SET007 Axioms: SET007+740.ax
%------------------------------------------------------------------------------
% File : SET007+740 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Subspaces and Cosets of Subspace of Real 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 : rusub_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 90 ( 0 unt; 0 def)
% Number of atoms : 1182 ( 77 equ)
% Maximal formula atoms : 27 ( 13 avg)
% Number of connectives : 1202 ( 110 ~; 2 |; 749 &)
% ( 25 <=>; 316 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 11 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 20 usr; 0 prp; 1-3 aty)
% Number of functors : 25 ( 25 usr; 4 con; 0-5 aty)
% Number of variables : 302 ( 293 !; 9 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(rc1_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ? [B] :
( m1_rusub_1(B,A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v1_bhsp_1(B)
& v2_bhsp_1(B) ) ) ).
fof(d1_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_bhsp_1(B)
& l1_bhsp_1(B) )
=> ( m1_rusub_1(B,A)
<=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
& u2_struct_0(B) = u2_struct_0(A)
& u1_rlvect_1(B) = k1_realset1(u1_rlvect_1(A),u1_struct_0(B))
& u2_rlvect_1(B) = k8_relset_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,u1_struct_0(B)))
& u1_bhsp_1(B) = k1_realset1(u1_bhsp_1(A),u1_struct_0(B)) ) ) ) ) ).
fof(t1_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ! [D] :
( ( r1_rlvect_1(B,D)
& m1_rusub_1(B,C) )
=> r1_rlvect_1(C,D) ) ) ) ) ).
fof(t2_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( r1_rlvect_1(B,C)
=> r1_rlvect_1(A,C) ) ) ) ).
fof(t3_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> m1_subset_1(C,u1_struct_0(A)) ) ) ) ).
fof(t4_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> k1_rlvect_1(B) = k1_rlvect_1(A) ) ) ).
fof(t5_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> k1_rlvect_1(B) = k1_rlvect_1(C) ) ) ) ).
fof(t6_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( E = D
& F = C )
=> k4_rlvect_1(B,E,F) = k4_rlvect_1(A,D,C) ) ) ) ) ) ) ) ).
fof(t7_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( D = C
=> k3_rlvect_1(B,D,E) = k3_rlvect_1(A,C,E) ) ) ) ) ) ) ).
fof(t8_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( E = C
& F = D )
=> k2_bhsp_1(B,E,F) = k2_bhsp_1(A,C,D) ) ) ) ) ) ) ) ).
fof(t9_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( D = C
=> k5_rlvect_1(A,C) = k5_rlvect_1(B,D) ) ) ) ) ) ).
fof(t10_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( E = D
& F = C )
=> k6_rlvect_1(B,E,F) = k6_rlvect_1(A,D,C) ) ) ) ) ) ) ) ).
fof(t11_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> r1_rlvect_1(B,k1_rlvect_1(A)) ) ) ).
fof(t12_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> r1_rlvect_1(C,k1_rlvect_1(B)) ) ) ) ).
fof(t13_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> r1_rlvect_1(A,k1_rlvect_1(B)) ) ) ).
fof(t14_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r1_rlvect_1(B,C)
& r1_rlvect_1(B,D) )
=> r1_rlvect_1(B,k4_rlvect_1(A,C,D)) ) ) ) ) ) ).
fof(t15_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r1_rlvect_1(B,C)
=> r1_rlvect_1(B,k3_rlvect_1(A,C,D)) ) ) ) ) ) ).
fof(t16_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_rlvect_1(B,C)
=> r1_rlvect_1(B,k5_rlvect_1(A,C)) ) ) ) ) ).
fof(t17_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r1_rlvect_1(B,C)
& r1_rlvect_1(B,D) )
=> r1_rlvect_1(B,k6_rlvect_1(A,C,D)) ) ) ) ) ) ).
fof(t18_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,C)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(C,C),C)
& m2_relset_1(E,k2_zfmisc_1(C,C),C) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(k1_numbers,C),C)
& m2_relset_1(F,k2_zfmisc_1(k1_numbers,C),C) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,k2_zfmisc_1(C,C),k1_numbers)
& m2_relset_1(G,k2_zfmisc_1(C,C),k1_numbers) )
=> ( ( B = C
& D = k1_rlvect_1(A)
& E = k1_realset1(u1_rlvect_1(A),B)
& F = k8_relset_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)),u1_struct_0(A),u2_rlvect_1(A),k2_zfmisc_1(k1_numbers,B))
& G = k1_realset1(u1_bhsp_1(A),B) )
=> m1_rusub_1(g1_bhsp_1(C,D,E,F,G),A) ) ) ) ) ) ) ) ) ).
fof(t19_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> m1_rusub_1(A,A) ) ).
fof(t20_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v1_bhsp_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v1_bhsp_1(B)
& v2_bhsp_1(B)
& l1_bhsp_1(B) )
=> ( ( m1_rusub_1(A,B)
& m1_rusub_1(B,A) )
=> A = B ) ) ) ).
fof(t21_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_bhsp_1(B)
& l1_bhsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v7_rlvect_1(C)
& v2_bhsp_1(C)
& l1_bhsp_1(C) )
=> ( ( m1_rusub_1(A,B)
& m1_rusub_1(B,C) )
=> m1_rusub_1(A,C) ) ) ) ) ).
fof(t22_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ( r1_tarski(u1_struct_0(B),u1_struct_0(C))
=> m1_rusub_1(B,C) ) ) ) ) ).
fof(t23_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_rlvect_1(B,D)
=> r1_rlvect_1(C,D) ) )
=> m1_rusub_1(B,C) ) ) ) ) ).
fof(t24_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_bhsp_1(B)
& m1_rusub_1(B,A) )
=> ! [C] :
( ( v1_bhsp_1(C)
& m1_rusub_1(C,A) )
=> ( u1_struct_0(B) = u1_struct_0(C)
=> B = C ) ) ) ) ).
fof(t25_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_bhsp_1(B)
& m1_rusub_1(B,A) )
=> ! [C] :
( ( v1_bhsp_1(C)
& m1_rusub_1(C,A) )
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_rlvect_1(B,D)
<=> r1_rlvect_1(C,D) ) )
=> B = C ) ) ) ) ).
fof(t26_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v1_bhsp_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_bhsp_1(B)
& m1_rusub_1(B,A) )
=> ( u1_struct_0(B) = u1_struct_0(A)
=> B = A ) ) ) ).
fof(t27_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v1_bhsp_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_bhsp_1(B)
& m1_rusub_1(B,A) )
=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_rlvect_1(B,C)
<=> r1_rlvect_1(A,C) ) )
=> B = A ) ) ) ).
fof(t28_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( u1_struct_0(B) = C
=> v1_rlsub_1(C,A) ) ) ) ) ).
fof(t29_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( B != k1_xboole_0
& v1_rlsub_1(B,A)
& ! [C] :
( ( v1_bhsp_1(C)
& m1_rusub_1(C,A) )
=> B != u1_struct_0(C) ) ) ) ) ).
fof(d2_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_bhsp_1(B)
& m1_rusub_1(B,A) )
=> ( B = k1_rusub_1(A)
<=> u1_struct_0(B) = k6_domain_1(u1_struct_0(A),k1_rlvect_1(A)) ) ) ) ).
fof(d3_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> k2_rusub_1(A) = g1_bhsp_1(u1_struct_0(A),u2_struct_0(A),u1_rlvect_1(A),u2_rlvect_1(A),u1_bhsp_1(A)) ) ).
fof(t30_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> k1_rusub_1(B) = k1_rusub_1(A) ) ) ).
fof(t31_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> k1_rusub_1(B) = k1_rusub_1(C) ) ) ) ).
fof(t32_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> m1_rusub_1(k1_rusub_1(B),A) ) ) ).
fof(t33_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> m1_rusub_1(k1_rusub_1(A),B) ) ) ).
fof(t34_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_rusub_1(C,A)
=> m1_rusub_1(k1_rusub_1(B),C) ) ) ) ).
fof(t35_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v1_bhsp_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> m1_rusub_1(A,k2_rusub_1(A)) ) ).
fof(d5_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( m2_rusub_1(C,A,B)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& C = k3_rusub_1(A,D,B) ) ) ) ) ) ).
fof(t36_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(k1_rlvect_1(A),k3_rusub_1(A,C,B))
<=> r1_rlvect_1(B,C) ) ) ) ) ).
fof(t37_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r2_hidden(C,k3_rusub_1(A,C,B)) ) ) ) ).
fof(t38_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> k3_rusub_1(A,k1_rlvect_1(A),B) = u1_struct_0(B) ) ) ).
fof(t39_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_rusub_1(A,B,k1_rusub_1(A)) = k6_domain_1(u1_struct_0(A),B) ) ) ).
fof(t40_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_rusub_1(A,B,k2_rusub_1(A)) = u1_struct_0(A) ) ) ).
fof(t41_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(k1_rlvect_1(A),k3_rusub_1(A,C,B))
<=> k3_rusub_1(A,C,B) = u1_struct_0(B) ) ) ) ) ).
fof(t42_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_rlvect_1(B,C)
<=> k3_rusub_1(A,C,B) = u1_struct_0(B) ) ) ) ) ).
fof(t43_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r1_rlvect_1(B,C)
=> k3_rusub_1(A,k3_rlvect_1(A,C,D),B) = u1_struct_0(B) ) ) ) ) ) ).
fof(t44_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( k3_rusub_1(A,k3_rlvect_1(A,C,D),B) = u1_struct_0(B)
=> ( D = np__0
| r1_rlvect_1(B,C) ) ) ) ) ) ) ).
fof(t45_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_rlvect_1(B,C)
<=> k3_rusub_1(A,k5_rlvect_1(A,C),B) = u1_struct_0(B) ) ) ) ) ).
fof(t46_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_rlvect_1(B,C)
<=> k3_rusub_1(A,D,B) = k3_rusub_1(A,k4_rlvect_1(A,D,C),B) ) ) ) ) ) ).
fof(t47_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_rlvect_1(B,C)
<=> k3_rusub_1(A,D,B) = k3_rusub_1(A,k6_rlvect_1(A,D,C),B) ) ) ) ) ) ).
fof(t48_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,k3_rusub_1(A,C,B))
<=> k3_rusub_1(A,C,B) = k3_rusub_1(A,D,B) ) ) ) ) ) ).
fof(t49_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k3_rusub_1(A,C,B) = k3_rusub_1(A,k5_rlvect_1(A,C),B)
<=> r1_rlvect_1(B,C) ) ) ) ) ).
fof(t50_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r2_hidden(C,k3_rusub_1(A,D,B))
& r2_hidden(C,k3_rusub_1(A,E,B)) )
=> k3_rusub_1(A,D,B) = k3_rusub_1(A,E,B) ) ) ) ) ) ) ).
fof(t51_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,k3_rusub_1(A,D,B))
& r2_hidden(C,k3_rusub_1(A,k5_rlvect_1(A,D),B)) )
=> r1_rlvect_1(B,D) ) ) ) ) ) ).
fof(t52_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(k3_rlvect_1(A,C,D),k3_rusub_1(A,C,B))
=> ( D = np__1
| r1_rlvect_1(B,C) ) ) ) ) ) ) ).
fof(t53_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r1_rlvect_1(B,C)
=> r2_hidden(k3_rlvect_1(A,C,D),k3_rusub_1(A,C,B)) ) ) ) ) ) ).
fof(t54_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_hidden(k5_rlvect_1(A,C),k3_rusub_1(A,C,B))
<=> r1_rlvect_1(B,C) ) ) ) ) ).
fof(t55_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(k4_rlvect_1(A,C,D),k3_rusub_1(A,D,B))
<=> r1_rlvect_1(B,C) ) ) ) ) ) ).
fof(t56_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(k6_rlvect_1(A,D,C),k3_rusub_1(A,D,B))
<=> r1_rlvect_1(B,C) ) ) ) ) ) ).
fof(t57_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(C,k3_rusub_1(A,D,B))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& r1_rlvect_1(B,E)
& C = k4_rlvect_1(A,D,E) ) ) ) ) ) ) ).
fof(t58_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(C,k3_rusub_1(A,D,B))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& r1_rlvect_1(B,E)
& C = k6_rlvect_1(A,D,E) ) ) ) ) ) ) ).
fof(t59_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& r2_hidden(C,k3_rusub_1(A,E,B))
& r2_hidden(D,k3_rusub_1(A,E,B)) )
<=> r1_rlvect_1(B,k6_rlvect_1(A,C,D)) ) ) ) ) ) ).
fof(t60_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( k3_rusub_1(A,D,B) = k3_rusub_1(A,C,B)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r1_rlvect_1(B,E)
& k4_rlvect_1(A,D,E) = C ) ) ) ) ) ) ) ).
fof(t61_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( k3_rusub_1(A,D,B) = k3_rusub_1(A,C,B)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r1_rlvect_1(B,E)
& k6_rlvect_1(A,D,E) = C ) ) ) ) ) ) ) ).
fof(t62_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_bhsp_1(B)
& m1_rusub_1(B,A) )
=> ! [C] :
( ( v1_bhsp_1(C)
& m1_rusub_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( k3_rusub_1(A,D,B) = k3_rusub_1(A,D,C)
<=> B = C ) ) ) ) ) ).
fof(t63_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_bhsp_1(B)
& m1_rusub_1(B,A) )
=> ! [C] :
( ( v1_bhsp_1(C)
& m1_rusub_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( k3_rusub_1(A,E,B) = k3_rusub_1(A,D,C)
=> B = C ) ) ) ) ) ) ).
fof(t64_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m2_rusub_1(C,A,B)
=> ( v1_rlsub_1(C,A)
<=> C = u1_struct_0(B) ) ) ) ) ).
fof(t65_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( ( v1_bhsp_1(B)
& m1_rusub_1(B,A) )
=> ! [C] :
( ( v1_bhsp_1(C)
& m1_rusub_1(C,A) )
=> ! [D] :
( m2_rusub_1(D,A,B)
=> ! [E] :
( m2_rusub_1(E,A,C)
=> ( D = E
=> B = C ) ) ) ) ) ) ).
fof(t66_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> m2_rusub_1(k6_domain_1(u1_struct_0(A),B),A,k1_rusub_1(A)) ) ) ).
fof(t67_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ~ ( m2_rusub_1(B,A,k1_rusub_1(A))
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> B != k6_domain_1(u1_struct_0(A),C) ) ) ) ) ).
fof(t68_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> m2_rusub_1(u1_struct_0(B),A,B) ) ) ).
fof(t69_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> m2_rusub_1(u1_struct_0(A),A,k2_rusub_1(A)) ) ).
fof(t70_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( m2_rusub_1(B,A,k2_rusub_1(A))
=> B = u1_struct_0(A) ) ) ) ).
fof(t71_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m2_rusub_1(C,A,B)
=> ( r2_hidden(k1_rlvect_1(A),C)
<=> C = u1_struct_0(B) ) ) ) ) ).
fof(t72_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m2_rusub_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,C)
<=> C = k3_rusub_1(A,D,B) ) ) ) ) ) ).
fof(t73_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m2_rusub_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& r2_hidden(E,C)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r1_rlvect_1(B,F)
& k4_rlvect_1(A,D,F) = E ) ) ) ) ) ) ) ) ).
fof(t74_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m2_rusub_1(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ~ ( r2_hidden(D,C)
& r2_hidden(E,C)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r1_rlvect_1(B,F)
& k6_rlvect_1(A,D,F) = E ) ) ) ) ) ) ) ) ).
fof(t75_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ? [E] :
( m2_rusub_1(E,A,B)
& r2_hidden(C,E)
& r2_hidden(D,E) )
<=> r1_rlvect_1(B,k6_rlvect_1(A,C,D)) ) ) ) ) ) ).
fof(t76_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m2_rusub_1(D,A,B)
=> ! [E] :
( m2_rusub_1(E,A,B)
=> ( ( r2_hidden(C,D)
& r2_hidden(C,E) )
=> D = E ) ) ) ) ) ) ).
fof(dt_m1_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_rusub_1(B,A)
=> ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v7_rlvect_1(B)
& v2_bhsp_1(B)
& l1_bhsp_1(B) ) ) ) ).
fof(existence_m1_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ? [B] : m1_rusub_1(B,A) ) ).
fof(dt_m2_rusub_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A)
& m1_rusub_1(B,A) )
=> ! [C] :
( m2_rusub_1(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(existence_m2_rusub_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A)
& m1_rusub_1(B,A) )
=> ? [C] : m2_rusub_1(C,A,B) ) ).
fof(dt_k1_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( v1_bhsp_1(k1_rusub_1(A))
& m1_rusub_1(k1_rusub_1(A),A) ) ) ).
fof(dt_k2_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ( v1_bhsp_1(k2_rusub_1(A))
& m1_rusub_1(k2_rusub_1(A),A) ) ) ).
fof(dt_k3_rusub_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_rusub_1(C,A) )
=> m1_subset_1(k3_rusub_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(d4_rusub_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& v2_bhsp_1(A)
& l1_bhsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_rusub_1(C,A)
=> k3_rusub_1(A,B,C) = a_3_0_rusub_1(A,B,C) ) ) ) ).
fof(fraenkel_a_3_0_rusub_1,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)
& v7_rlvect_1(B)
& v2_bhsp_1(B)
& l1_bhsp_1(B)
& m1_subset_1(C,u1_struct_0(B))
& m1_rusub_1(D,B) )
=> ( r2_hidden(A,a_3_0_rusub_1(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k4_rlvect_1(B,C,E)
& r1_rlvect_1(D,E) ) ) ) ).
%------------------------------------------------------------------------------