SET007 Axioms: SET007+817.ax
%------------------------------------------------------------------------------
% File : SET007+817 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Convergent Sequences in Complex Unitary Space
% 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 : clvect_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 135 ( 0 unt; 0 def)
% Number of atoms : 2110 ( 91 equ)
% Maximal formula atoms : 22 ( 15 avg)
% Number of connectives : 2140 ( 165 ~; 5 |;1434 &)
% ( 24 <=>; 512 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 12 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 30 ( 29 usr; 0 prp; 1-3 aty)
% Number of functors : 41 ( 41 usr; 5 con; 0-4 aty)
% Number of variables : 478 ( 458 !; 20 ?)
% 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(d1_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_clvect_2(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& r1_xreal_0(E,F)
& r1_xreal_0(D,k15_csspace(A,k2_normsp_1(A,B,F),C)) ) ) ) ) ) ) ) ) ).
fof(t1_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v5_seqm_3(B)
=> v1_clvect_2(B,A) ) ) ) ).
fof(t2_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_clvect_2(B,A)
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& r1_xreal_0(D,E)
& k2_normsp_1(A,C,E) != k2_normsp_1(A,B,E) ) )
| v1_clvect_2(C,A) ) ) ) ) ) ).
fof(t3_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(B,A)
& v1_clvect_2(C,A) )
=> v1_clvect_2(k18_csspace(A,B,C),A) ) ) ) ) ).
fof(t4_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(B,A)
& v1_clvect_2(C,A) )
=> v1_clvect_2(k7_clvect_1(A,B,C),A) ) ) ) ) ).
fof(t5_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_clvect_2(C,A)
=> v1_clvect_2(k9_clvect_1(A,C,B),A) ) ) ) ) ).
fof(t6_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_clvect_2(B,A)
=> v1_clvect_2(k16_csspace(A,B),A) ) ) ) ).
fof(t7_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_clvect_2(C,A)
=> v1_clvect_2(k17_csspace(A,C,B),A) ) ) ) ) ).
fof(t8_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_clvect_2(C,A)
=> v1_clvect_2(k8_clvect_1(A,C,B),A) ) ) ) ) ).
fof(t9_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_clvect_2(B,A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& r1_xreal_0(E,F)
& r1_xreal_0(D,k13_csspace(A,k6_rlvect_1(A,k2_normsp_1(A,B,F),C))) ) ) ) ) ) ) ) ) ).
fof(d2_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_clvect_2(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( C = k1_clvect_2(A,B)
<=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& r1_xreal_0(E,F)
& r1_xreal_0(D,k15_csspace(A,k2_normsp_1(A,B,F),C)) ) ) ) ) ) ) ) ) ) ).
fof(t10_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v5_seqm_3(C)
& r2_hidden(B,k2_relat_1(C)) )
=> k1_clvect_2(A,C) = B ) ) ) ) ).
fof(t11_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v5_seqm_3(C)
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_normsp_1(A,C,D) != B )
| k1_clvect_2(A,C) = B ) ) ) ) ) ).
fof(t12_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_clvect_2(B,A)
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& r1_xreal_0(D,E)
& k2_normsp_1(A,C,E) != k2_normsp_1(A,B,E) ) )
| k1_clvect_2(A,B) = k1_clvect_2(A,C) ) ) ) ) ) ).
fof(t13_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(B,A)
& v1_clvect_2(C,A) )
=> k1_clvect_2(A,k18_csspace(A,B,C)) = k4_rlvect_1(A,k1_clvect_2(A,B),k1_clvect_2(A,C)) ) ) ) ) ).
fof(t14_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(B,A)
& v1_clvect_2(C,A) )
=> k1_clvect_2(A,k7_clvect_1(A,B,C)) = k6_rlvect_1(A,k1_clvect_2(A,B),k1_clvect_2(A,C)) ) ) ) ) ).
fof(t15_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_clvect_2(C,A)
=> k1_clvect_2(A,k9_clvect_1(A,C,B)) = k1_clvect_1(A,k1_clvect_2(A,C),B) ) ) ) ) ).
fof(t16_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_clvect_2(B,A)
=> k1_clvect_2(A,k16_csspace(A,B)) = k5_rlvect_1(A,k1_clvect_2(A,B)) ) ) ) ).
fof(t17_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_clvect_2(C,A)
=> k1_clvect_2(A,k17_csspace(A,C,B)) = k4_rlvect_1(A,k1_clvect_2(A,C),B) ) ) ) ) ).
fof(t18_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_clvect_2(C,A)
=> k1_clvect_2(A,k8_clvect_1(A,C,B)) = k6_rlvect_1(A,k1_clvect_2(A,C),B) ) ) ) ) ).
fof(t19_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_clvect_2(C,A)
=> ( k1_clvect_2(A,C) = B
<=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& r1_xreal_0(E,F)
& r1_xreal_0(D,k13_csspace(A,k6_rlvect_1(A,k2_normsp_1(A,C,F),B))) ) ) ) ) ) ) ) ) ) ).
fof(d3_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ( C = k2_clvect_2(A,B)
<=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,C,D) = k13_csspace(A,k2_normsp_1(A,B,D)) ) ) ) ) ) ).
fof(t20_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_clvect_2(B,A)
=> v4_seq_2(k2_clvect_2(A,B)) ) ) ) ).
fof(t21_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(C,A)
& k1_clvect_2(A,C) = B )
=> ( v4_seq_2(k2_clvect_2(A,C))
& k2_seq_2(k2_clvect_2(A,C)) = k13_csspace(A,B) ) ) ) ) ) ).
fof(t22_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(C,A)
& k1_clvect_2(A,C) = B )
=> ( v4_seq_2(k2_clvect_2(A,k8_clvect_1(A,C,B)))
& k2_seq_2(k2_clvect_2(A,k8_clvect_1(A,C,B))) = np__0 ) ) ) ) ) ).
fof(d4_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_numbers)
& m2_relset_1(D,k5_numbers,k1_numbers) )
=> ( D = k3_clvect_2(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k2_seq_1(k5_numbers,k1_numbers,D,E) = k15_csspace(A,k2_normsp_1(A,B,E),C) ) ) ) ) ) ) ).
fof(t23_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(C,A)
& k1_clvect_2(A,C) = B )
=> v4_seq_2(k3_clvect_2(A,C,B)) ) ) ) ) ).
fof(t24_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(C,A)
& k1_clvect_2(A,C) = B )
=> ( v4_seq_2(k3_clvect_2(A,C,B))
& k2_seq_2(k3_clvect_2(A,C,B)) = np__0 ) ) ) ) ) ).
fof(t25_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,u1_struct_0(A))
& m2_relset_1(E,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(D,A)
& k1_clvect_2(A,D) = B
& v1_clvect_2(E,A)
& k1_clvect_2(A,E) = C )
=> ( v4_seq_2(k2_clvect_2(A,k18_csspace(A,D,E)))
& k2_seq_2(k2_clvect_2(A,k18_csspace(A,D,E))) = k13_csspace(A,k4_rlvect_1(A,B,C)) ) ) ) ) ) ) ) ).
fof(t26_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,u1_struct_0(A))
& m2_relset_1(E,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(D,A)
& k1_clvect_2(A,D) = B
& v1_clvect_2(E,A)
& k1_clvect_2(A,E) = C )
=> ( v4_seq_2(k2_clvect_2(A,k8_clvect_1(A,k18_csspace(A,D,E),k4_rlvect_1(A,B,C))))
& k2_seq_2(k2_clvect_2(A,k8_clvect_1(A,k18_csspace(A,D,E),k4_rlvect_1(A,B,C)))) = np__0 ) ) ) ) ) ) ) ).
fof(t27_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,u1_struct_0(A))
& m2_relset_1(E,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(D,A)
& k1_clvect_2(A,D) = B
& v1_clvect_2(E,A)
& k1_clvect_2(A,E) = C )
=> ( v4_seq_2(k2_clvect_2(A,k7_clvect_1(A,D,E)))
& k2_seq_2(k2_clvect_2(A,k7_clvect_1(A,D,E))) = k13_csspace(A,k6_rlvect_1(A,B,C)) ) ) ) ) ) ) ) ).
fof(t28_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,u1_struct_0(A))
& m2_relset_1(E,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(D,A)
& k1_clvect_2(A,D) = B
& v1_clvect_2(E,A)
& k1_clvect_2(A,E) = C )
=> ( v4_seq_2(k2_clvect_2(A,k8_clvect_1(A,k7_clvect_1(A,D,E),k6_rlvect_1(A,B,C))))
& k2_seq_2(k2_clvect_2(A,k8_clvect_1(A,k7_clvect_1(A,D,E),k6_rlvect_1(A,B,C)))) = np__0 ) ) ) ) ) ) ) ).
fof(t29_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(D,A)
& k1_clvect_2(A,D) = B )
=> ( v4_seq_2(k2_clvect_2(A,k9_clvect_1(A,D,C)))
& k2_seq_2(k2_clvect_2(A,k9_clvect_1(A,D,C))) = k13_csspace(A,k1_clvect_1(A,B,C)) ) ) ) ) ) ) ).
fof(t30_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(D,A)
& k1_clvect_2(A,D) = B )
=> ( v4_seq_2(k2_clvect_2(A,k8_clvect_1(A,k9_clvect_1(A,D,C),k1_clvect_1(A,B,C))))
& k2_seq_2(k2_clvect_2(A,k8_clvect_1(A,k9_clvect_1(A,D,C),k1_clvect_1(A,B,C)))) = np__0 ) ) ) ) ) ) ).
fof(t31_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(C,A)
& k1_clvect_2(A,C) = B )
=> ( v4_seq_2(k2_clvect_2(A,k16_csspace(A,C)))
& k2_seq_2(k2_clvect_2(A,k16_csspace(A,C))) = k13_csspace(A,k5_rlvect_1(A,B)) ) ) ) ) ) ).
fof(t32_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(C,A)
& k1_clvect_2(A,C) = B )
=> ( v4_seq_2(k2_clvect_2(A,k8_clvect_1(A,k16_csspace(A,C),k5_rlvect_1(A,B))))
& k2_seq_2(k2_clvect_2(A,k8_clvect_1(A,k16_csspace(A,C),k5_rlvect_1(A,B)))) = np__0 ) ) ) ) ) ).
fof(t33_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(D,A)
& k1_clvect_2(A,D) = B )
=> ( v4_seq_2(k2_clvect_2(A,k8_clvect_1(A,k17_csspace(A,D,C),k4_rlvect_1(A,B,C))))
& k2_seq_2(k2_clvect_2(A,k8_clvect_1(A,k17_csspace(A,D,C),k4_rlvect_1(A,B,C)))) = np__0 ) ) ) ) ) ) ).
fof(t34_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(D,A)
& k1_clvect_2(A,D) = B )
=> ( v4_seq_2(k2_clvect_2(A,k8_clvect_1(A,D,C)))
& k2_seq_2(k2_clvect_2(A,k8_clvect_1(A,D,C))) = k13_csspace(A,k6_rlvect_1(A,B,C)) ) ) ) ) ) ) ).
fof(t35_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(D,A)
& k1_clvect_2(A,D) = B )
=> ( v4_seq_2(k2_clvect_2(A,k8_clvect_1(A,k8_clvect_1(A,D,C),k6_rlvect_1(A,B,C))))
& k2_seq_2(k2_clvect_2(A,k8_clvect_1(A,k8_clvect_1(A,D,C),k6_rlvect_1(A,B,C)))) = np__0 ) ) ) ) ) ) ).
fof(t36_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,u1_struct_0(A))
& m2_relset_1(E,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(D,A)
& k1_clvect_2(A,D) = B
& v1_clvect_2(E,A)
& k1_clvect_2(A,E) = C )
=> ( v4_seq_2(k3_clvect_2(A,k18_csspace(A,D,E),k4_rlvect_1(A,B,C)))
& k2_seq_2(k3_clvect_2(A,k18_csspace(A,D,E),k4_rlvect_1(A,B,C))) = np__0 ) ) ) ) ) ) ) ).
fof(t37_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,u1_struct_0(A))
& m2_relset_1(E,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(D,A)
& k1_clvect_2(A,D) = B
& v1_clvect_2(E,A)
& k1_clvect_2(A,E) = C )
=> ( v4_seq_2(k3_clvect_2(A,k7_clvect_1(A,D,E),k6_rlvect_1(A,B,C)))
& k2_seq_2(k3_clvect_2(A,k7_clvect_1(A,D,E),k6_rlvect_1(A,B,C))) = np__0 ) ) ) ) ) ) ) ).
fof(t38_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(D,A)
& k1_clvect_2(A,D) = B )
=> ( v4_seq_2(k3_clvect_2(A,k9_clvect_1(A,D,C),k1_clvect_1(A,B,C)))
& k2_seq_2(k3_clvect_2(A,k9_clvect_1(A,D,C),k1_clvect_1(A,B,C))) = np__0 ) ) ) ) ) ) ).
fof(t39_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(D,A)
& k1_clvect_2(A,D) = B )
=> ( v4_seq_2(k3_clvect_2(A,k17_csspace(A,D,C),k4_rlvect_1(A,B,C)))
& k2_seq_2(k3_clvect_2(A,k17_csspace(A,D,C),k4_rlvect_1(A,B,C))) = np__0 ) ) ) ) ) ) ).
fof(t40_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)
=> ( r2_hidden(B,k4_clvect_2(A,C,D))
<=> ~ r1_xreal_0(D,k13_csspace(A,k6_rlvect_1(A,C,B))) ) ) ) ) ) ).
fof(t41_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)
=> ( r2_hidden(B,k4_clvect_2(A,C,D))
<=> ~ r1_xreal_0(D,k15_csspace(A,C,B)) ) ) ) ) ) ).
fof(t42_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( ~ r1_xreal_0(C,np__0)
=> r2_hidden(B,k4_clvect_2(A,B,C)) ) ) ) ) ).
fof(t43_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ~ ( r2_hidden(B,k4_clvect_2(A,C,E))
& r2_hidden(D,k4_clvect_2(A,C,E))
& r1_xreal_0(k4_real_1(np__2,E),k15_csspace(A,B,D)) ) ) ) ) ) ) ).
fof(t44_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r2_hidden(B,k4_clvect_2(A,C,E))
=> r2_hidden(k6_rlvect_1(A,B,D),k4_clvect_2(A,k6_rlvect_1(A,C,D),E)) ) ) ) ) ) ) ).
fof(t45_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)
=> ( r2_hidden(B,k4_clvect_2(A,C,D))
=> r2_hidden(k6_rlvect_1(A,B,C),k4_clvect_2(A,k1_rlvect_1(A),D)) ) ) ) ) ) ).
fof(t46_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)
=> ( ( r2_hidden(B,k4_clvect_2(A,C,D))
& r1_xreal_0(D,E) )
=> r2_hidden(B,k4_clvect_2(A,C,E)) ) ) ) ) ) ) ).
fof(t47_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)
=> ( r2_hidden(B,k5_clvect_2(A,C,D))
<=> r1_xreal_0(k13_csspace(A,k6_rlvect_1(A,C,B)),D) ) ) ) ) ) ).
fof(t48_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)
=> ( r2_hidden(B,k5_clvect_2(A,C,D))
<=> r1_xreal_0(k15_csspace(A,C,B),D) ) ) ) ) ) ).
fof(t49_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r1_xreal_0(np__0,C)
=> r2_hidden(B,k5_clvect_2(A,B,C)) ) ) ) ) ).
fof(t50_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)
=> ( r2_hidden(B,k4_clvect_2(A,C,D))
=> r2_hidden(B,k5_clvect_2(A,C,D)) ) ) ) ) ) ).
fof(t51_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)
=> ( r2_hidden(B,k6_clvect_2(A,C,D))
<=> k13_csspace(A,k6_rlvect_1(A,C,B)) = D ) ) ) ) ) ).
fof(t52_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)
=> ( r2_hidden(B,k6_clvect_2(A,C,D))
<=> k15_csspace(A,C,B) = D ) ) ) ) ) ).
fof(t53_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(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)
=> ( r2_hidden(B,k6_clvect_2(A,C,D))
=> r2_hidden(B,k5_clvect_2(A,C,D)) ) ) ) ) ) ).
fof(t54_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> r1_tarski(k4_clvect_2(A,B,C),k5_clvect_2(A,B,C)) ) ) ) ).
fof(t55_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> r1_tarski(k6_clvect_2(A,B,C),k5_clvect_2(A,B,C)) ) ) ) ).
fof(t56_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k4_subset_1(u1_struct_0(A),k4_clvect_2(A,B,C),k6_clvect_2(A,B,C)) = k5_clvect_2(A,B,C) ) ) ) ).
fof(d8_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v2_clvect_2(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( ~ r1_xreal_0(C,np__0)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& r1_xreal_0(D,E)
& r1_xreal_0(D,F)
& r1_xreal_0(C,k15_csspace(A,k2_normsp_1(A,B,E),k2_normsp_1(A,B,F))) ) ) ) ) ) ) ) ) ).
fof(t57_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v5_seqm_3(B)
=> v2_clvect_2(B,A) ) ) ) ).
fof(t58_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v2_clvect_2(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( ~ r1_xreal_0(C,np__0)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& r1_xreal_0(D,E)
& r1_xreal_0(D,F)
& r1_xreal_0(C,k13_csspace(A,k6_rlvect_1(A,k2_normsp_1(A,B,E),k2_normsp_1(A,B,F)))) ) ) ) ) ) ) ) ) ).
fof(t59_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v2_clvect_2(B,A)
& v2_clvect_2(C,A) )
=> v2_clvect_2(k18_csspace(A,B,C),A) ) ) ) ) ).
fof(t60_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v2_clvect_2(B,A)
& v2_clvect_2(C,A) )
=> v2_clvect_2(k7_clvect_1(A,B,C),A) ) ) ) ) ).
fof(t61_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v2_clvect_2(C,A)
=> v2_clvect_2(k9_clvect_1(A,C,B),A) ) ) ) ) ).
fof(t62_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v2_clvect_2(B,A)
=> v2_clvect_2(k16_csspace(A,B),A) ) ) ) ).
fof(t63_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v2_clvect_2(C,A)
=> v2_clvect_2(k17_csspace(A,C,B),A) ) ) ) ) ).
fof(t64_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v2_clvect_2(C,A)
=> v2_clvect_2(k8_clvect_1(A,C,B),A) ) ) ) ) ).
fof(t65_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_clvect_2(B,A)
=> v2_clvect_2(B,A) ) ) ) ).
fof(d9_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( r1_clvect_2(A,B,C)
<=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& r1_xreal_0(E,F)
& r1_xreal_0(D,k15_csspace(A,k2_normsp_1(A,B,F),k2_normsp_1(A,C,F))) ) ) ) ) ) ) ) ) ).
fof(t66_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> r1_clvect_2(A,B,B) ) ) ).
fof(t67_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( r1_clvect_2(A,B,C)
=> r1_clvect_2(A,C,B) ) ) ) ) ).
fof(t68_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( ( r2_clvect_2(A,B,C)
& r2_clvect_2(A,C,D) )
=> r2_clvect_2(A,B,D) ) ) ) ) ) ).
fof(t69_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( r2_clvect_2(A,B,C)
<=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ~ ( ~ r1_xreal_0(D,np__0)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& r1_xreal_0(E,F)
& r1_xreal_0(D,k13_csspace(A,k6_rlvect_1(A,k2_normsp_1(A,B,F),k2_normsp_1(A,C,F)))) ) ) ) ) ) ) ) ) ).
fof(t70_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r1_xreal_0(D,E)
=> k2_normsp_1(A,B,E) = k2_normsp_1(A,C,E) ) ) )
=> r2_clvect_2(A,B,C) ) ) ) ) ).
fof(t71_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v2_clvect_2(B,A)
& r2_clvect_2(A,B,C) )
=> v2_clvect_2(C,A) ) ) ) ) ).
fof(t72_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(B,A)
& r2_clvect_2(A,B,C) )
=> v1_clvect_2(C,A) ) ) ) ) ).
fof(t73_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(C,A)
& k1_clvect_2(A,C) = B
& r2_clvect_2(A,C,D) )
=> ( v1_clvect_2(D,A)
& k1_clvect_2(A,D) = B ) ) ) ) ) ) ).
fof(d10_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v3_clvect_2(B,A)
<=> ? [C] :
( m1_subset_1(C,k1_numbers)
& ~ r1_xreal_0(C,np__0)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r1_xreal_0(k13_csspace(A,k2_normsp_1(A,B,D)),C) ) ) ) ) ) ).
fof(t74_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v3_clvect_2(B,A)
& v3_clvect_2(C,A) )
=> v3_clvect_2(k18_csspace(A,B,C),A) ) ) ) ) ).
fof(t75_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v3_clvect_2(B,A)
=> v3_clvect_2(k16_csspace(A,B),A) ) ) ) ).
fof(t76_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v3_clvect_2(B,A)
& v3_clvect_2(C,A) )
=> v3_clvect_2(k7_clvect_1(A,B,C),A) ) ) ) ) ).
fof(t77_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v3_clvect_2(C,A)
=> v3_clvect_2(k9_clvect_1(A,C,B),A) ) ) ) ) ).
fof(t78_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v5_seqm_3(B)
=> v3_clvect_2(B,A) ) ) ) ).
fof(t79_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ? [D] :
( m1_subset_1(D,k1_numbers)
& ~ r1_xreal_0(D,np__0)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(E,C)
& r1_xreal_0(D,k13_csspace(A,k2_normsp_1(A,B,E))) ) ) ) ) ) ) ).
fof(t80_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_clvect_2(B,A)
=> v3_clvect_2(B,A) ) ) ) ).
fof(t81_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v3_clvect_2(B,A)
& r2_clvect_2(A,B,C) )
=> v3_clvect_2(C,A) ) ) ) ) ).
fof(t82_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k1_numbers)
& v1_seqm_3(C)
& v7_seqm_3(C)
& m2_relset_1(C,k5_numbers,k1_numbers) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_normsp_1(A,k7_clvect_2(A,C,B),D) = k2_normsp_1(A,B,k2_seqm_3(C,D)) ) ) ) ) ).
fof(t83_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> m1_bhsp_3(B,A,B) ) ) ).
fof(t84_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( ( m1_bhsp_3(B,A,C)
& m1_bhsp_3(C,A,D) )
=> m1_bhsp_3(B,A,D) ) ) ) ) ) ).
fof(t85_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v5_seqm_3(B)
& m1_bhsp_3(C,A,B) )
=> v5_seqm_3(C) ) ) ) ) ).
fof(t86_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v5_seqm_3(B)
& m1_bhsp_3(C,A,B) )
=> B = C ) ) ) ) ).
fof(t87_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v3_clvect_2(B,A)
& m1_bhsp_3(C,A,B) )
=> v3_clvect_2(C,A) ) ) ) ) ).
fof(t88_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v1_clvect_2(B,A)
& m1_bhsp_3(C,A,B) )
=> v1_clvect_2(C,A) ) ) ) ) ).
fof(t89_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( m1_bhsp_3(B,A,C)
& v1_clvect_2(C,A) )
=> k1_clvect_2(A,B) = k1_clvect_2(A,C) ) ) ) ) ).
fof(t90_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( ( v2_clvect_2(B,A)
& m1_bhsp_3(C,A,B) )
=> v2_clvect_2(C,A) ) ) ) ) ).
fof(d11_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,u1_struct_0(A))
& m2_relset_1(D,k5_numbers,u1_struct_0(A)) )
=> ( D = k8_clvect_2(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k2_normsp_1(A,D,E) = k2_normsp_1(A,B,k1_nat_1(E,C)) ) ) ) ) ) ) ).
fof(t91_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> k8_clvect_2(A,B,np__0) = B ) ) ).
fof(t92_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k8_clvect_2(A,k8_clvect_2(A,B,C),D) = k8_clvect_2(A,k8_clvect_2(A,B,D),C) ) ) ) ) ).
fof(t93_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k8_clvect_2(A,k8_clvect_2(A,B,C),D) = k8_clvect_2(A,B,k1_nat_1(C,D)) ) ) ) ) ).
fof(t94_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k8_clvect_2(A,k18_csspace(A,B,C),D) = k18_csspace(A,k8_clvect_2(A,B,D),k8_clvect_2(A,C,D)) ) ) ) ) ).
fof(t95_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k8_clvect_2(A,k16_csspace(A,B),C) = k16_csspace(A,k8_clvect_2(A,B,C)) ) ) ) ).
fof(t96_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k8_clvect_2(A,k7_clvect_1(A,B,C),D) = k7_clvect_1(A,k8_clvect_2(A,B,D),k8_clvect_2(A,C,D)) ) ) ) ) ).
fof(t97_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k8_clvect_2(A,k9_clvect_1(A,C,B),D) = k9_clvect_1(A,k8_clvect_2(A,C,D),B) ) ) ) ) ).
fof(t98_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k5_numbers,k1_numbers)
& v1_seqm_3(D)
& v7_seqm_3(D)
& m2_relset_1(D,k5_numbers,k1_numbers) )
=> k8_clvect_2(A,k7_clvect_2(A,D,B),C) = k7_clvect_2(A,k1_seqm_3(D,C),B) ) ) ) ) ).
fof(t99_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> m1_bhsp_3(k8_clvect_2(A,B,C),A,B) ) ) ) ).
fof(t100_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( v1_clvect_2(B,A)
=> ( v1_clvect_2(k8_clvect_2(A,B,C),A)
& k1_clvect_2(A,k8_clvect_2(A,B,C)) = k1_clvect_2(A,B) ) ) ) ) ) ).
fof(t101_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_clvect_2(B,A)
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> B != k8_clvect_2(A,C,D) )
| v1_clvect_2(C,A) ) ) ) ) ) ).
fof(t102_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v2_clvect_2(B,A)
=> ( ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> B != k8_clvect_2(A,C,D) )
| v2_clvect_2(C,A) ) ) ) ) ) ).
fof(t103_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( v2_clvect_2(B,A)
=> v2_clvect_2(k8_clvect_2(A,B,C),A) ) ) ) ) ).
fof(t104_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m2_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_clvect_2(A,B,C)
=> r2_clvect_2(A,k8_clvect_2(A,B,D),k8_clvect_2(A,C,D)) ) ) ) ) ) ).
fof(t105_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( v3_clvect_2(B,A)
=> v3_clvect_2(k8_clvect_2(A,B,C),A) ) ) ) ) ).
fof(t106_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( v5_seqm_3(B)
=> v5_seqm_3(k8_clvect_2(A,B,C)) ) ) ) ) ).
fof(d12_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ( v4_clvect_2(A)
<=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v2_clvect_2(B,A)
=> v1_clvect_2(B,A) ) ) ) ) ).
fof(t107_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m2_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( ( v4_clvect_2(A)
& v2_clvect_2(B,A) )
=> v3_clvect_2(B,A) ) ) ) ).
fof(d13_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ( v5_clvect_2(A)
<=> ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& v4_clvect_2(A) ) ) ) ).
fof(symmetry_r2_clvect_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A))
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( r2_clvect_2(A,B,C)
=> r2_clvect_2(A,C,B) ) ) ).
fof(reflexivity_r2_clvect_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A))
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> r2_clvect_2(A,B,B) ) ).
fof(redefinition_r2_clvect_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A))
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( r2_clvect_2(A,B,C)
<=> r1_clvect_2(A,B,C) ) ) ).
fof(dt_k1_clvect_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> m1_subset_1(k1_clvect_2(A,B),u1_struct_0(A)) ) ).
fof(dt_k2_clvect_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A)) )
=> ( v1_funct_1(k2_clvect_2(A,B))
& v1_funct_2(k2_clvect_2(A,B),k5_numbers,k1_numbers)
& m2_relset_1(k2_clvect_2(A,B),k5_numbers,k1_numbers) ) ) ).
fof(dt_k3_clvect_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( v1_funct_1(k3_clvect_2(A,B,C))
& v1_funct_2(k3_clvect_2(A,B,C),k5_numbers,k1_numbers)
& m2_relset_1(k3_clvect_2(A,B,C),k5_numbers,k1_numbers) ) ) ).
fof(dt_k4_clvect_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,k1_numbers) )
=> m1_subset_1(k4_clvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k5_clvect_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,k1_numbers) )
=> m1_subset_1(k5_clvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k6_clvect_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,k1_numbers) )
=> m1_subset_1(k6_clvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k7_clvect_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& v1_seqm_3(B)
& v7_seqm_3(B)
& m1_relset_1(B,k5_numbers,k1_numbers)
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> ( v1_funct_1(k7_clvect_2(A,B,C))
& v1_funct_2(k7_clvect_2(A,B,C),k5_numbers,u1_struct_0(A))
& m2_relset_1(k7_clvect_2(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ).
fof(redefinition_k7_clvect_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,k1_numbers)
& v1_seqm_3(B)
& v7_seqm_3(B)
& m1_relset_1(B,k5_numbers,k1_numbers)
& v1_funct_1(C)
& v1_funct_2(C,k5_numbers,u1_struct_0(A))
& m1_relset_1(C,k5_numbers,u1_struct_0(A)) )
=> k7_clvect_2(A,B,C) = k5_relat_1(B,C) ) ).
fof(dt_k8_clvect_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A)
& v1_funct_1(B)
& v1_funct_2(B,k5_numbers,u1_struct_0(A))
& m1_relset_1(B,k5_numbers,u1_struct_0(A))
& m1_subset_1(C,k5_numbers) )
=> ( v1_funct_1(k8_clvect_2(A,B,C))
& v1_funct_2(k8_clvect_2(A,B,C),k5_numbers,u1_struct_0(A))
& m2_relset_1(k8_clvect_2(A,B,C),k5_numbers,u1_struct_0(A)) ) ) ).
fof(d5_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k4_clvect_2(A,B,C) = a_3_0_clvect_2(A,B,C) ) ) ) ).
fof(d6_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k5_clvect_2(A,B,C) = a_3_1_clvect_2(A,B,C) ) ) ) ).
fof(d7_clvect_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v2_clvect_1(A)
& v2_csspace(A)
& l1_csspace(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k6_clvect_2(A,B,C) = a_3_2_clvect_2(A,B,C) ) ) ) ).
fof(fraenkel_a_3_0_clvect_2,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v2_csspace(B)
& l1_csspace(B)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,k1_numbers) )
=> ( r2_hidden(A,a_3_0_clvect_2(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = E
& ~ r1_xreal_0(D,k13_csspace(B,k6_rlvect_1(B,C,E))) ) ) ) ).
fof(fraenkel_a_3_1_clvect_2,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v2_csspace(B)
& l1_csspace(B)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,k1_numbers) )
=> ( r2_hidden(A,a_3_1_clvect_2(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = E
& r1_xreal_0(k13_csspace(B,k6_rlvect_1(B,C,E)),D) ) ) ) ).
fof(fraenkel_a_3_2_clvect_2,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v2_clvect_1(B)
& v2_csspace(B)
& l1_csspace(B)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,k1_numbers) )
=> ( r2_hidden(A,a_3_2_clvect_2(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = E
& k13_csspace(B,k6_rlvect_1(B,C,E)) = D ) ) ) ).
%------------------------------------------------------------------------------