) = k2_finseq_2(A,np__1) ) ).
fof(d8_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k5_jordan2c(A) = k4_jordan2c(A) ) ).
fof(t34_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k10_euclid(A,k4_jordan2c(A)) = k2_finseq_2(A,np__1) ) ).
fof(t35_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k12_euclid(k4_jordan2c(A)) = k9_square_1(A) ) ).
fof(t36_jordan2c,axiom,
k5_jordan2c(np__1) = k13_binarith(k1_numbers,np__1) ).
fof(t37_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k5_toprns_1(A,k5_jordan2c(A)) = k9_square_1(A) ) ).
fof(t38_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,A)
=> r1_xreal_0(np__1,k5_toprns_1(A,k5_jordan2c(A))) ) ) ).
fof(t39_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k14_euclid(A))))
=> ~ ( r1_xreal_0(np__1,A)
& B = k1_euclid(A)
& v6_tbsp_1(B,k14_euclid(A)) ) ) ) ).
fof(t40_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( v1_jordan2c(B,A)
<=> ? [C] :
( m1_subset_1(C,k1_numbers)
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ~ ( r2_hidden(D,B)
& r1_xreal_0(C,k5_toprns_1(A,D)) ) ) ) ) ) ) ).
fof(t41_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,A)
& v1_jordan2c(k2_pre_topc(k15_euclid(A)),A) ) ) ).
fof(t42_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,A)
=> k2_jordan2c(A,k1_pre_topc(k15_euclid(A))) = k1_euclid(A) ) ) ).
fof(t43_jordan2c,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,u1_struct_0(k15_euclid(A)))
=> ! [E] :
( ( ~ v1_xboole_0(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),E)))
& m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),E))) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),E)))
& m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),E))) )
=> ~ ( v5_pre_topc(F,k5_topmetr,k3_pre_topc(k15_euclid(A),E))
& B = k1_funct_1(F,np__0)
& C = k1_funct_1(F,np__1)
& v5_pre_topc(G,k5_topmetr,k3_pre_topc(k15_euclid(A),E))
& C = k1_funct_1(G,np__0)
& D = k1_funct_1(G,np__1)
& ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),E)))
& m2_relset_1(H,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),E))) )
=> ~ ( v5_pre_topc(H,k5_topmetr,k3_pre_topc(k15_euclid(A),E))
& B = k1_funct_1(H,np__0)
& D = k1_funct_1(H,np__1) ) ) ) ) ) ) ) ) ) ) ).
fof(t44_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( 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] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> ~ ( r2_hidden(C,B)
& r2_hidden(D,B)
& r2_hidden(E,B)
& r1_tarski(k3_topreal1(A,C,D),B)
& r1_tarski(k3_topreal1(A,D,E),B)
& ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),B)))
& m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),B))) )
=> ~ ( v5_pre_topc(F,k5_topmetr,k3_pre_topc(k15_euclid(A),B))
& C = k1_funct_1(F,np__0)
& E = k1_funct_1(F,np__1) ) ) ) ) ) ) ) ) ).
fof(t45_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( 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] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
=> ~ ( r2_hidden(C,B)
& r2_hidden(D,B)
& r2_hidden(E,B)
& r2_hidden(F,B)
& r1_tarski(k3_topreal1(A,C,D),B)
& r1_tarski(k3_topreal1(A,D,E),B)
& r1_tarski(k3_topreal1(A,E,F),B)
& ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),B)))
& m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),B))) )
=> ~ ( v5_pre_topc(G,k5_topmetr,k3_pre_topc(k15_euclid(A),B))
& C = k1_funct_1(G,np__0)
& F = k1_funct_1(G,np__1) ) ) ) ) ) ) ) ) ) ).
fof(t46_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( 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] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(A)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k15_euclid(A)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k15_euclid(A)))
=> ~ ( r2_hidden(C,B)
& r2_hidden(D,B)
& r2_hidden(E,B)
& r2_hidden(F,B)
& r2_hidden(G,B)
& r2_hidden(H,B)
& r2_hidden(I,B)
& r1_tarski(k3_topreal1(A,C,D),B)
& r1_tarski(k3_topreal1(A,D,E),B)
& r1_tarski(k3_topreal1(A,E,F),B)
& r1_tarski(k3_topreal1(A,F,G),B)
& r1_tarski(k3_topreal1(A,G,H),B)
& r1_tarski(k3_topreal1(A,H,I),B)
& ! [J] :
( ( v1_funct_1(J)
& v1_funct_2(J,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),B)))
& m2_relset_1(J,u1_struct_0(k5_topmetr),u1_struct_0(k3_pre_topc(k15_euclid(A),B))) )
=> ~ ( v5_pre_topc(J,k5_topmetr,k3_pre_topc(k15_euclid(A),B))
& C = k1_funct_1(J,np__0)
& I = k1_funct_1(J,np__1) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t47_jordan2c,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_numbers)
=> ( B != k18_euclid(D,A,C)
& C != k18_euclid(D,A,B) ) )
& r2_hidden(k16_euclid(A),k3_topreal1(A,B,C)) ) ) ) ) ).
fof(t48_jordan2c,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(k5_pcomps_1(k14_euclid(A)))))
=> ~ ( D = k3_topreal1(A,B,C)
& ~ r2_hidden(k16_euclid(A),k3_topreal1(A,B,C))
& ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> ~ ( r2_hidden(E,k3_topreal1(A,B,C))
& ~ r1_xreal_0(k5_toprns_1(A,E),np__0)
& k5_toprns_1(A,E) = k1_funct_1(k8_weierstr(k14_euclid(A),D),k16_euclid(A)) ) ) ) ) ) ) ) ).
fof(t51_jordan2c,axiom,
$true ).
fof(t52_jordan2c,axiom,
! [A] :
( m2_finseq_1(A,k1_numbers)
=> ( m2_finseq_2(A,k1_numbers,k1_euclid(k3_finseq_1(A)))
& m1_subset_1(A,u1_struct_0(k15_euclid(k3_finseq_1(A)))) ) ) ).
fof(t53_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k1_numbers,k1_euclid(A))
=> ! [C] :
( m2_finseq_1(C,k1_numbers)
=> ! [D] :
( m2_finseq_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( ( C = B
& D = k9_euclid(A,E,B) )
=> ( k3_finseq_1(C) = k3_finseq_1(D)
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,F)
& r1_xreal_0(F,k3_finseq_1(C)) )
=> k4_finseq_4(k5_numbers,k1_numbers,D,F) = k11_binop_2(E,k4_finseq_4(k5_numbers,k1_numbers,C,F)) ) ) ) ) ) ) ) ) ) ).
fof(t54_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k1_numbers,k1_euclid(A))
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_finseq_1(C) )
=> ~ ( B != k5_euclid(A)
& B = C
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,A)
& k1_funct_1(C,D) != np__0 ) ) ) ) ) ) ).
fof(t55_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k1_numbers,k1_euclid(A))
=> ~ ( r1_xreal_0(np__2,A)
& B != k5_euclid(A)
& ! [C] :
( m2_finseq_2(C,k1_numbers,k1_euclid(A))
=> ~ ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( C != k9_euclid(A,D,B)
& B != k9_euclid(A,D,C) ) ) ) ) ) ) ).
fof(t71_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k14_euclid(A))))
=> ( ( B = E
& v2_connsp_1(B,k15_euclid(A))
& C = k1_connsp_3(k3_pre_topc(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),D)),k4_connsp_3(k15_euclid(A),B,k3_subset_1(u1_struct_0(k15_euclid(A)),D)))
& r1_xboole_0(E,D) )
=> ( v6_tbsp_1(E,k14_euclid(A))
| r2_jordan2c(A,D,C) ) ) ) ) ) ) ) ).
fof(t72_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k14_euclid(A))))
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k14_euclid(A)))) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k1_topmetr(k14_euclid(A),C))))
=> ( ( r1_tarski(B,C)
& B = D
& v6_tbsp_1(D,k1_topmetr(k14_euclid(A),C)) )
=> v6_tbsp_1(B,k14_euclid(A)) ) ) ) ) ) ).
fof(t73_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( v6_compts_1(B,k15_euclid(A))
=> v1_jordan2c(B,A) ) ) ) ).
fof(t74_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ~ ( r1_xreal_0(np__1,A)
& v1_jordan2c(B,A)
& k3_subset_1(u1_struct_0(k15_euclid(A)),B) = k1_xboole_0 ) ) ) ).
fof(t76_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ~ ( r1_xreal_0(np__2,A)
& v1_jordan2c(B,A)
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ~ ( r2_jordan2c(A,B,C)
& C = k2_jordan2c(A,B) ) ) ) ) ) ).
fof(t78_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k14_euclid(A)))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( D = k9_metric_1(k14_euclid(A),B,C)
=> v1_jordan1(D,A) ) ) ) ) ) ).
fof(t80_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k14_euclid(A)))
=> ~ ( C != D
& r2_hidden(C,k9_metric_1(k14_euclid(A),E,B))
& r2_hidden(D,k9_metric_1(k14_euclid(A),E,B))
& ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)))
& m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) )
=> ~ ( v5_pre_topc(F,k5_topmetr,k15_euclid(A))
& k1_funct_1(F,np__0) = C
& k1_funct_1(F,np__1) = D
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)),F),k9_metric_1(k14_euclid(A),E,B)) ) ) ) ) ) ) ) ) ).
fof(t81_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k14_euclid(A)))
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)))
& m2_relset_1(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) )
=> ~ ( v5_pre_topc(G,k5_topmetr,k15_euclid(A))
& k1_funct_1(G,np__0) = C
& k1_funct_1(G,np__1) = D
& r2_hidden(E,k9_metric_1(k14_euclid(A),F,B))
& r2_hidden(D,k9_metric_1(k14_euclid(A),F,B))
& ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)))
& m2_relset_1(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) )
=> ~ ( v5_pre_topc(H,k5_topmetr,k15_euclid(A))
& k1_funct_1(H,np__0) = C
& k1_funct_1(H,np__1) = E
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)),H),k2_xboole_0(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)),G),k9_metric_1(k14_euclid(A),F,B))) ) ) ) ) ) ) ) ) ) ) ).
fof(t82_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k14_euclid(A)))
=> ! [G] :
( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)))
& m2_relset_1(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) )
=> ~ ( v5_pre_topc(H,k5_topmetr,k15_euclid(A))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)),H),G)
& k1_funct_1(H,np__0) = C
& k1_funct_1(H,np__1) = D
& r2_hidden(E,k9_metric_1(k14_euclid(A),F,B))
& r2_hidden(D,k9_metric_1(k14_euclid(A),F,B))
& r1_tarski(k9_metric_1(k14_euclid(A),F,B),G)
& ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)))
& m2_relset_1(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) )
=> ~ ( v5_pre_topc(I,k5_topmetr,k15_euclid(A))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)),I),G)
& k1_funct_1(I,np__0) = C
& k1_funct_1(I,np__1) = E ) ) ) ) ) ) ) ) ) ) ) ).
fof(t87_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( 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] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ~ ( v2_connsp_1(B,k15_euclid(A))
& v3_pre_topc(B,k15_euclid(A))
& r2_hidden(C,B)
& r2_hidden(D,B)
& C != D
& ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)))
& m2_relset_1(E,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) )
=> ~ ( v5_pre_topc(E,k5_topmetr,k15_euclid(A))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)),E),B)
& k1_funct_1(E,np__0) = C
& k1_funct_1(E,np__1) = D ) ) ) ) ) ) ) ).
fof(t89_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
=> ( v3_pre_topc(B,k15_euclid(A))
=> v1_connsp_2(k3_pre_topc(k15_euclid(A),B)) ) ) ) ).
fof(t91_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k15_euclid(A)),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(k15_euclid(A)),u1_struct_0(k3_topmetr)) )
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> k8_funct_2(u1_struct_0(k15_euclid(A)),u1_struct_0(k3_topmetr),B,C) = k5_toprns_1(A,C) )
=> v5_pre_topc(B,k15_euclid(A),k3_topmetr) ) ) ) ).
fof(t92_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ? [B] :
( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k15_euclid(A)),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(k15_euclid(A)),u1_struct_0(k3_topmetr))
& ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> k8_funct_2(u1_struct_0(k15_euclid(A)),u1_struct_0(k3_topmetr),B,C) = k5_toprns_1(A,C) )
& v5_pre_topc(B,k15_euclid(A),k3_topmetr) ) ) ).
fof(d9_jordan2c,axiom,
$true ).
fof(d10_jordan2c,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_struct_0(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)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k6_jordan2c(A,B,C,D) = k1_funct_1(C,D) ) ) ) ) ).
fof(t93_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)))
& m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) )
=> ~ ( v5_pre_topc(B,k5_topmetr,k15_euclid(A))
& ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr))
& m2_relset_1(C,u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr)) )
=> ~ ( ! [D] :
( m1_subset_1(D,u1_struct_0(k5_topmetr))
=> k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr),C,D) = k5_toprns_1(A,k8_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)),B,D)) )
& v5_pre_topc(C,k5_topmetr,k3_topmetr) ) ) ) ) ) ).
fof(t94_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)))
& m2_relset_1(B,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) )
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( v5_pre_topc(B,k5_topmetr,k15_euclid(A))
& r1_xreal_0(k5_toprns_1(A,k6_jordan2c(k5_topmetr,k15_euclid(A),B,np__0)),C)
& r1_xreal_0(C,k5_toprns_1(A,k6_jordan2c(k5_topmetr,k15_euclid(A),B,np__1)))
& ! [D] :
( m1_subset_1(D,u1_struct_0(k5_topmetr))
=> k5_toprns_1(A,k6_jordan2c(k5_topmetr,k15_euclid(A),B,D)) != C ) ) ) ) ) ).
fof(t95_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(A)))
=> ( C = k13_binarith(k1_numbers,B)
=> k5_toprns_1(A,C) = k18_complex1(B) ) ) ) ) ).
fof(t97_jordan2c,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)))) )
=> ( k3_finseq_1(k3_goboard2(k1_sprect_1(A))) = np__2
& k1_matrix_1(k3_goboard2(k1_sprect_1(A))) = np__2
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_sprect_1(A),np__1) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(k1_sprect_1(A)),np__1,np__2)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_sprect_1(A),np__2) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(k1_sprect_1(A)),np__2,np__2)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_sprect_1(A),np__3) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(k1_sprect_1(A)),np__2,np__1)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_sprect_1(A),np__4) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(k1_sprect_1(A)),np__1,np__1)
& k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),k1_sprect_1(A),np__5) = k3_matrix_1(u1_struct_0(k15_euclid(np__2)),k3_goboard2(k1_sprect_1(A)),np__1,np__2) ) ) ).
fof(t98_jordan2c,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)))) )
=> ~ v1_jordan2c(k2_goboard9(k1_sprect_1(A)),np__2) ) ).
fof(t99_jordan2c,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)))) )
=> r1_tarski(k2_goboard9(k1_sprect_1(A)),k2_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A)))) ) ).
fof(t100_jordan2c,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r3_connsp_1(A,B)
& r3_connsp_1(A,C)
& v2_connsp_1(D,A) )
=> ( r1_xboole_0(B,D)
| r1_xboole_0(C,D)
| B = C ) ) ) ) ) ) ).
fof(t101_jordan2c,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] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( r4_connsp_1(k15_euclid(np__2),k3_subset_1(u1_struct_0(k15_euclid(np__2)),k5_topreal1(np__2,k1_sprect_1(A))),B)
=> ( v1_jordan2c(B,np__2)
| B = k2_goboard9(k1_sprect_1(A)) ) ) ) ) ).
fof(t102_jordan2c,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)))) )
=> ( r1_tarski(k3_goboard9(k1_sprect_1(A)),k1_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A))))
& v1_jordan2c(k3_goboard9(k1_sprect_1(A)),np__2) ) ) ).
fof(t103_jordan2c,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)))) )
=> ( k2_goboard9(k1_sprect_1(A)) = k2_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A)))
& k3_goboard9(k1_sprect_1(A)) = k1_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A))) ) ) ).
fof(t104_jordan2c,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)))) )
=> ( k2_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A))) != k1_xboole_0
& r2_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A)),k2_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A))))
& k1_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A))) != k1_xboole_0
& r1_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A)),k1_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A)))) ) ) ).
fof(t105_jordan2c,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( k3_subset_1(u1_struct_0(A),B) != k1_xboole_0
=> ( v2_tops_1(B,A)
<=> ! [C,D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r2_hidden(C,B)
& r2_hidden(C,D)
& v3_pre_topc(D,A)
& ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( r4_connsp_1(A,k3_subset_1(u1_struct_0(A),B),E)
& ~ r1_xboole_0(D,E) ) ) ) ) ) ) ) ) ).
fof(t106_jordan2c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( k3_subset_1(u1_struct_0(k15_euclid(np__2)),A) != k1_xboole_0
=> ( ( v2_tops_1(A,k15_euclid(np__2))
& v2_jordan1(A) )
<=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
& 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)
& A = k6_subset_1(u1_struct_0(k15_euclid(np__2)),k6_pre_topc(k15_euclid(np__2),B),B)
& ! [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(t107_jordan2c,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( ( r1_xreal_0(np__1,A)
& C = k1_struct_0(k15_euclid(A),B) )
=> v2_tops_1(C,k15_euclid(A)) ) ) ) ) ).
fof(t108_jordan2c,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,k1_numbers)
=> ( ( k21_euclid(A) = k22_euclid(B)
& k7_binop_2(k22_euclid(A)) = k21_euclid(B)
& A = k18_euclid(C,np__2,B) )
=> ( k21_euclid(A) = np__0
& k22_euclid(A) = np__0
& A = k16_euclid(np__2) ) ) ) ) ) ).
fof(t109_jordan2c,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)))
=> v2_tops_1(k3_topreal1(np__2,A,B),k15_euclid(np__2)) ) ) ).
fof(t110_jordan2c,axiom,
! [A] :
( m2_finseq_1(A,u1_struct_0(k15_euclid(np__2)))
=> v2_tops_1(k5_topreal1(np__2,A),k15_euclid(np__2)) ) ).
fof(t111_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k14_euclid(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> ( ( D = C
& r2_hidden(E,k9_metric_1(k14_euclid(A),C,B)) )
=> ( ~ r1_xreal_0(B,k5_toprns_1(A,k20_euclid(A,D,E)))
& ~ r1_xreal_0(B,k5_toprns_1(A,k20_euclid(A,E,D))) ) ) ) ) ) ) ) ).
fof(t112_jordan2c,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] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( ~ r1_xreal_0(B,np__0)
& r2_hidden(C,k5_topreal1(np__2,k1_sprect_1(A)))
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(D,k2_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A))))
& ~ r1_xreal_0(B,k5_toprns_1(np__2,k20_euclid(np__2,C,D))) ) ) ) ) ) ) ).
fof(t113_jordan2c,axiom,
k1_euclid(np__0) = k1_struct_0(k15_euclid(np__0),k16_euclid(np__0)) ).
fof(t114_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( v1_jordan2c(B,A)
=> v1_jordan2c(k1_jordan2c(A,B),A) ) ) ) ).
fof(t115_jordan2c,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r3_connsp_1(A,B)
& r3_connsp_1(A,C)
& r3_connsp_1(A,D)
& k4_subset_1(u1_struct_0(A),B,C) = u1_struct_0(A)
& r1_xboole_0(D,B) )
=> D = C ) ) ) ) ) ) ).
fof(t116_jordan2c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( v1_jordan2c(A,np__2)
& v2_jordan1(A) )
=> r1_jordan2c(np__2,A,k1_jordan2c(np__2,A)) ) ) ).
fof(t117_jordan2c,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] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__2)))
=> ~ ( ~ r1_xreal_0(B,np__0)
& r2_hidden(C,k5_topreal1(np__2,k1_sprect_1(A)))
& ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(np__2)))
=> ~ ( r2_hidden(D,k1_jordan2c(np__2,k5_topreal1(np__2,k1_sprect_1(A))))
& ~ r1_xreal_0(B,k5_toprns_1(np__2,k20_euclid(np__2,C,D))) ) ) ) ) ) ) ).
fof(t118_jordan2c,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
=> ( r1_xreal_0(k18_pscomp_1(k5_topreal1(np__2,A)),k21_euclid(B))
| r2_hidden(B,k2_goboard9(A)) ) ) ) ) ).
fof(t119_jordan2c,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
=> ( r1_xreal_0(k21_euclid(B),k20_pscomp_1(k5_topreal1(np__2,A)))
| r2_hidden(B,k2_goboard9(A)) ) ) ) ) ).
fof(t120_jordan2c,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
=> ( r1_xreal_0(k21_pscomp_1(k5_topreal1(np__2,A)),k22_euclid(B))
| r2_hidden(B,k2_goboard9(A)) ) ) ) ) ).
fof(t121_jordan2c,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& ~ v5_seqm_3(A)
& v1_topreal1(A)
& v2_topreal1(A)
& v1_finseq_6(A,u1_struct_0(k15_euclid(np__2)))
& v1_goboard5(A)
& v2_goboard5(A)
& v1_sprect_2(A)
& m2_finseq_1(A,u1_struct_0(k15_euclid(np__2))) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k15_euclid(np__2)))
=> ( k4_finseq_4(k5_numbers,u1_struct_0(k15_euclid(np__2)),A,np__1) = k32_pscomp_1(k5_topreal1(np__2,A))
=> ( r1_xreal_0(k22_euclid(B),k19_pscomp_1(k5_topreal1(np__2,A)))
| r2_hidden(B,k2_goboard9(A)) ) ) ) ) ).
fof(dt_k1_jordan2c,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
=> m1_subset_1(k1_jordan2c(A,B),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ).
fof(dt_k2_jordan2c,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
=> m1_subset_1(k2_jordan2c(A,B),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ).
fof(dt_k3_jordan2c,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> m2_finseq_1(k3_jordan2c(A),k1_numbers) ) ).
fof(dt_k4_jordan2c,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> m2_finseq_2(k4_jordan2c(A),k1_numbers,k1_euclid(A)) ) ).
fof(redefinition_k4_jordan2c,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> k4_jordan2c(A) = k3_jordan2c(A) ) ).
fof(dt_k5_jordan2c,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> m1_subset_1(k5_jordan2c(A),u1_struct_0(k15_euclid(A))) ) ).
fof(dt_k6_jordan2c,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A)
& ~ v3_struct_0(B)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> m1_subset_1(k6_jordan2c(A,B,C,D),u1_struct_0(B)) ) ).
fof(d5_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> k1_jordan2c(A,B) = k3_tarski(a_2_0_jordan2c(A,B)) ) ) ).
fof(d6_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> k2_jordan2c(A,B) = k3_tarski(a_2_1_jordan2c(A,B)) ) ) ).
fof(t49_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> ~ ( C = a_2_2_jordan2c(A,B)
& r2_hidden(D,C)
& r2_hidden(E,C)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( D != k18_euclid(F,A,E)
& E != k18_euclid(F,A,D) ) )
& ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(A)))
=> ~ ( r2_hidden(F,C)
& r2_hidden(G,C)
& r1_tarski(k3_topreal1(A,D,F),C)
& r1_tarski(k3_topreal1(A,F,G),C)
& r1_tarski(k3_topreal1(A,G,E),C) ) ) ) ) ) ) ) ) ) ).
fof(t50_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> ~ ( C = k4_xboole_0(k1_euclid(A),a_2_3_jordan2c(A,B))
& r2_hidden(D,C)
& r2_hidden(E,C)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( D != k18_euclid(F,A,E)
& E != k18_euclid(F,A,D) ) )
& ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(A)))
=> ~ ( r2_hidden(F,C)
& r2_hidden(G,C)
& r1_tarski(k3_topreal1(A,D,F),C)
& r1_tarski(k3_topreal1(A,F,G),C)
& r1_tarski(k3_topreal1(A,G,E),C) ) ) ) ) ) ) ) ) ) ).
fof(t56_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> ~ ( r1_xreal_0(np__2,A)
& C = a_2_2_jordan2c(A,B)
& r2_hidden(D,C)
& r2_hidden(E,C)
& ~ ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( D != k18_euclid(F,A,E)
& E != k18_euclid(F,A,D) ) )
& ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(A)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k15_euclid(A)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k15_euclid(A)))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(k15_euclid(A)))
=> ~ ( r2_hidden(F,C)
& r2_hidden(G,C)
& r2_hidden(H,C)
& r2_hidden(I,C)
& r2_hidden(J,C)
& r1_tarski(k3_topreal1(A,D,F),C)
& r1_tarski(k3_topreal1(A,F,G),C)
& r1_tarski(k3_topreal1(A,G,H),C)
& r1_tarski(k3_topreal1(A,H,I),C)
& r1_tarski(k3_topreal1(A,I,J),C)
& r1_tarski(k3_topreal1(A,J,E),C) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t57_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(A)))
=> ~ ( r1_xreal_0(np__2,A)
& C = k4_xboole_0(k1_euclid(A),a_2_3_jordan2c(A,B))
& r2_hidden(D,C)
& r2_hidden(E,C)
& ~ ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( D != k18_euclid(F,A,E)
& E != k18_euclid(F,A,D) ) )
& ! [F] :
( m1_subset_1(F,u1_struct_0(k15_euclid(A)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k15_euclid(A)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k15_euclid(A)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k15_euclid(A)))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(k15_euclid(A)))
=> ~ ( r2_hidden(F,C)
& r2_hidden(G,C)
& r2_hidden(H,C)
& r2_hidden(I,C)
& r2_hidden(J,C)
& r1_tarski(k3_topreal1(A,D,F),C)
& r1_tarski(k3_topreal1(A,F,G),C)
& r1_tarski(k3_topreal1(A,G,H),C)
& r1_tarski(k3_topreal1(A,H,I),C)
& r1_tarski(k3_topreal1(A,I,J),C)
& r1_tarski(k3_topreal1(A,J,E),C) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t58_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ~ ( r1_xreal_0(np__1,A)
& a_2_2_jordan2c(A,B) = k1_xboole_0 ) ) ) ).
fof(t59_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( ( r1_xreal_0(np__2,A)
& C = a_2_2_jordan2c(A,B) )
=> v2_connsp_1(C,k15_euclid(A)) ) ) ) ) ).
fof(t60_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ~ ( r1_xreal_0(np__1,A)
& k4_xboole_0(k1_euclid(A),a_2_3_jordan2c(A,B)) = k1_xboole_0 ) ) ) ).
fof(t61_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( ( r1_xreal_0(np__2,A)
& C = k4_xboole_0(k1_euclid(A),a_2_3_jordan2c(A,B)) )
=> v2_connsp_1(C,k15_euclid(A)) ) ) ) ) ).
fof(t62_jordan2c,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B))))
=> ~ ( r1_xreal_0(np__1,B)
& C = k4_xboole_0(k1_euclid(B),a_2_4_jordan2c(A,B))
& v1_jordan2c(C,B) ) ) ) ) ).
fof(t63_jordan2c,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__1))))
=> ( B = a_1_0_jordan2c(A)
=> v1_jordan1(B,np__1) ) ) ) ).
fof(t64_jordan2c,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__1))))
=> ( B = a_1_1_jordan2c(A)
=> v1_jordan1(B,np__1) ) ) ) ).
fof(t65_jordan2c,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__1))))
=> ( B = a_1_0_jordan2c(A)
=> v2_connsp_1(B,k15_euclid(np__1)) ) ) ) ).
fof(t66_jordan2c,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__1))))
=> ( B = a_1_1_jordan2c(A)
=> v2_connsp_1(B,k15_euclid(np__1)) ) ) ) ).
fof(t67_jordan2c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k14_euclid(np__1))))
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__1))))
=> ( ( A = a_1_0_jordan2c(B)
& C = A )
=> ( v2_connsp_1(C,k15_euclid(np__1))
& ~ v6_tbsp_1(A,k14_euclid(np__1)) ) ) ) ) ) ).
fof(t68_jordan2c,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k14_euclid(np__1))))
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(np__1))))
=> ( ( A = a_1_1_jordan2c(B)
& C = A )
=> ( v2_connsp_1(C,k15_euclid(np__1))
& ~ v6_tbsp_1(A,k14_euclid(np__1)) ) ) ) ) ) ).
fof(t69_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k14_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( ( r1_xreal_0(np__2,A)
& B = a_2_2_jordan2c(A,C)
& D = B )
=> ( v2_connsp_1(D,k15_euclid(A))
& ~ v6_tbsp_1(B,k14_euclid(A)) ) ) ) ) ) ) ).
fof(t70_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k14_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( ( r1_xreal_0(np__2,A)
& B = k4_xboole_0(k1_euclid(A),a_2_3_jordan2c(A,C))
& D = B )
=> ( v2_connsp_1(D,k15_euclid(A))
& ~ v6_tbsp_1(B,k14_euclid(A)) ) ) ) ) ) ) ).
fof(t75_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k14_euclid(A))))
& C = a_2_3_jordan2c(A,B) )
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k14_euclid(A))))
=> ( C = a_2_3_jordan2c(A,B)
=> v6_tbsp_1(C,k14_euclid(A)) ) ) ) ) ) ).
fof(t77_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( C = a_2_3_jordan2c(A,B)
=> v1_jordan1(C,A) ) ) ) ) ).
fof(t79_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( C = a_2_3_jordan2c(A,B)
=> v2_connsp_1(C,k15_euclid(A)) ) ) ) ) ).
fof(t83_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( 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] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( ( v2_connsp_1(B,k15_euclid(A))
& v3_pre_topc(B,k15_euclid(A))
& D = a_3_0_jordan2c(A,B,C) )
=> v3_pre_topc(D,k15_euclid(A)) ) ) ) ) ) ).
fof(t84_jordan2c,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( ( v2_connsp_1(C,k15_euclid(A))
& v3_pre_topc(C,k15_euclid(A))
& r2_hidden(B,C)
& D = a_3_1_jordan2c(A,B,C) )
=> v3_pre_topc(D,k15_euclid(A)) ) ) ) ) ) ).
fof(t85_jordan2c,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,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ( ( r2_hidden(B,D)
& C = a_3_1_jordan2c(A,B,D) )
=> r1_tarski(C,D) ) ) ) ) ) ).
fof(t86_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(A)))
=> ( ( v2_connsp_1(C,k15_euclid(A))
& v3_pre_topc(C,k15_euclid(A))
& r2_hidden(D,C)
& B = a_3_2_jordan2c(A,C,D) )
=> r1_tarski(C,B) ) ) ) ) ) ).
fof(t88_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( v1_xreal_0(C)
=> ( B = a_2_5_jordan2c(A,C)
=> ( v3_pre_topc(k3_subset_1(u1_struct_0(k15_euclid(A)),B),k15_euclid(A))
& v4_pre_topc(B,k15_euclid(A)) ) ) ) ) ) ).
fof(t90_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [D] :
( v1_xreal_0(D)
=> ( ( C = a_2_5_jordan2c(A,D)
& k3_subset_1(u1_struct_0(k15_euclid(A)),C) = B )
=> v1_connsp_2(k3_pre_topc(k15_euclid(A),B)) ) ) ) ) ) ).
fof(t96_jordan2c,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( r1_xreal_0(np__1,A)
& ~ r1_xreal_0(C,np__0)
& B = a_2_6_jordan2c(A,C)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A))))
=> ~ ( r1_jordan2c(A,B,D)
& D = k1_jordan2c(A,B) ) ) ) ) ) ) ).
fof(fraenkel_a_2_0_jordan2c,axiom,
! [A,B,C] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) )
=> ( r2_hidden(A,a_2_0_jordan2c(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B))))
& A = D
& r1_jordan2c(B,C,D) ) ) ) ).
fof(fraenkel_a_2_1_jordan2c,axiom,
! [A,B,C] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) )
=> ( r2_hidden(A,a_2_1_jordan2c(B,C))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B))))
& A = D
& r2_jordan2c(B,C,D) ) ) ) ).
fof(fraenkel_a_2_2_jordan2c,axiom,
! [A,B,C] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m1_subset_1(C,k1_numbers) )
=> ( r2_hidden(A,a_2_2_jordan2c(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(B)))
& A = D
& ~ r1_xreal_0(k5_toprns_1(B,D),C) ) ) ) ).
fof(fraenkel_a_2_3_jordan2c,axiom,
! [A,B,C] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m1_subset_1(C,k1_numbers) )
=> ( r2_hidden(A,a_2_3_jordan2c(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(B)))
& A = D
& ~ r1_xreal_0(C,k5_toprns_1(B,D)) ) ) ) ).
fof(fraenkel_a_2_4_jordan2c,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_numbers)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(A,a_2_4_jordan2c(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(C)))
& A = D
& ~ r1_xreal_0(B,k5_toprns_1(C,D)) ) ) ) ).
fof(fraenkel_a_1_0_jordan2c,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(A,a_1_0_jordan2c(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__1)))
& A = C
& ? [D] :
( m1_subset_1(D,k1_numbers)
& C = k13_binarith(k1_numbers,D)
& ~ r1_xreal_0(D,B) ) ) ) ) ).
fof(fraenkel_a_1_1_jordan2c,axiom,
! [A,B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(A,a_1_1_jordan2c(B))
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(k15_euclid(np__1)))
& A = C
& ? [D] :
( m1_subset_1(D,k1_numbers)
& C = k13_binarith(k1_numbers,D)
& ~ r1_xreal_0(k7_binop_2(B),D) ) ) ) ) ).
fof(fraenkel_a_3_0_jordan2c,axiom,
! [A,B,C,D] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B))))
& m1_subset_1(D,u1_struct_0(k15_euclid(B))) )
=> ( r2_hidden(A,a_3_0_jordan2c(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(B)))
& A = E
& E != D
& r2_hidden(E,C)
& ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B)))
& m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B))) )
=> ~ ( v5_pre_topc(F,k5_topmetr,k15_euclid(B))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B)),F),C)
& k1_funct_1(F,np__0) = D
& k1_funct_1(F,np__1) = E ) ) ) ) ) ).
fof(fraenkel_a_3_1_jordan2c,axiom,
! [A,B,C,D] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m1_subset_1(C,u1_struct_0(k15_euclid(B)))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) )
=> ( r2_hidden(A,a_3_1_jordan2c(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(B)))
& A = E
& ~ ( E != C
& ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B)))
& m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B))) )
=> ~ ( v5_pre_topc(F,k5_topmetr,k15_euclid(B))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B)),F),D)
& k1_funct_1(F,np__0) = C
& k1_funct_1(F,np__1) = E ) ) ) ) ) ) ).
fof(fraenkel_a_3_2_jordan2c,axiom,
! [A,B,C,D] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B))))
& m1_subset_1(D,u1_struct_0(k15_euclid(B))) )
=> ( r2_hidden(A,a_3_2_jordan2c(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(k15_euclid(B)))
& A = E
& ~ ( E != D
& ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B)))
& m2_relset_1(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B))) )
=> ~ ( v5_pre_topc(F,k5_topmetr,k15_euclid(B))
& r1_tarski(k1_pscomp_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B)),F),C)
& k1_funct_1(F,np__0) = D
& k1_funct_1(F,np__1) = E ) ) ) ) ) ) ).
fof(fraenkel_a_2_5_jordan2c,axiom,
! [A,B,C] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& v1_xreal_0(C) )
=> ( r2_hidden(A,a_2_5_jordan2c(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(B)))
& A = D
& k5_toprns_1(B,D) = C ) ) ) ).
fof(fraenkel_a_2_6_jordan2c,axiom,
! [A,B,C] :
( ( m2_subset_1(B,k1_numbers,k5_numbers)
& m1_subset_1(C,k1_numbers) )
=> ( r2_hidden(A,a_2_6_jordan2c(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(k15_euclid(B)))
& A = D
& k5_toprns_1(B,D) = C ) ) ) ).
%------------------------------------------------------------------------------