SET007 Axioms: SET007+369.ax
%------------------------------------------------------------------------------
% File : SET007+369 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Domains of Submodules
% Version : [Urb08] axioms.
% English : Join and Meet of Finite Sequences of Submodules and Quotient
% Modules
% 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 : lmod_7 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 116 ( 9 unt; 0 def)
% Number of atoms : 2009 ( 75 equ)
% Maximal formula atoms : 27 ( 17 avg)
% Number of connectives : 2097 ( 204 ~; 2 |;1554 &)
% ( 40 <=>; 297 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 15 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 55 ( 53 usr; 1 prp; 0-4 aty)
% Number of functors : 83 ( 83 usr; 28 con; 0-10 aty)
% Number of variables : 401 ( 375 !; 26 ?)
% 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_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_lmod_7(C,A,B) )
=> ? [D] :
( m1_subset_1(D,C)
& ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v11_vectsp_1(D,A)
& v12_vectsp_1(D,A) ) ) ).
fof(fc1_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B) )
=> ~ v1_xboole_0(k7_lmod_7(A,B,C)) ) ).
fof(fc2_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B) )
=> ( ~ v3_struct_0(k13_lmod_7(A,B,C))
& v1_rlvect_1(k13_lmod_7(A,B,C)) ) ) ).
fof(fc3_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B) )
=> ( ~ v3_struct_0(k13_lmod_7(A,B,C))
& v1_rlvect_1(k13_lmod_7(A,B,C))
& v3_rlvect_1(k13_lmod_7(A,B,C))
& v4_rlvect_1(k13_lmod_7(A,B,C))
& v5_rlvect_1(k13_lmod_7(A,B,C))
& v6_rlvect_1(k13_lmod_7(A,B,C)) ) ) ).
fof(fc4_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B) )
=> ( ~ v3_struct_0(k17_lmod_7(A,B,C))
& v11_vectsp_1(k17_lmod_7(A,B,C),A) ) ) ).
fof(fc5_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B) )
=> ( ~ v3_struct_0(k17_lmod_7(A,B,C))
& v11_vectsp_1(k17_lmod_7(A,B,C),A)
& v12_vectsp_1(k17_lmod_7(A,B,C),A) ) ) ).
fof(t1_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ~ ( ~ v3_realset2(A)
& v1_lmod_5(C,A,B)
& r2_hidden(k1_rlvect_1(B),C) ) ) ) ) ).
fof(t2_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ! [E] :
( m2_vectsp_6(E,A,B,D)
=> ( ~ r2_hidden(C,D)
=> k8_funct_2(u1_struct_0(B),u1_struct_0(A),E,C) = k1_rlvect_1(A) ) ) ) ) ) ) ).
fof(t3_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( v3_realset2(A)
=> ( ! [D] :
( m2_vectsp_6(D,A,B,C)
=> k1_vectsp_6(A,B,D) = k1_xboole_0 )
& v3_realset2(k1_mod_3(A,B,C)) ) ) ) ) ) ).
fof(t4_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ( ~ v3_realset2(B)
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ~ ( v1_mod_3(C,A,B)
& C = k1_xboole_0 ) ) ) ) ) ).
fof(t5_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( v1_lmod_5(k4_subset_1(u1_struct_0(B),C,D),A,B)
& r1_xboole_0(C,D) )
=> k2_vectsp_5(A,B,k1_mod_3(A,B,C),k1_mod_3(A,B,D)) = k1_vectsp_4(A,B) ) ) ) ) ) ).
fof(t6_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( v1_mod_3(C,A,B)
& C = k4_subset_1(u1_struct_0(B),D,E)
& r1_xboole_0(D,E) )
=> r1_vectsp_5(A,B,k1_mod_3(A,B,D),k1_mod_3(A,B,E)) ) ) ) ) ) ) ).
fof(d1_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ( m1_lmod_7(C,A,B)
<=> ! [D] :
( r2_hidden(D,C)
=> ( v11_vectsp_1(D,A)
& m1_vectsp_4(D,A,B) ) ) ) ) ) ) ).
fof(d2_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ( ~ v3_realset2(B)
=> ! [C] :
( ( v11_vectsp_1(C,A)
& m1_vectsp_4(C,A,B) )
=> ( m3_lmod_7(C,A,B)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& D != k1_rlvect_1(B)
& C = k4_lmod_6(A,B,D) ) ) ) ) ) ) ).
fof(d3_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ( m4_lmod_7(C,A,B)
<=> ! [D] :
( r2_hidden(D,C)
=> m3_lmod_7(D,A,B) ) ) ) ) ) ).
fof(d4_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m4_lmod_7(C,A,B)
=> ( C = k2_lmod_7(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> m3_lmod_7(D,A,B) ) ) ) ) ) ).
fof(d5_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ( v2_mod_3(B,A)
=> ( v3_realset2(B)
| ! [C] :
( ( v11_vectsp_1(C,A)
& m1_vectsp_4(C,A,B) )
=> ( m6_lmod_7(C,A,B)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& D != k1_rlvect_1(B)
& r1_vectsp_5(A,B,k4_lmod_6(A,B,D),C) ) ) ) ) ) ) ) ).
fof(d6_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ( m7_lmod_7(C,A,B)
<=> ! [D] :
( r2_hidden(D,C)
=> m6_lmod_7(D,A,B) ) ) ) ) ) ).
fof(d7_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m7_lmod_7(C,A,B)
=> ( C = k3_lmod_7(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> m6_lmod_7(D,A,B) ) ) ) ) ) ).
fof(d8_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m2_finseq_1(C,k3_vectsp_5(A,B))
=> k4_lmod_7(A,B,C) = k2_finsop_1(k3_vectsp_5(A,B),C,k5_vectsp_5(A,B)) ) ) ) ).
fof(d9_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m2_finseq_1(C,k3_vectsp_5(A,B))
=> k5_lmod_7(A,B,C) = k2_finsop_1(k3_vectsp_5(A,B),C,k6_vectsp_5(A,B)) ) ) ) ).
fof(t7_lmod_7,axiom,
$true ).
fof(t8_lmod_7,axiom,
$true ).
fof(t9_lmod_7,axiom,
$true ).
fof(t10_lmod_7,axiom,
$true ).
fof(t11_lmod_7,axiom,
$true ).
fof(t12_lmod_7,axiom,
$true ).
fof(t13_lmod_7,axiom,
$true ).
fof(t14_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ( v1_binop_1(k5_vectsp_5(A,B),k3_vectsp_5(A,B))
& v2_binop_1(k5_vectsp_5(A,B),k3_vectsp_5(A,B))
& v1_setwiseo(k5_vectsp_5(A,B),k3_vectsp_5(A,B))
& k1_vectsp_4(A,B) = k3_binop_1(k3_vectsp_5(A,B),k5_vectsp_5(A,B)) ) ) ) ).
fof(t15_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ( v1_binop_1(k6_vectsp_5(A,B),k3_vectsp_5(A,B))
& v2_binop_1(k6_vectsp_5(A,B),k3_vectsp_5(A,B))
& v1_setwiseo(k6_vectsp_5(A,B),k3_vectsp_5(A,B))
& k2_vectsp_4(A,B) = k3_binop_1(k3_vectsp_5(A,B),k6_vectsp_5(A,B)) ) ) ) ).
fof(d10_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B)))
=> ( E = k6_lmod_7(A,B,C,D)
<=> ! [F] :
( r2_hidden(F,E)
<=> ? [G] :
( m1_subset_1(G,u1_struct_0(B))
& ? [H] :
( m1_subset_1(H,u1_struct_0(B))
& r2_hidden(G,C)
& r2_hidden(H,D)
& F = k4_rlvect_1(B,G,H) ) ) ) ) ) ) ) ) ) ).
fof(d11_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( C != k1_xboole_0
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( m9_lmod_7(D,A,B,C)
<=> m1_subset_1(D,C) ) ) ) ) ) ) ).
fof(t16_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( r1_tarski(C,D)
=> ( C = k1_xboole_0
| ! [E] :
( m9_lmod_7(E,A,B,C)
=> m9_lmod_7(E,A,B,D) ) ) ) ) ) ) ) ).
fof(t17_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_vectsp_4(E,A,B)
=> ( r2_hidden(C,k3_vectsp_4(A,B,D,E))
<=> r1_rlvect_1(E,k6_rlvect_1(B,D,C)) ) ) ) ) ) ) ).
fof(t18_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_vectsp_4(E,A,B)
=> ( k3_vectsp_4(A,B,C,E) = k3_vectsp_4(A,B,D,E)
<=> r1_rlvect_1(E,k6_rlvect_1(B,C,D)) ) ) ) ) ) ) ).
fof(d12_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( D = k7_lmod_7(A,B,C)
<=> ! [E] :
( r2_hidden(E,D)
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& E = k3_vectsp_4(A,B,F,C) ) ) ) ) ) ) ).
fof(d13_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k8_lmod_7(A,B,C,D) = k3_vectsp_4(A,B,D,C) ) ) ) ) ).
fof(t19_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_subset_1(D,k7_lmod_7(A,B,C))
=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& D = k8_lmod_7(A,B,C,E) ) ) ) ) ) ).
fof(t20_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_vectsp_4(E,A,B)
=> ( k8_lmod_7(A,B,E,C) = k8_lmod_7(A,B,E,D)
<=> r1_rlvect_1(E,k6_rlvect_1(B,C,D)) ) ) ) ) ) ) ).
fof(d14_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_subset_1(D,k7_lmod_7(A,B,C))
=> ! [E] :
( m1_subset_1(E,k7_lmod_7(A,B,C))
=> ( E = k9_lmod_7(A,B,C,D)
<=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( D = k8_lmod_7(A,B,C,F)
=> E = k8_lmod_7(A,B,C,k5_rlvect_1(B,F)) ) ) ) ) ) ) ) ) ).
fof(d15_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_subset_1(D,k7_lmod_7(A,B,C))
=> ! [E] :
( m1_subset_1(E,k7_lmod_7(A,B,C))
=> ! [F] :
( m1_subset_1(F,k7_lmod_7(A,B,C))
=> ( F = k10_lmod_7(A,B,C,D,E)
<=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(B))
=> ( ( D = k8_lmod_7(A,B,C,G)
& E = k8_lmod_7(A,B,C,H) )
=> F = k8_lmod_7(A,B,C,k4_rlvect_1(B,G,H)) ) ) ) ) ) ) ) ) ) ) ).
fof(d16_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k7_lmod_7(A,B,C),k7_lmod_7(A,B,C))
& m2_relset_1(D,k7_lmod_7(A,B,C),k7_lmod_7(A,B,C)) )
=> ( D = k11_lmod_7(A,B,C)
<=> ! [E] :
( m1_subset_1(E,k7_lmod_7(A,B,C))
=> k8_funct_2(k7_lmod_7(A,B,C),k7_lmod_7(A,B,C),D,E) = k9_lmod_7(A,B,C,E) ) ) ) ) ) ) ).
fof(d17_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(k7_lmod_7(A,B,C),k7_lmod_7(A,B,C)),k7_lmod_7(A,B,C))
& m2_relset_1(D,k2_zfmisc_1(k7_lmod_7(A,B,C),k7_lmod_7(A,B,C)),k7_lmod_7(A,B,C)) )
=> ( D = k12_lmod_7(A,B,C)
<=> ! [E] :
( m1_subset_1(E,k7_lmod_7(A,B,C))
=> ! [F] :
( m1_subset_1(F,k7_lmod_7(A,B,C))
=> k2_binop_1(k7_lmod_7(A,B,C),k7_lmod_7(A,B,C),k7_lmod_7(A,B,C),D,E,F) = k10_lmod_7(A,B,C,E,F) ) ) ) ) ) ) ) ).
fof(d18_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> k13_lmod_7(A,B,C) = g1_rlvect_1(k7_lmod_7(A,B,C),k12_lmod_7(A,B,C),k8_lmod_7(A,B,C,k1_rlvect_1(B))) ) ) ) ).
fof(t21_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_vectsp_4(D,A,B)
=> m1_subset_1(k8_lmod_7(A,B,D,C),u1_struct_0(k13_lmod_7(A,B,D))) ) ) ) ) ).
fof(d19_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k14_lmod_7(A,B,C,D) = k8_lmod_7(A,B,C,D) ) ) ) ) ).
fof(t22_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k13_lmod_7(A,B,C)))
=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& D = k14_lmod_7(A,B,C,E) ) ) ) ) ) ).
fof(t23_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_vectsp_4(E,A,B)
=> ( k14_lmod_7(A,B,E,C) = k14_lmod_7(A,B,E,D)
<=> r1_rlvect_1(E,k6_rlvect_1(B,C,D)) ) ) ) ) ) ) ).
fof(t24_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_vectsp_4(E,A,B)
=> ( k2_rlvect_1(k13_lmod_7(A,B,E),k14_lmod_7(A,B,E,C),k14_lmod_7(A,B,E,D)) = k14_lmod_7(A,B,E,k4_rlvect_1(B,C,D))
& k1_rlvect_1(k13_lmod_7(A,B,E)) = k14_lmod_7(A,B,E,k1_rlvect_1(B)) ) ) ) ) ) ) ).
fof(d20_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k13_lmod_7(A,B,C)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k13_lmod_7(A,B,C)))
=> ( F = k15_lmod_7(A,B,C,D,E)
<=> ! [G] :
( m1_subset_1(G,u1_struct_0(B))
=> ( E = k14_lmod_7(A,B,C,G)
=> F = k14_lmod_7(A,B,C,k6_vectsp_1(A,B,D,G)) ) ) ) ) ) ) ) ) ) ).
fof(d21_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k13_lmod_7(A,B,C))),u1_struct_0(k13_lmod_7(A,B,C)))
& m2_relset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k13_lmod_7(A,B,C))),u1_struct_0(k13_lmod_7(A,B,C))) )
=> ( D = k16_lmod_7(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k13_lmod_7(A,B,C)))
=> k2_binop_1(u1_struct_0(A),u1_struct_0(k13_lmod_7(A,B,C)),u1_struct_0(k13_lmod_7(A,B,C)),D,E,F) = k15_lmod_7(A,B,C,E,F) ) ) ) ) ) ) ) ).
fof(d22_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> k17_lmod_7(A,B,C) = g4_vectsp_1(A,u1_struct_0(k13_lmod_7(A,B,C)),u1_rlvect_1(k13_lmod_7(A,B,C)),u2_struct_0(k13_lmod_7(A,B,C)),k16_lmod_7(A,B,C)) ) ) ) ).
fof(t25_lmod_7,axiom,
$true ).
fof(t26_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_vectsp_4(D,A,B)
=> m1_subset_1(k14_lmod_7(A,B,D,C),u1_struct_0(k17_lmod_7(A,B,D))) ) ) ) ) ).
fof(t27_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k17_lmod_7(A,B,C)))
=> m1_subset_1(D,u1_struct_0(k13_lmod_7(A,B,C))) ) ) ) ) ).
fof(d23_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> k18_lmod_7(A,B,C,D) = k14_lmod_7(A,B,C,D) ) ) ) ) ).
fof(t28_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k17_lmod_7(A,B,C)))
=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& D = k18_lmod_7(A,B,C,E) ) ) ) ) ) ).
fof(t29_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_vectsp_4(E,A,B)
=> ( k18_lmod_7(A,B,E,C) = k18_lmod_7(A,B,E,D)
<=> r1_rlvect_1(E,k6_rlvect_1(B,C,D)) ) ) ) ) ) ) ).
fof(t30_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> ! [F] :
( m1_vectsp_4(F,A,C)
=> ( k2_rlvect_1(k17_lmod_7(A,C,F),k18_lmod_7(A,C,F,D),k18_lmod_7(A,C,F,E)) = k18_lmod_7(A,C,F,k4_rlvect_1(C,D,E))
& k6_vectsp_1(A,k17_lmod_7(A,C,F),B,k18_lmod_7(A,C,F,D)) = k18_lmod_7(A,C,F,k6_vectsp_1(A,C,B,D)) ) ) ) ) ) ) ) ).
fof(t31_lmod_7,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_vectsp_4(C,A,B)
=> ( ~ v3_struct_0(k17_lmod_7(A,B,C))
& v3_rlvect_1(k17_lmod_7(A,B,C))
& v4_rlvect_1(k17_lmod_7(A,B,C))
& v5_rlvect_1(k17_lmod_7(A,B,C))
& v6_rlvect_1(k17_lmod_7(A,B,C))
& v11_vectsp_1(k17_lmod_7(A,B,C),A)
& v12_vectsp_1(k17_lmod_7(A,B,C),A)
& l4_vectsp_1(k17_lmod_7(A,B,C),A) ) ) ) ) ).
fof(s1_lmod_7,axiom,
! [A] :
( m1_subset_1(A,f1_s1_lmod_7)
=> ! [B] :
( m1_subset_1(B,f1_s1_lmod_7)
=> ( ( ! [C] :
( r2_hidden(C,A)
<=> p1_s1_lmod_7(C) )
& ! [C] :
( r2_hidden(C,B)
<=> p1_s1_lmod_7(C) ) )
=> A = B ) ) ) ).
fof(s2_lmod_7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,f1_s2_lmod_7,f1_s2_lmod_7)
& m2_relset_1(A,f1_s2_lmod_7,f1_s2_lmod_7) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,f1_s2_lmod_7,f1_s2_lmod_7)
& m2_relset_1(B,f1_s2_lmod_7,f1_s2_lmod_7) )
=> ( ( ! [C] :
( m1_subset_1(C,f1_s2_lmod_7)
=> k8_funct_2(f1_s2_lmod_7,f1_s2_lmod_7,A,C) = f2_s2_lmod_7(C) )
& ! [C] :
( m1_subset_1(C,f1_s2_lmod_7)
=> k8_funct_2(f1_s2_lmod_7,f1_s2_lmod_7,B,C) = f2_s2_lmod_7(C) ) )
=> A = B ) ) ) ).
fof(s3_lmod_7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k3_zfmisc_1(f1_s3_lmod_7,f1_s3_lmod_7,f1_s3_lmod_7),f1_s3_lmod_7)
& m2_relset_1(A,k3_zfmisc_1(f1_s3_lmod_7,f1_s3_lmod_7,f1_s3_lmod_7),f1_s3_lmod_7) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k3_zfmisc_1(f1_s3_lmod_7,f1_s3_lmod_7,f1_s3_lmod_7),f1_s3_lmod_7)
& m2_relset_1(B,k3_zfmisc_1(f1_s3_lmod_7,f1_s3_lmod_7,f1_s3_lmod_7),f1_s3_lmod_7) )
=> ( ( ! [C] :
( m1_subset_1(C,f1_s3_lmod_7)
=> ! [D] :
( m1_subset_1(D,f1_s3_lmod_7)
=> ! [E] :
( m1_subset_1(E,f1_s3_lmod_7)
=> k2_multop_1(f1_s3_lmod_7,f1_s3_lmod_7,f1_s3_lmod_7,f1_s3_lmod_7,A,C,D,E) = f2_s3_lmod_7(C,D,E) ) ) )
& ! [C] :
( m1_subset_1(C,f1_s3_lmod_7)
=> ! [D] :
( m1_subset_1(D,f1_s3_lmod_7)
=> ! [E] :
( m1_subset_1(E,f1_s3_lmod_7)
=> k2_multop_1(f1_s3_lmod_7,f1_s3_lmod_7,f1_s3_lmod_7,f1_s3_lmod_7,B,C,D,E) = f2_s3_lmod_7(C,D,E) ) ) ) )
=> A = B ) ) ) ).
fof(s4_lmod_7,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k4_zfmisc_1(f1_s4_lmod_7,f1_s4_lmod_7,f1_s4_lmod_7,f1_s4_lmod_7),f1_s4_lmod_7)
& m2_relset_1(A,k4_zfmisc_1(f1_s4_lmod_7,f1_s4_lmod_7,f1_s4_lmod_7,f1_s4_lmod_7),f1_s4_lmod_7) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k4_zfmisc_1(f1_s4_lmod_7,f1_s4_lmod_7,f1_s4_lmod_7,f1_s4_lmod_7),f1_s4_lmod_7)
& m2_relset_1(B,k4_zfmisc_1(f1_s4_lmod_7,f1_s4_lmod_7,f1_s4_lmod_7,f1_s4_lmod_7),f1_s4_lmod_7) )
=> ( ( ! [C] :
( m1_subset_1(C,f1_s4_lmod_7)
=> ! [D] :
( m1_subset_1(D,f1_s4_lmod_7)
=> ! [E] :
( m1_subset_1(E,f1_s4_lmod_7)
=> ! [F] :
( m1_subset_1(F,f1_s4_lmod_7)
=> k4_multop_1(f1_s4_lmod_7,f1_s4_lmod_7,f1_s4_lmod_7,f1_s4_lmod_7,f1_s4_lmod_7,A,C,D,E,F) = f2_s4_lmod_7(C,D,E,F) ) ) ) )
& ! [C] :
( m1_subset_1(C,f1_s4_lmod_7)
=> ! [D] :
( m1_subset_1(D,f1_s4_lmod_7)
=> ! [E] :
( m1_subset_1(E,f1_s4_lmod_7)
=> ! [F] :
( m1_subset_1(F,f1_s4_lmod_7)
=> k4_multop_1(f1_s4_lmod_7,f1_s4_lmod_7,f1_s4_lmod_7,f1_s4_lmod_7,f1_s4_lmod_7,B,C,D,E,F) = f2_s4_lmod_7(C,D,E,F) ) ) ) ) )
=> A = B ) ) ) ).
fof(dt_m1_lmod_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m1_lmod_7(C,A,B)
=> ~ v1_xboole_0(C) ) ) ).
fof(existence_m1_lmod_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ? [C] : m1_lmod_7(C,A,B) ) ).
fof(dt_m2_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_lmod_7(C,A,B) )
=> ! [D] :
( m2_lmod_7(D,A,B,C)
=> ( v11_vectsp_1(D,A)
& m1_vectsp_4(D,A,B) ) ) ) ).
fof(existence_m2_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_lmod_7(C,A,B) )
=> ? [D] : m2_lmod_7(D,A,B,C) ) ).
fof(redefinition_m2_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_lmod_7(C,A,B) )
=> ! [D] :
( m2_lmod_7(D,A,B,C)
<=> m1_subset_1(D,C) ) ) ).
fof(dt_m3_lmod_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m3_lmod_7(C,A,B)
=> ( v11_vectsp_1(C,A)
& m1_vectsp_4(C,A,B) ) ) ) ).
fof(existence_m3_lmod_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ? [C] : m3_lmod_7(C,A,B) ) ).
fof(dt_m4_lmod_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m4_lmod_7(C,A,B)
=> ~ v1_xboole_0(C) ) ) ).
fof(existence_m4_lmod_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ? [C] : m4_lmod_7(C,A,B) ) ).
fof(dt_m5_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m4_lmod_7(C,A,B) )
=> ! [D] :
( m5_lmod_7(D,A,B,C)
=> m3_lmod_7(D,A,B) ) ) ).
fof(existence_m5_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m4_lmod_7(C,A,B) )
=> ? [D] : m5_lmod_7(D,A,B,C) ) ).
fof(redefinition_m5_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m4_lmod_7(C,A,B) )
=> ! [D] :
( m5_lmod_7(D,A,B,C)
<=> m1_subset_1(D,C) ) ) ).
fof(dt_m6_lmod_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m6_lmod_7(C,A,B)
=> ( v11_vectsp_1(C,A)
& m1_vectsp_4(C,A,B) ) ) ) ).
fof(existence_m6_lmod_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ? [C] : m6_lmod_7(C,A,B) ) ).
fof(dt_m7_lmod_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( m7_lmod_7(C,A,B)
=> ~ v1_xboole_0(C) ) ) ).
fof(existence_m7_lmod_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ? [C] : m7_lmod_7(C,A,B) ) ).
fof(dt_m8_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m7_lmod_7(C,A,B) )
=> ! [D] :
( m8_lmod_7(D,A,B,C)
=> m6_lmod_7(D,A,B) ) ) ).
fof(existence_m8_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m7_lmod_7(C,A,B) )
=> ? [D] : m8_lmod_7(D,A,B,C) ) ).
fof(redefinition_m8_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m7_lmod_7(C,A,B) )
=> ! [D] :
( m8_lmod_7(D,A,B,C)
<=> m1_subset_1(D,C) ) ) ).
fof(dt_m9_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ! [D] :
( m9_lmod_7(D,A,B,C)
=> m1_subset_1(D,u1_struct_0(B)) ) ) ).
fof(existence_m9_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
=> ? [D] : m9_lmod_7(D,A,B,C) ) ).
fof(dt_k1_lmod_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> m1_lmod_7(k1_lmod_7(A,B),A,B) ) ).
fof(redefinition_k1_lmod_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> k1_lmod_7(A,B) = k3_vectsp_5(A,B) ) ).
fof(dt_k2_lmod_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> m4_lmod_7(k2_lmod_7(A,B),A,B) ) ).
fof(dt_k3_lmod_7,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> m7_lmod_7(k3_lmod_7(A,B),A,B) ) ).
fof(dt_k4_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_finseq_1(C,k3_vectsp_5(A,B)) )
=> m2_lmod_7(k4_lmod_7(A,B,C),A,B,k1_lmod_7(A,B)) ) ).
fof(dt_k5_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_finseq_1(C,k3_vectsp_5(A,B)) )
=> m2_lmod_7(k5_lmod_7(A,B,C),A,B,k1_lmod_7(A,B)) ) ).
fof(dt_k6_lmod_7,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> m1_subset_1(k6_lmod_7(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))) ) ).
fof(dt_k7_lmod_7,axiom,
$true ).
fof(dt_k8_lmod_7,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B)
& m1_subset_1(D,u1_struct_0(B)) )
=> m1_subset_1(k8_lmod_7(A,B,C,D),k7_lmod_7(A,B,C)) ) ).
fof(dt_k9_lmod_7,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B)
& m1_subset_1(D,k7_lmod_7(A,B,C)) )
=> m1_subset_1(k9_lmod_7(A,B,C,D),k7_lmod_7(A,B,C)) ) ).
fof(dt_k10_lmod_7,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B)
& m1_subset_1(D,k7_lmod_7(A,B,C))
& m1_subset_1(E,k7_lmod_7(A,B,C)) )
=> m1_subset_1(k10_lmod_7(A,B,C,D,E),k7_lmod_7(A,B,C)) ) ).
fof(dt_k11_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B) )
=> ( v1_funct_1(k11_lmod_7(A,B,C))
& v1_funct_2(k11_lmod_7(A,B,C),k7_lmod_7(A,B,C),k7_lmod_7(A,B,C))
& m2_relset_1(k11_lmod_7(A,B,C),k7_lmod_7(A,B,C),k7_lmod_7(A,B,C)) ) ) ).
fof(dt_k12_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B) )
=> ( v1_funct_1(k12_lmod_7(A,B,C))
& v1_funct_2(k12_lmod_7(A,B,C),k2_zfmisc_1(k7_lmod_7(A,B,C),k7_lmod_7(A,B,C)),k7_lmod_7(A,B,C))
& m2_relset_1(k12_lmod_7(A,B,C),k2_zfmisc_1(k7_lmod_7(A,B,C),k7_lmod_7(A,B,C)),k7_lmod_7(A,B,C)) ) ) ).
fof(dt_k13_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B) )
=> ( v1_rlvect_1(k13_lmod_7(A,B,C))
& l1_rlvect_1(k13_lmod_7(A,B,C)) ) ) ).
fof(dt_k14_lmod_7,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B)
& m1_subset_1(D,u1_struct_0(B)) )
=> m1_subset_1(k14_lmod_7(A,B,C,D),u1_struct_0(k13_lmod_7(A,B,C))) ) ).
fof(dt_k15_lmod_7,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B)
& m1_subset_1(D,u1_struct_0(A))
& m1_subset_1(E,u1_struct_0(k13_lmod_7(A,B,C))) )
=> m1_subset_1(k15_lmod_7(A,B,C,D,E),u1_struct_0(k13_lmod_7(A,B,C))) ) ).
fof(dt_k16_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B) )
=> ( v1_funct_1(k16_lmod_7(A,B,C))
& v1_funct_2(k16_lmod_7(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k13_lmod_7(A,B,C))),u1_struct_0(k13_lmod_7(A,B,C)))
& m2_relset_1(k16_lmod_7(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k13_lmod_7(A,B,C))),u1_struct_0(k13_lmod_7(A,B,C))) ) ) ).
fof(dt_k17_lmod_7,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B) )
=> ( v11_vectsp_1(k17_lmod_7(A,B,C),A)
& l4_vectsp_1(k17_lmod_7(A,B,C),A) ) ) ).
fof(dt_k18_lmod_7,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& m1_vectsp_4(C,A,B)
& m1_subset_1(D,u1_struct_0(B)) )
=> m1_subset_1(k18_lmod_7(A,B,C,D),u1_struct_0(k17_lmod_7(A,B,C))) ) ).
fof(s5_lmod_7,axiom,
? [A] :
( m1_subset_1(A,k1_zfmisc_1(f2_s5_lmod_7))
& A = a_0_0_lmod_7 ) ).
fof(s6_lmod_7,axiom,
( r2_hidden(f2_s6_lmod_7,a_0_1_lmod_7)
=> p1_s6_lmod_7(f2_s6_lmod_7) ) ).
fof(s7_lmod_7,axiom,
( f1_s7_lmod_7 = a_0_2_lmod_7
=> ( r2_hidden(f3_s7_lmod_7,f1_s7_lmod_7)
<=> p1_s7_lmod_7(f3_s7_lmod_7) ) ) ).
fof(s8_lmod_7,axiom,
( ( r2_hidden(f3_s8_lmod_7,f1_s8_lmod_7)
& f1_s8_lmod_7 = a_0_3_lmod_7 )
=> p1_s8_lmod_7(f3_s8_lmod_7) ) ).
fof(s9_lmod_7,axiom,
( f2_s9_lmod_7 = a_0_4_lmod_7
=> ( r2_hidden(f1_s9_lmod_7,f2_s9_lmod_7)
<=> ? [A] :
( m1_subset_1(A,f3_s9_lmod_7)
& f1_s9_lmod_7 = A
& p1_s9_lmod_7(A) ) ) ) ).
fof(s10_lmod_7,axiom,
( ( f5_s10_lmod_7(f3_s10_lmod_7) = a_0_5_lmod_7
& ( p2_s10_lmod_7(f4_s10_lmod_7,f3_s10_lmod_7)
<=> ! [A] :
( m1_subset_1(A,f2_s10_lmod_7)
=> ( r2_hidden(A,f3_s10_lmod_7)
=> p1_s10_lmod_7(f4_s10_lmod_7,A) ) ) ) )
=> ( r2_hidden(f4_s10_lmod_7,f5_s10_lmod_7(f3_s10_lmod_7))
<=> ! [A] :
( m1_subset_1(A,f2_s10_lmod_7)
=> ( r2_hidden(A,f3_s10_lmod_7)
=> p1_s10_lmod_7(f4_s10_lmod_7,A) ) ) ) ) ).
fof(fraenkel_a_0_0_lmod_7,axiom,
! [A] :
( r2_hidden(A,a_0_0_lmod_7)
<=> ? [B] :
( m1_subset_1(B,f1_s5_lmod_7)
& A = f3_s5_lmod_7(B)
& p1_s5_lmod_7(B) ) ) ).
fof(fraenkel_a_0_1_lmod_7,axiom,
! [A] :
( r2_hidden(A,a_0_1_lmod_7)
<=> ? [B] :
( m1_subset_1(B,f1_s6_lmod_7)
& A = B
& p1_s6_lmod_7(B) ) ) ).
fof(fraenkel_a_0_2_lmod_7,axiom,
! [A] :
( r2_hidden(A,a_0_2_lmod_7)
<=> ? [B] :
( m1_subset_1(B,f2_s7_lmod_7)
& A = B
& p1_s7_lmod_7(B) ) ) ).
fof(fraenkel_a_0_3_lmod_7,axiom,
! [A] :
( r2_hidden(A,a_0_3_lmod_7)
<=> ? [B] :
( m1_subset_1(B,f2_s8_lmod_7)
& A = B
& p1_s8_lmod_7(B) ) ) ).
fof(fraenkel_a_0_4_lmod_7,axiom,
! [A] :
( r2_hidden(A,a_0_4_lmod_7)
<=> ? [B] :
( m1_subset_1(B,f3_s9_lmod_7)
& A = B
& p1_s9_lmod_7(B) ) ) ).
fof(fraenkel_a_0_5_lmod_7,axiom,
! [A] :
( r2_hidden(A,a_0_5_lmod_7)
<=> ? [B] :
( m1_subset_1(B,f1_s10_lmod_7)
& A = B
& p2_s10_lmod_7(B,f3_s10_lmod_7) ) ) ).
%------------------------------------------------------------------------------