SET007 Axioms: SET007+260.ax
%------------------------------------------------------------------------------
% File : SET007+260 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Directed Geometrical Bundles and Their Analytical Representation
% 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 : afvect0 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 105 ( 24 unt; 0 def)
% Number of atoms : 885 ( 63 equ)
% Maximal formula atoms : 41 ( 8 avg)
% Number of connectives : 969 ( 189 ~; 3 |; 420 &)
% ( 19 <=>; 338 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 26 ( 24 usr; 1 prp; 0-5 aty)
% Number of functors : 20 ( 20 usr; 0 con; 1-6 aty)
% Number of variables : 339 ( 325 !; 14 ?)
% 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_afvect0,axiom,
? [A] :
( l1_analoaf(A)
& ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_analoaf(A)
& v1_afvect0(A) ) ).
fof(cc1_afvect0,axiom,
! [A] :
( l1_analoaf(A)
=> ( ( ~ v3_struct_0(A)
& v2_tdgroup(A) )
=> ( ~ v3_struct_0(A)
& v1_afvect0(A) ) ) ) ).
fof(fc1_afvect0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k5_afvect0(A,B))
& v1_rlvect_1(k5_afvect0(A,B)) ) ) ).
fof(fc2_afvect0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k5_afvect0(A,B))
& v1_rlvect_1(k5_afvect0(A,B))
& v3_rlvect_1(k5_afvect0(A,B))
& v4_rlvect_1(k5_afvect0(A,B))
& v5_rlvect_1(k5_afvect0(A,B))
& v6_rlvect_1(k5_afvect0(A,B)) ) ) ).
fof(fc3_afvect0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k5_afvect0(A,B))
& v1_rlvect_1(k5_afvect0(A,B))
& v3_rlvect_1(k5_afvect0(A,B))
& v4_rlvect_1(k5_afvect0(A,B))
& v5_rlvect_1(k5_afvect0(A,B))
& v6_rlvect_1(k5_afvect0(A,B))
& v1_tdgroup(k5_afvect0(A,B)) ) ) ).
fof(fc4_afvect0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_tdgroup(A)
& l1_analoaf(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k5_afvect0(A,B))
& v1_rlvect_1(k5_afvect0(A,B))
& v3_rlvect_1(k5_afvect0(A,B))
& v4_rlvect_1(k5_afvect0(A,B))
& v5_rlvect_1(k5_afvect0(A,B))
& v6_rlvect_1(k5_afvect0(A,B))
& v13_vectsp_1(k5_afvect0(A,B))
& v1_tdgroup(k5_afvect0(A,B)) ) ) ).
fof(rc2_afvect0,axiom,
? [A] :
( l1_rlvect_1(A)
& ~ v3_struct_0(A)
& v1_rlvect_1(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& ~ v3_realset2(A)
& v1_tdgroup(A) ) ).
fof(fc5_afvect0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_tdgroup(A)
& l1_analoaf(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( ~ v3_struct_0(k5_afvect0(A,B))
& v1_rlvect_1(k5_afvect0(A,B))
& v3_rlvect_1(k5_afvect0(A,B))
& v4_rlvect_1(k5_afvect0(A,B))
& v5_rlvect_1(k5_afvect0(A,B))
& v6_rlvect_1(k5_afvect0(A,B))
& v13_vectsp_1(k5_afvect0(A,B))
& ~ v3_realset2(k5_afvect0(A,B))
& v1_tdgroup(k5_afvect0(A,B)) ) ) ).
fof(fc6_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& ~ v3_realset2(A)
& v1_tdgroup(A)
& l1_rlvect_1(A) )
=> ( ~ v3_struct_0(k2_tdgroup(A))
& ~ v3_realset2(k2_tdgroup(A))
& v1_analoaf(k2_tdgroup(A))
& v2_tdgroup(k2_tdgroup(A))
& v1_afvect0(k2_tdgroup(A)) ) ) ).
fof(d1_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analoaf(A) )
=> ( v1_afvect0(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))
=> ( r2_analoaf(A,B,C,D,D)
=> B = C ) ) ) )
& ! [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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( ( r2_analoaf(A,B,C,F,G)
& r2_analoaf(A,D,E,F,G) )
=> r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) )
& ! [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,u1_struct_0(A))
& r2_analoaf(A,B,C,D,E) ) ) ) )
& ! [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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( ( r2_analoaf(A,B,C,E,F)
& r2_analoaf(A,B,D,E,G) )
=> r2_analoaf(A,C,D,F,G) ) ) ) ) ) ) )
& ! [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))
& r2_analoaf(A,B,D,D,C) ) ) )
& ! [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,u1_struct_0(A))
=> ( r2_analoaf(A,B,C,D,E)
=> r2_analoaf(A,B,D,C,E) ) ) ) ) ) ) ) ) ).
fof(t1_afvect0,axiom,
$true ).
fof(t2_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r2_analoaf(A,B,C,B,C) ) ) ) ).
fof(t3_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r2_analoaf(A,B,B,B,B) ) ) ).
fof(t4_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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,u1_struct_0(A))
=> ( r2_analoaf(A,B,C,D,E)
=> r2_analoaf(A,D,E,B,C) ) ) ) ) ) ) ).
fof(t5_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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))
=> ( r2_analoaf(A,B,C,B,D)
=> C = D ) ) ) ) ) ).
fof(t6_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r2_analoaf(A,B,C,D,E)
& r2_analoaf(A,B,C,D,F) )
=> E = F ) ) ) ) ) ) ) ).
fof(t7_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r2_analoaf(A,B,B,C,C) ) ) ) ).
fof(t8_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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,u1_struct_0(A))
=> ( r2_analoaf(A,B,C,D,E)
=> r2_analoaf(A,C,B,E,D) ) ) ) ) ) ) ).
fof(t9_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r2_analoaf(A,B,C,D,E)
& r2_analoaf(A,B,D,F,E) )
=> C = F ) ) ) ) ) ) ) ).
fof(t10_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ( ( r2_analoaf(A,B,C,D,E)
& r2_analoaf(A,F,G,B,C)
& r2_analoaf(A,F,H,D,E) )
=> G = H ) ) ) ) ) ) ) ) ) ).
fof(t11_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ( ( r2_analoaf(A,B,C,D,E)
& r2_analoaf(A,F,G,C,B)
& r2_analoaf(A,F,H,E,D) )
=> G = H ) ) ) ) ) ) ) ) ) ).
fof(t12_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ( ( r2_analoaf(A,B,C,D,E)
& r2_analoaf(A,F,G,H,I)
& r2_analoaf(A,C,J,F,G)
& r2_analoaf(A,E,K,H,I) )
=> r2_analoaf(A,B,J,D,K) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t13_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( ( r2_analoaf(A,B,C,D,E)
& r2_analoaf(A,B,F,G,E) )
=> r2_analoaf(A,C,F,G,D) ) ) ) ) ) ) ) ) ).
fof(d2_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_afvect0(A,B,C)
<=> ( r2_analoaf(A,B,C,C,B)
& B != C ) ) ) ) ) ).
fof(t14_afvect0,axiom,
$true ).
fof(t15_afvect0,axiom,
$true ).
fof(t16_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A) )
=> ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& B != C
& ~ r1_afvect0(A,B,C) ) ) ) ).
fof(t17_afvect0,axiom,
$true ).
fof(t18_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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))
=> ~ ( r1_afvect0(A,B,C)
& r1_afvect0(A,B,D)
& C != D
& ~ r1_afvect0(A,C,D) ) ) ) ) ) ).
fof(t19_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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,u1_struct_0(A))
=> ( ( r1_afvect0(A,B,C)
& r2_analoaf(A,B,C,D,E) )
=> r1_afvect0(A,D,E) ) ) ) ) ) ) ).
fof(d3_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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))
=> ( r2_afvect0(A,B,C,D)
<=> r2_analoaf(A,B,C,C,D) ) ) ) ) ) ).
fof(t20_afvect0,axiom,
$true ).
fof(t21_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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))
=> ( r2_afvect0(A,B,C,D)
=> r2_afvect0(A,D,C,B) ) ) ) ) ) ).
fof(t22_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_afvect0(A,B,C,C)
<=> B = C ) ) ) ) ).
fof(t23_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_afvect0(A,B,C,B)
<=> ( B = C
| r1_afvect0(A,B,C) ) ) ) ) ) ).
fof(t24_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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))
& r2_afvect0(A,B,D,C) ) ) ) ) ).
fof(t25_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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,u1_struct_0(A))
=> ~ ( r2_afvect0(A,B,C,D)
& r2_afvect0(A,B,E,D)
& C != E
& ~ r1_afvect0(A,C,E) ) ) ) ) ) ) ).
fof(t26_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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))
& r2_afvect0(A,B,C,D) ) ) ) ) ).
fof(t27_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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,u1_struct_0(A))
=> ( ( r2_afvect0(A,B,C,D)
& r2_afvect0(A,B,C,E) )
=> D = E ) ) ) ) ) ) ).
fof(t28_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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,u1_struct_0(A))
=> ( ( r2_afvect0(A,B,C,D)
& r1_afvect0(A,C,E) )
=> r2_afvect0(A,B,E,D) ) ) ) ) ) ) ).
fof(t29_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r2_afvect0(A,B,C,D)
& r2_afvect0(A,B,E,F)
& r1_afvect0(A,C,E) )
=> D = F ) ) ) ) ) ) ) ).
fof(t30_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r2_afvect0(A,B,C,D)
& r2_afvect0(A,E,C,F) )
=> r2_analoaf(A,B,E,F,D) ) ) ) ) ) ) ) ).
fof(t31_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( ( r2_afvect0(A,B,C,D)
& r2_afvect0(A,E,F,G)
& r1_afvect0(A,C,F) )
=> r2_analoaf(A,B,E,G,D) ) ) ) ) ) ) ) ) ).
fof(d4_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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))
=> ( D = k1_afvect0(A,B,C)
<=> r2_afvect0(A,C,B,D) ) ) ) ) ) ).
fof(t32_afvect0,axiom,
$true ).
fof(t33_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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))
=> ( k1_afvect0(A,B,C) = D
<=> r2_analoaf(A,C,B,B,D) ) ) ) ) ) ).
fof(t34_afvect0,axiom,
$true ).
fof(t35_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k1_afvect0(A,B,C) = C
<=> ( C = B
| r1_afvect0(A,C,B) ) ) ) ) ) ).
fof(t36_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_afvect0(A,B,k1_afvect0(A,B,C)) = C ) ) ) ).
fof(t37_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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))
=> ( k1_afvect0(A,B,C) = k1_afvect0(A,B,D)
=> C = D ) ) ) ) ) ).
fof(t38_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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))
& k1_afvect0(A,B,D) = C ) ) ) ) ).
fof(t39_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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))
=> r2_analoaf(A,B,C,k1_afvect0(A,D,C),k1_afvect0(A,D,B)) ) ) ) ) ).
fof(t40_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( r2_analoaf(A,B,C,D,E)
<=> r2_analoaf(A,k1_afvect0(A,F,B),k1_afvect0(A,F,C),k1_afvect0(A,F,D),k1_afvect0(A,F,E)) ) ) ) ) ) ) ) ).
fof(t41_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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))
=> ( r1_afvect0(A,B,C)
<=> r1_afvect0(A,k1_afvect0(A,D,B),k1_afvect0(A,D,C)) ) ) ) ) ) ).
fof(t42_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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,u1_struct_0(A))
=> ( r2_afvect0(A,B,C,D)
<=> r2_afvect0(A,k1_afvect0(A,E,B),k1_afvect0(A,E,C),k1_afvect0(A,E,D)) ) ) ) ) ) ) ).
fof(t43_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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))
=> ( k1_afvect0(A,B,C) = k1_afvect0(A,D,C)
<=> ( B = D
| r1_afvect0(A,B,D) ) ) ) ) ) ) ).
fof(t44_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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))
=> k1_afvect0(A,B,k1_afvect0(A,C,k1_afvect0(A,B,D))) = k1_afvect0(A,k1_afvect0(A,B,C),D) ) ) ) ) ).
fof(t45_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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))
=> ( k1_afvect0(A,B,k1_afvect0(A,C,D)) = k1_afvect0(A,C,k1_afvect0(A,B,D))
<=> ~ ( B != C
& ~ r1_afvect0(A,B,C)
& ~ r1_afvect0(A,C,k1_afvect0(A,B,C)) ) ) ) ) ) ) ).
fof(t46_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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,u1_struct_0(A))
=> k1_afvect0(A,B,k1_afvect0(A,C,k1_afvect0(A,D,E))) = k1_afvect0(A,D,k1_afvect0(A,C,k1_afvect0(A,B,E))) ) ) ) ) ) ).
fof(t47_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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,u1_struct_0(A))
=> ? [F] :
( m1_subset_1(F,u1_struct_0(A))
& k1_afvect0(A,B,k1_afvect0(A,C,k1_afvect0(A,D,E))) = k1_afvect0(A,F,E) ) ) ) ) ) ) ).
fof(t48_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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,u1_struct_0(A))
& k1_afvect0(A,B,k1_afvect0(A,E,C)) = k1_afvect0(A,E,k1_afvect0(A,D,C)) ) ) ) ) ) ).
fof(d5_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(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,u1_struct_0(A))
=> ( E = k2_afvect0(A,B,C,D)
<=> r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ).
fof(d6_afvect0,axiom,
$true ).
fof(d7_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) )
=> ( C = k3_afvect0(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,D,E) = k2_afvect0(A,B,D,E) ) ) ) ) ) ) ).
fof(d8_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( C = k4_afvect0(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,D) = k1_afvect0(A,B,D) ) ) ) ) ) ).
fof(d9_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_afvect0(A,B) = g1_rlvect_1(u1_struct_0(A),k3_afvect0(A,B),B) ) ) ).
fof(t49_afvect0,axiom,
$true ).
fof(t50_afvect0,axiom,
$true ).
fof(t51_afvect0,axiom,
$true ).
fof(t52_afvect0,axiom,
$true ).
fof(t53_afvect0,axiom,
$true ).
fof(t54_afvect0,axiom,
$true ).
fof(t55_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( u1_struct_0(k5_afvect0(A,B)) = u1_struct_0(A)
& u1_rlvect_1(k5_afvect0(A,B)) = k3_afvect0(A,B)
& u2_struct_0(k5_afvect0(A,B)) = B ) ) ) ).
fof(t56_afvect0,axiom,
$true ).
fof(t57_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k5_afvect0(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k5_afvect0(A,B)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( C = E
& D = F )
=> k2_rlvect_1(k5_afvect0(A,B),C,D) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k3_afvect0(A,B),E,F) ) ) ) ) ) ) ) ).
fof(t58_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k5_afvect0(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( C = D
=> k5_rlvect_1(k5_afvect0(A,B),C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),k4_afvect0(A,B),D) ) ) ) ) ) ).
fof(t59_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k1_rlvect_1(k5_afvect0(A,B)) = B ) ) ).
fof(t60_afvect0,axiom,
$true ).
fof(t61_afvect0,axiom,
$true ).
fof(t62_afvect0,axiom,
$true ).
fof(t63_afvect0,axiom,
$true ).
fof(t64_afvect0,axiom,
$true ).
fof(t65_afvect0,axiom,
$true ).
fof(t66_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k5_afvect0(A,B)))
=> ? [D] :
( m1_subset_1(D,u1_struct_0(k5_afvect0(A,B)))
& k4_rlvect_1(k5_afvect0(A,B),D,D) = C ) ) ) ) ).
fof(t67_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_tdgroup(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k5_afvect0(A,B)))
=> ( k4_rlvect_1(k5_afvect0(A,B),C,C) = k1_rlvect_1(k5_afvect0(A,B))
=> C = k1_rlvect_1(k5_afvect0(A,B)) ) ) ) ) ).
fof(t68_afvect0,axiom,
$true ).
fof(t69_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_tdgroup(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ~ v3_struct_0(k5_afvect0(A,B))
& v3_rlvect_1(k5_afvect0(A,B))
& v4_rlvect_1(k5_afvect0(A,B))
& v5_rlvect_1(k5_afvect0(A,B))
& v6_rlvect_1(k5_afvect0(A,B))
& v13_vectsp_1(k5_afvect0(A,B))
& ~ v3_realset2(k5_afvect0(A,B))
& v1_tdgroup(k5_afvect0(A,B))
& l1_rlvect_1(k5_afvect0(A,B)) ) ) ) ).
fof(t70_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& ~ v3_realset2(A)
& v1_tdgroup(A)
& l1_rlvect_1(A) )
=> ( ~ v3_struct_0(k2_tdgroup(A))
& ~ v3_realset2(k2_tdgroup(A))
& v2_tdgroup(k2_tdgroup(A))
& l1_analoaf(k2_tdgroup(A)) ) ) ).
fof(t71_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_analoaf(A)
& v2_tdgroup(A)
& l1_analoaf(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> A = k2_tdgroup(k5_afvect0(A,B)) ) ) ).
fof(t72_afvect0,axiom,
! [A] :
( ( v1_analoaf(A)
& l1_analoaf(A) )
=> ( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_tdgroup(A)
& l1_analoaf(A) )
<=> ? [B] :
( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v13_vectsp_1(B)
& ~ v3_realset2(B)
& v1_tdgroup(B)
& l1_rlvect_1(B)
& A = k2_tdgroup(B) ) ) ) ).
fof(d10_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_rlvect_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( r3_afvect0(A,B,C)
<=> ( v2_funct_1(C)
& k2_relat_1(C) = u1_struct_0(B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k2_rlvect_1(A,D,E)) = k2_rlvect_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E))
& k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k1_rlvect_1(A)) = k1_rlvect_1(B)
& k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k5_rlvect_1(A,D)) = k5_rlvect_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)) ) ) ) ) ) ) ) ) ).
fof(d11_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_rlvect_1(B) )
=> ( r4_afvect0(A,B)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& r3_afvect0(A,B,C) ) ) ) ) ).
fof(t73_afvect0,axiom,
$true ).
fof(t74_afvect0,axiom,
$true ).
fof(t75_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& ~ v3_realset2(A)
& v1_tdgroup(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k2_tdgroup(A)))
=> ( ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E) = k4_rlvect_1(A,C,E) )
& D = C )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k4_rlvect_1(A,E,F)) = k1_binop_1(k3_afvect0(k2_tdgroup(A),D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,F))
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k1_rlvect_1(A)) = k1_rlvect_1(k5_afvect0(k2_tdgroup(A),D))
& k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k5_rlvect_1(A,E)) = k1_funct_1(k4_afvect0(k2_tdgroup(A),D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E)) ) ) ) ) ) ) ) ) ).
fof(t76_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& ~ v3_realset2(A)
& v1_tdgroup(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D) = k4_rlvect_1(A,C,D) )
=> v2_funct_1(B) ) ) ) ) ).
fof(t77_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& ~ v3_realset2(A)
& v1_tdgroup(A)
& l1_rlvect_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k2_tdgroup(A)))
=> ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E) = k4_rlvect_1(A,C,E) )
=> k2_relat_1(B) = u1_struct_0(k5_afvect0(k2_tdgroup(A),D)) ) ) ) ) ) ).
fof(t78_afvect0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v13_vectsp_1(A)
& ~ v3_realset2(A)
& v1_tdgroup(A)
& l1_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_tdgroup(A)))
=> ( C = B
=> r4_afvect0(A,k5_afvect0(k2_tdgroup(A),C)) ) ) ) ) ).
fof(symmetry_r1_afvect0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( r1_afvect0(A,B,C)
=> r1_afvect0(A,C,B) ) ) ).
fof(irreflexivity_r1_afvect0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ~ r1_afvect0(A,B,B) ) ).
fof(dt_k1_afvect0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k1_afvect0(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k2_afvect0,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A))
& m1_subset_1(D,u1_struct_0(A)) )
=> m1_subset_1(k2_afvect0(A,B,C,D),u1_struct_0(A)) ) ).
fof(dt_k3_afvect0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_funct_1(k3_afvect0(A,B))
& v1_funct_2(k3_afvect0(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
& m2_relset_1(k3_afvect0(A,B),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ).
fof(dt_k4_afvect0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_funct_1(k4_afvect0(A,B))
& v1_funct_2(k4_afvect0(A,B),u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(k4_afvect0(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(dt_k5_afvect0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_afvect0(A)
& l1_analoaf(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_rlvect_1(k5_afvect0(A,B))
& l1_rlvect_1(k5_afvect0(A,B)) ) ) ).
%------------------------------------------------------------------------------