SET007 Axioms: SET007+437.ax
%------------------------------------------------------------------------------
% File : SET007+437 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Theorem of Weierstrass
% 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 : weierstr [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 64 ( 0 unt; 0 def)
% Number of atoms : 719 ( 63 equ)
% Maximal formula atoms : 25 ( 11 avg)
% Number of connectives : 771 ( 116 ~; 6 |; 407 &)
% ( 7 <=>; 235 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 12 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 29 ( 28 usr; 0 prp; 1-3 aty)
% Number of functors : 39 ( 39 usr; 6 con; 0-4 aty)
% Number of variables : 235 ( 227 !; 8 ?)
% 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(t1_weierstr,axiom,
! [A] :
( ( v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ? [F] :
( m1_subset_1(F,u1_struct_0(A))
& ? [G] :
( m1_subset_1(G,k1_numbers)
& r1_tarski(k4_subset_1(u1_struct_0(A),k9_metric_1(A,B,D),k9_metric_1(A,C,E)),k9_metric_1(A,F,G)) ) ) ) ) ) ) ) ).
fof(t2_weierstr,axiom,
! [A] :
( ( v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> ~ ( v1_finset_1(C)
& v1_topmetr(C,A)
& k2_relat_1(D) = C
& k4_finseq_1(D) = k2_finseq_1(k1_nat_1(B,np__1))
& ! [E] :
( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ~ ( v1_finset_1(E)
& v1_topmetr(E,A)
& ? [F] :
( v1_relat_1(F)
& v1_funct_1(F)
& v1_finseq_1(F)
& k2_relat_1(F) = E
& k4_finseq_1(F) = k2_finseq_1(B)
& ? [G] :
( m1_subset_1(G,u1_struct_0(A))
& ? [H] :
( m1_subset_1(H,k1_numbers)
& r1_tarski(k3_tarski(C),k2_xboole_0(k3_tarski(E),k9_metric_1(A,G,H))) ) ) ) ) ) ) ) ) ) ) ).
fof(t3_weierstr,axiom,
! [A] :
( ( v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ~ ( v1_finset_1(B)
& v1_topmetr(B,A)
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ r1_tarski(k3_tarski(B),k9_metric_1(A,C,D)) ) ) ) ) ) ).
fof(d1_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(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)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( E = k1_weierstr(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
=> ( r2_hidden(F,E)
<=> ? [G] :
( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(B)))
& r2_hidden(G,D)
& F = k5_pre_topc(A,B,C,G) ) ) ) ) ) ) ) ) ) ).
fof(t4_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(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)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B))))
=> ( r1_tarski(D,E)
=> r1_tarski(k1_weierstr(A,B,C,D),k1_weierstr(A,B,C,E)) ) ) ) ) ) ) ).
fof(t5_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(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)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B))))
=> ( ( v5_pre_topc(C,A,B)
& v1_tops_2(D,B) )
=> v1_tops_2(k1_weierstr(A,B,C,D),A) ) ) ) ) ) ).
fof(d2_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(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)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B))))
=> ( E = k2_weierstr(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
=> ( r2_hidden(F,E)
<=> ? [G] :
( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A)))
& r2_hidden(G,D)
& F = k4_pre_topc(A,B,C,G) ) ) ) ) ) ) ) ) ) ).
fof(t6_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(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)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( r1_tarski(D,E)
=> r1_tarski(k2_weierstr(A,B,C,D),k2_weierstr(A,B,C,E)) ) ) ) ) ) ) ).
fof(t7_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(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)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ( r1_compts_1(B,k2_weierstr(A,B,C,k1_weierstr(A,B,C,D)),E)
=> r1_compts_1(B,D,E) ) ) ) ) ) ) ).
fof(t8_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(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)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( r1_compts_1(A,D,E)
=> r1_compts_1(A,k1_weierstr(A,B,C,k2_weierstr(A,B,C,D)),E) ) ) ) ) ) ) ).
fof(t9_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(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)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B))))
=> r1_tarski(k3_tarski(k2_weierstr(A,B,C,k1_weierstr(A,B,C,D))),k3_tarski(D)) ) ) ) ) ).
fof(t10_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(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)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> r1_tarski(k3_tarski(D),k3_tarski(k1_weierstr(A,B,C,k2_weierstr(A,B,C,D)))) ) ) ) ) ).
fof(t11_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(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)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B))))
=> ( v1_finset_1(D)
=> v1_finset_1(k1_weierstr(A,B,C,D)) ) ) ) ) ) ).
fof(t12_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(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)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
=> ( v1_finset_1(D)
=> v1_finset_1(k2_weierstr(A,B,C,D)) ) ) ) ) ) ).
fof(t13_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(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)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B))))
=> ~ ( ? [F] :
( m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
& r1_tarski(F,k1_weierstr(A,B,C,E))
& r1_compts_1(A,F,D)
& v1_finset_1(F) )
& ! [F] :
( m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B))))
=> ~ ( r1_tarski(F,E)
& r1_compts_1(B,F,k4_pre_topc(A,B,C,D))
& v1_finset_1(F) ) ) ) ) ) ) ) ) ).
fof(t14_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_pre_topc(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)) )
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v6_compts_1(D,A)
& v5_pre_topc(C,A,B) )
=> v6_compts_1(k4_pre_topc(A,B,C,D),B) ) ) ) ) ) ).
fof(t15_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v6_compts_1(C,A)
& v5_pre_topc(B,A,k3_topmetr) )
=> v6_compts_1(k4_pre_topc(A,k3_topmetr,B,C),k3_topmetr) ) ) ) ) ).
fof(t16_weierstr,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k3_topmetr))
& m2_relset_1(A,u1_struct_0(k15_euclid(np__2)),u1_struct_0(k3_topmetr)) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(np__2))))
=> ( ( v6_compts_1(B,k15_euclid(np__2))
& v5_pre_topc(A,k15_euclid(np__2),k3_topmetr) )
=> v6_compts_1(k4_pre_topc(k15_euclid(np__2),k3_topmetr,A,B),k3_topmetr) ) ) ) ).
fof(d3_weierstr,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> k3_weierstr(A) = A ) ).
fof(t17_weierstr,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ( v6_compts_1(A,k3_topmetr)
=> v3_seq_4(k3_weierstr(A)) ) ) ).
fof(t18_weierstr,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ( v6_compts_1(A,k3_topmetr)
=> v2_rcomp_1(k3_weierstr(A)) ) ) ).
fof(t19_weierstr,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> ( v6_compts_1(A,k3_topmetr)
=> v1_rcomp_1(k3_weierstr(A)) ) ) ).
fof(d4_weierstr,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> k4_weierstr(A) = k4_seq_4(k3_weierstr(A)) ) ).
fof(d5_weierstr,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> k5_weierstr(A) = k5_seq_4(k3_weierstr(A)) ) ).
fof(t20_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( C != k1_xboole_0
& v6_compts_1(C,A)
& v5_pre_topc(B,A,k3_topmetr)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,D) = k4_weierstr(k4_pre_topc(A,k3_topmetr,B,C)) ) ) ) ) ) ) ).
fof(t21_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( C != k1_xboole_0
& v6_compts_1(C,A)
& v5_pre_topc(B,A,k3_topmetr)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& k8_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,D) = k5_weierstr(k4_pre_topc(A,k3_topmetr,B,C)) ) ) ) ) ) ) ).
fof(d6_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k5_pcomps_1(A)),u1_struct_0(k3_topmetr))
& m2_relset_1(C,u1_struct_0(k5_pcomps_1(A)),u1_struct_0(k3_topmetr)) )
=> ( C = k6_weierstr(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_funct_1(C,D) = k4_metric_1(A,D,B) ) ) ) ) ) ).
fof(t22_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> v5_pre_topc(k6_weierstr(A,B),k5_pcomps_1(A),k3_topmetr) ) ) ).
fof(t23_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ~ ( C != k1_xboole_0
& v6_compts_1(C,k5_pcomps_1(A))
& ! [D] :
( m1_subset_1(D,u1_struct_0(k5_pcomps_1(A)))
=> ~ ( r2_hidden(D,C)
& k8_funct_2(u1_struct_0(k5_pcomps_1(A)),u1_struct_0(k3_topmetr),k6_weierstr(A,B),D) = k4_weierstr(k4_pre_topc(k5_pcomps_1(A),k3_topmetr,k6_weierstr(A,B),C)) ) ) ) ) ) ) ).
fof(t24_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ~ ( C != k1_xboole_0
& v6_compts_1(C,k5_pcomps_1(A))
& ! [D] :
( m1_subset_1(D,u1_struct_0(k5_pcomps_1(A)))
=> ~ ( r2_hidden(D,C)
& k8_funct_2(u1_struct_0(k5_pcomps_1(A)),u1_struct_0(k3_topmetr),k6_weierstr(A,B),D) = k5_weierstr(k4_pre_topc(k5_pcomps_1(A),k3_topmetr,k6_weierstr(A,B),C)) ) ) ) ) ) ) ).
fof(d7_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k5_pcomps_1(A)),u1_struct_0(k3_topmetr))
& m2_relset_1(C,u1_struct_0(k5_pcomps_1(A)),u1_struct_0(k3_topmetr)) )
=> ( C = k7_weierstr(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_funct_1(C,D) = k4_weierstr(k4_pre_topc(k5_pcomps_1(A),k3_topmetr,k6_weierstr(A,D),B)) ) ) ) ) ) ).
fof(d8_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k5_pcomps_1(A)),u1_struct_0(k3_topmetr))
& m2_relset_1(C,u1_struct_0(k5_pcomps_1(A)),u1_struct_0(k3_topmetr)) )
=> ( C = k8_weierstr(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_funct_1(C,D) = k5_weierstr(k4_pre_topc(k5_pcomps_1(A),k3_topmetr,k6_weierstr(A,D),B)) ) ) ) ) ) ).
fof(t25_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ( v6_compts_1(B,k5_pcomps_1(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(C,B)
=> ( r1_xreal_0(k4_metric_1(A,C,D),k4_weierstr(k4_pre_topc(k5_pcomps_1(A),k3_topmetr,k6_weierstr(A,D),B)))
& r1_xreal_0(k5_weierstr(k4_pre_topc(k5_pcomps_1(A),k3_topmetr,k6_weierstr(A,D),B)),k4_metric_1(A,C,D)) ) ) ) ) ) ) ) ).
fof(t26_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ( v6_compts_1(B,k5_pcomps_1(A))
=> ( B = k1_xboole_0
| ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r1_xreal_0(k18_complex1(k5_real_1(k4_weierstr(k4_pre_topc(k5_pcomps_1(A),k3_topmetr,k6_weierstr(A,C),B)),k4_weierstr(k4_pre_topc(k5_pcomps_1(A),k3_topmetr,k6_weierstr(A,D),B)))),k4_metric_1(A,C,D)) ) ) ) ) ) ) ).
fof(t27_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ( v6_compts_1(B,k5_pcomps_1(A))
=> ( B = k1_xboole_0
| ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( ( E = k1_funct_1(k7_weierstr(A,B),C)
& F = k1_funct_1(k7_weierstr(A,B),D) )
=> r1_xreal_0(k18_complex1(k5_real_1(E,F)),k4_metric_1(A,C,D)) ) ) ) ) ) ) ) ) ) ).
fof(t28_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ( v6_compts_1(B,k5_pcomps_1(A))
=> ( B = k1_xboole_0
| ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r1_xreal_0(k18_complex1(k5_real_1(k5_weierstr(k4_pre_topc(k5_pcomps_1(A),k3_topmetr,k6_weierstr(A,C),B)),k5_weierstr(k4_pre_topc(k5_pcomps_1(A),k3_topmetr,k6_weierstr(A,D),B)))),k4_metric_1(A,C,D)) ) ) ) ) ) ) ).
fof(t29_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ( v6_compts_1(B,k5_pcomps_1(A))
=> ( B = k1_xboole_0
| ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( ( E = k1_funct_1(k8_weierstr(A,B),C)
& F = k1_funct_1(k8_weierstr(A,B),D) )
=> r1_xreal_0(k18_complex1(k5_real_1(E,F)),k4_metric_1(A,C,D)) ) ) ) ) ) ) ) ) ) ).
fof(t30_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ( v6_compts_1(B,k5_pcomps_1(A))
=> ( B = k1_xboole_0
| v5_pre_topc(k7_weierstr(A,B),k5_pcomps_1(A),k3_topmetr) ) ) ) ) ).
fof(t31_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ~ ( B != k1_xboole_0
& v6_compts_1(B,k5_pcomps_1(A))
& C != k1_xboole_0
& v6_compts_1(C,k5_pcomps_1(A))
& ! [D] :
( m1_subset_1(D,u1_struct_0(k5_pcomps_1(A)))
=> ~ ( r2_hidden(D,C)
& k8_funct_2(u1_struct_0(k5_pcomps_1(A)),u1_struct_0(k3_topmetr),k7_weierstr(A,B),D) = k4_weierstr(k4_pre_topc(k5_pcomps_1(A),k3_topmetr,k7_weierstr(A,B),C)) ) ) ) ) ) ) ).
fof(t32_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ~ ( B != k1_xboole_0
& v6_compts_1(B,k5_pcomps_1(A))
& C != k1_xboole_0
& v6_compts_1(C,k5_pcomps_1(A))
& ! [D] :
( m1_subset_1(D,u1_struct_0(k5_pcomps_1(A)))
=> ~ ( r2_hidden(D,C)
& k8_funct_2(u1_struct_0(k5_pcomps_1(A)),u1_struct_0(k3_topmetr),k7_weierstr(A,B),D) = k5_weierstr(k4_pre_topc(k5_pcomps_1(A),k3_topmetr,k7_weierstr(A,B),C)) ) ) ) ) ) ) ).
fof(t33_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ( v6_compts_1(B,k5_pcomps_1(A))
=> ( B = k1_xboole_0
| v5_pre_topc(k8_weierstr(A,B),k5_pcomps_1(A),k3_topmetr) ) ) ) ) ).
fof(t34_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ~ ( B != k1_xboole_0
& v6_compts_1(B,k5_pcomps_1(A))
& C != k1_xboole_0
& v6_compts_1(C,k5_pcomps_1(A))
& ! [D] :
( m1_subset_1(D,u1_struct_0(k5_pcomps_1(A)))
=> ~ ( r2_hidden(D,C)
& k8_funct_2(u1_struct_0(k5_pcomps_1(A)),u1_struct_0(k3_topmetr),k8_weierstr(A,B),D) = k4_weierstr(k4_pre_topc(k5_pcomps_1(A),k3_topmetr,k8_weierstr(A,B),C)) ) ) ) ) ) ) ).
fof(t35_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ~ ( B != k1_xboole_0
& v6_compts_1(B,k5_pcomps_1(A))
& C != k1_xboole_0
& v6_compts_1(C,k5_pcomps_1(A))
& ! [D] :
( m1_subset_1(D,u1_struct_0(k5_pcomps_1(A)))
=> ~ ( r2_hidden(D,C)
& k8_funct_2(u1_struct_0(k5_pcomps_1(A)),u1_struct_0(k3_topmetr),k8_weierstr(A,B),D) = k5_weierstr(k4_pre_topc(k5_pcomps_1(A),k3_topmetr,k8_weierstr(A,B),C)) ) ) ) ) ) ) ).
fof(d9_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> k9_weierstr(A,B,C) = k5_weierstr(k4_pre_topc(k5_pcomps_1(A),k3_topmetr,k8_weierstr(A,B),C)) ) ) ) ).
fof(d10_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> k10_weierstr(A,B,C) = k4_weierstr(k4_pre_topc(k5_pcomps_1(A),k3_topmetr,k8_weierstr(A,B),C)) ) ) ) ).
fof(d11_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> k11_weierstr(A,B,C) = k5_weierstr(k4_pre_topc(k5_pcomps_1(A),k3_topmetr,k7_weierstr(A,B),C)) ) ) ) ).
fof(d12_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> k12_weierstr(A,B,C) = k4_weierstr(k4_pre_topc(k5_pcomps_1(A),k3_topmetr,k7_weierstr(A,B),C)) ) ) ) ).
fof(t36_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ~ ( B != k1_xboole_0
& v6_compts_1(B,k5_pcomps_1(A))
& C != k1_xboole_0
& v6_compts_1(C,k5_pcomps_1(A))
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(D,B)
& r2_hidden(E,C)
& k4_metric_1(A,D,E) = k9_weierstr(A,B,C) ) ) ) ) ) ) ) ).
fof(t37_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ~ ( B != k1_xboole_0
& v6_compts_1(B,k5_pcomps_1(A))
& C != k1_xboole_0
& v6_compts_1(C,k5_pcomps_1(A))
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(D,B)
& r2_hidden(E,C)
& k4_metric_1(A,D,E) = k11_weierstr(A,B,C) ) ) ) ) ) ) ) ).
fof(t38_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ~ ( B != k1_xboole_0
& v6_compts_1(B,k5_pcomps_1(A))
& C != k1_xboole_0
& v6_compts_1(C,k5_pcomps_1(A))
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(D,B)
& r2_hidden(E,C)
& k4_metric_1(A,D,E) = k10_weierstr(A,B,C) ) ) ) ) ) ) ) ).
fof(t39_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ~ ( B != k1_xboole_0
& v6_compts_1(B,k5_pcomps_1(A))
& C != k1_xboole_0
& v6_compts_1(C,k5_pcomps_1(A))
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(D,B)
& r2_hidden(E,C)
& k4_metric_1(A,D,E) = k12_weierstr(A,B,C) ) ) ) ) ) ) ) ).
fof(t40_weierstr,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
=> ( ( v6_compts_1(B,k5_pcomps_1(A))
& v6_compts_1(C,k5_pcomps_1(A)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r2_hidden(D,B)
& r2_hidden(E,C) )
=> ( r1_xreal_0(k9_weierstr(A,B,C),k4_metric_1(A,D,E))
& r1_xreal_0(k4_metric_1(A,D,E),k12_weierstr(A,B,C)) ) ) ) ) ) ) ) ) ).
fof(dt_k1_weierstr,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(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(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) )
=> m1_subset_1(k1_weierstr(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_k2_weierstr,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_pre_topc(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(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) )
=> m1_subset_1(k2_weierstr(A,B,C,D),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) ).
fof(dt_k3_weierstr,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> m1_subset_1(k3_weierstr(A),k1_zfmisc_1(k1_numbers)) ) ).
fof(dt_k4_weierstr,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> m1_subset_1(k4_weierstr(A),k1_numbers) ) ).
fof(dt_k5_weierstr,axiom,
! [A] :
( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr)))
=> m1_subset_1(k5_weierstr(A),k1_numbers) ) ).
fof(dt_k6_weierstr,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_funct_1(k6_weierstr(A,B))
& v1_funct_2(k6_weierstr(A,B),u1_struct_0(k5_pcomps_1(A)),u1_struct_0(k3_topmetr))
& m2_relset_1(k6_weierstr(A,B),u1_struct_0(k5_pcomps_1(A)),u1_struct_0(k3_topmetr)) ) ) ).
fof(dt_k7_weierstr,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A)))) )
=> ( v1_funct_1(k7_weierstr(A,B))
& v1_funct_2(k7_weierstr(A,B),u1_struct_0(k5_pcomps_1(A)),u1_struct_0(k3_topmetr))
& m2_relset_1(k7_weierstr(A,B),u1_struct_0(k5_pcomps_1(A)),u1_struct_0(k3_topmetr)) ) ) ).
fof(dt_k8_weierstr,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A)))) )
=> ( v1_funct_1(k8_weierstr(A,B))
& v1_funct_2(k8_weierstr(A,B),u1_struct_0(k5_pcomps_1(A)),u1_struct_0(k3_topmetr))
& m2_relset_1(k8_weierstr(A,B),u1_struct_0(k5_pcomps_1(A)),u1_struct_0(k3_topmetr)) ) ) ).
fof(dt_k9_weierstr,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A)))) )
=> m1_subset_1(k9_weierstr(A,B,C),k1_numbers) ) ).
fof(dt_k10_weierstr,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A)))) )
=> m1_subset_1(k10_weierstr(A,B,C),k1_numbers) ) ).
fof(dt_k11_weierstr,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A)))) )
=> m1_subset_1(k11_weierstr(A,B,C),k1_numbers) ) ).
fof(dt_k12_weierstr,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_metric_1(A)
& v7_metric_1(A)
& v8_metric_1(A)
& v9_metric_1(A)
& l1_metric_1(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A))))
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pcomps_1(A)))) )
=> m1_subset_1(k12_weierstr(A,B,C),k1_numbers) ) ).
%------------------------------------------------------------------------------