SET007 Axioms: SET007+392.ax
%------------------------------------------------------------------------------
% File : SET007+392 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Boolean Properties of Lattices
% 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 : boolealg [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 102 ( 10 unt; 0 def)
% Number of atoms : 737 ( 7 equ)
% Maximal formula atoms : 13 ( 7 avg)
% Number of connectives : 746 ( 111 ~; 6 |; 303 &)
% ( 12 <=>; 314 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 0 con; 1-3 aty)
% Number of variables : 305 ( 305 !; 0 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(d1_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_boolealg(A,B,C) = k4_lattices(A,B,k7_lattices(A,C)) ) ) ) ).
fof(d2_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k2_boolealg(A,B,C) = k3_lattices(A,k1_boolealg(A,B,C),k1_boolealg(A,C,B)) ) ) ) ).
fof(d3_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_boolealg(A,B,C)
<=> ( r3_lattices(A,B,C)
& r3_lattices(A,C,B) ) ) ) ) ) ).
fof(d4_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_boolealg(A,B,C)
<=> k4_lattices(A,B,C) != k5_lattices(A) ) ) ) ) ).
fof(t1_boolealg,axiom,
$true ).
fof(t2_boolealg,axiom,
$true ).
fof(t3_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(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))
=> ( r3_lattices(A,k3_lattices(A,B,C),D)
=> ( r3_lattices(A,B,D)
& r3_lattices(A,C,D) ) ) ) ) ) ) ).
fof(t4_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(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))
=> r3_lattices(A,k4_lattices(A,B,C),k3_lattices(A,B,D)) ) ) ) ) ).
fof(t5_boolealg,axiom,
$true ).
fof(t6_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(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))
=> ( r3_lattices(A,B,C)
=> r3_lattices(A,k1_boolealg(A,B,D),C) ) ) ) ) ) ).
fof(t7_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(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))
=> ( r3_lattices(A,B,C)
=> r3_lattices(A,k1_boolealg(A,B,D),k1_boolealg(A,C,D)) ) ) ) ) ) ).
fof(t8_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r3_lattices(A,k1_boolealg(A,B,C),B) ) ) ) ).
fof(t9_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r3_lattices(A,k1_boolealg(A,B,C),k2_boolealg(A,B,C)) ) ) ) ).
fof(t10_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(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))
=> ( ( r3_lattices(A,k1_boolealg(A,B,C),D)
& r3_lattices(A,k1_boolealg(A,C,B),D) )
=> r3_lattices(A,k2_boolealg(A,B,C),D) ) ) ) ) ) ).
fof(t11_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(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_boolealg(A,B,k3_lattices(A,C,D))
<=> ( r3_lattices(A,C,B)
& r3_lattices(A,D,B)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r3_lattices(A,C,E)
& r3_lattices(A,D,E) )
=> r3_lattices(A,B,E) ) ) ) ) ) ) ) ) ).
fof(t12_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(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_boolealg(A,B,k4_lattices(A,C,D))
<=> ( r3_lattices(A,B,C)
& r3_lattices(A,B,D)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( ( r3_lattices(A,E,C)
& r3_lattices(A,E,D) )
=> r3_lattices(A,E,B) ) ) ) ) ) ) ) ) ).
fof(t13_boolealg,axiom,
$true ).
fof(t14_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(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_boolealg(A,k4_lattices(A,B,k1_boolealg(A,C,D)),k1_boolealg(A,k4_lattices(A,B,C),D)) ) ) ) ) ).
fof(t15_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_boolealg(A,B,C)
=> r2_boolealg(A,C,B) ) ) ) ) ).
fof(t16_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( r2_boolealg(A,B,B)
<=> B != k5_lattices(A) ) ) ) ).
fof(t17_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_boolealg(A,k2_boolealg(A,B,C),k2_boolealg(A,C,B)) ) ) ) ).
fof(t18_boolealg,axiom,
$true ).
fof(t19_boolealg,axiom,
$true ).
fof(t20_boolealg,axiom,
$true ).
fof(t21_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v12_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( ~ r2_boolealg(A,B,C)
& r2_boolealg(A,C,B) ) ) ) ) ).
fof(t22_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v11_lattices(A)
& l3_lattices(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_boolealg(A,k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,B,D)),B)
=> r3_lattices(A,B,k3_lattices(A,C,D)) ) ) ) ) ) ).
fof(t23_boolealg,axiom,
$true ).
fof(t24_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v11_lattices(A)
& l3_lattices(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_boolealg(A,k1_boolealg(A,k3_lattices(A,B,C),D),k3_lattices(A,k1_boolealg(A,B,D),k1_boolealg(A,C,D))) ) ) ) ) ).
fof(t25_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( r3_lattices(A,B,k5_lattices(A))
=> r1_boolealg(A,B,k5_lattices(A)) ) ) ) ).
fof(t26_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(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))
=> ( ( r3_lattices(A,B,C)
& r3_lattices(A,B,D)
& r1_boolealg(A,k4_lattices(A,C,D),k5_lattices(A)) )
=> r1_boolealg(A,B,k5_lattices(A)) ) ) ) ) ) ).
fof(t27_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_boolealg(A,k3_lattices(A,B,C),k5_lattices(A))
<=> ( r1_boolealg(A,B,k5_lattices(A))
& r1_boolealg(A,C,k5_lattices(A)) ) ) ) ) ) ).
fof(t28_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(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))
=> ( ( r3_lattices(A,B,C)
& r1_boolealg(A,k4_lattices(A,C,D),k5_lattices(A)) )
=> r1_boolealg(A,k4_lattices(A,B,D),k5_lattices(A)) ) ) ) ) ) ).
fof(t29_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r1_boolealg(A,k1_boolealg(A,k5_lattices(A),B),k5_lattices(A)) ) ) ).
fof(t30_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(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))
=> ( ( r3_boolealg(A,B,C)
& r3_lattices(A,C,D) )
=> r3_boolealg(A,B,D) ) ) ) ) ) ).
fof(t31_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(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))
=> ( r3_boolealg(A,B,k4_lattices(A,C,D))
=> ( r3_boolealg(A,B,C)
& r3_boolealg(A,B,D) ) ) ) ) ) ) ).
fof(t32_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(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))
=> ( r3_boolealg(A,B,k1_boolealg(A,C,D))
=> r3_boolealg(A,B,C) ) ) ) ) ) ).
fof(t33_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ~ r2_boolealg(A,B,k5_lattices(A)) ) ) ).
fof(t34_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(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_boolealg(A,B,C)
& r3_lattices(A,D,C)
& r2_boolealg(A,B,D) ) ) ) ) ) ).
fof(t35_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(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_boolealg(A,B,C)
& r2_boolealg(A,B,D) )
& r2_boolealg(A,B,k4_lattices(A,C,D)) ) ) ) ) ) ).
fof(t36_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(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))
=> ( ( r3_lattices(A,B,C)
& r3_lattices(A,B,D) )
=> ( r2_boolealg(A,C,D)
| r1_boolealg(A,B,k5_lattices(A)) ) ) ) ) ) ) ).
fof(t37_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v13_lattices(A)
& l3_lattices(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_boolealg(A,B,C)
=> ( ~ r2_boolealg(A,k4_lattices(A,D,B),k4_lattices(A,D,C))
& ~ r2_boolealg(A,k4_lattices(A,B,D),k4_lattices(A,C,D)) ) ) ) ) ) ) ).
fof(t38_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(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))
=> ( r3_lattices(A,k1_boolealg(A,B,C),D)
=> r3_lattices(A,B,k3_lattices(A,C,D)) ) ) ) ) ) ).
fof(t39_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(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))
=> ( r3_lattices(A,B,C)
=> r3_lattices(A,k1_boolealg(A,D,C),k1_boolealg(A,D,B)) ) ) ) ) ) ).
fof(t40_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(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))
=> ( ( r3_lattices(A,B,C)
& r3_lattices(A,D,E) )
=> r3_lattices(A,k1_boolealg(A,B,E),k1_boolealg(A,C,D)) ) ) ) ) ) ) ).
fof(t41_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(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))
=> ( r3_lattices(A,B,k3_lattices(A,C,D))
=> ( r3_lattices(A,k1_boolealg(A,B,C),D)
& r3_lattices(A,k1_boolealg(A,B,D),C) ) ) ) ) ) ) ).
fof(t42_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_lattices(A,k7_lattices(A,B),k7_lattices(A,k4_lattices(A,B,C)))
& r3_lattices(A,k7_lattices(A,C),k7_lattices(A,k4_lattices(A,B,C))) ) ) ) ) ).
fof(t43_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_lattices(A,k7_lattices(A,k3_lattices(A,B,C)),k7_lattices(A,B))
& r3_lattices(A,k7_lattices(A,k3_lattices(A,B,C)),k7_lattices(A,C)) ) ) ) ) ).
fof(t44_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_lattices(A,B,k1_boolealg(A,C,B))
=> r1_boolealg(A,B,k5_lattices(A)) ) ) ) ) ).
fof(t45_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_lattices(A,B,C)
=> r1_boolealg(A,C,k3_lattices(A,B,k1_boolealg(A,C,B))) ) ) ) ) ).
fof(t46_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_boolealg(A,k1_boolealg(A,B,C),k5_lattices(A))
<=> r3_lattices(A,B,C) ) ) ) ) ).
fof(t47_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(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))
=> ( ( r3_lattices(A,B,k3_lattices(A,C,D))
& r1_boolealg(A,k4_lattices(A,B,D),k5_lattices(A)) )
=> r3_lattices(A,B,C) ) ) ) ) ) ).
fof(t48_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_boolealg(A,k3_lattices(A,B,C),k3_lattices(A,k1_boolealg(A,B,C),C)) ) ) ) ).
fof(t49_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_boolealg(A,k1_boolealg(A,B,k3_lattices(A,B,C)),k5_lattices(A)) ) ) ) ).
fof(t50_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_boolealg(A,k1_boolealg(A,B,k4_lattices(A,B,C)),k1_boolealg(A,B,C))
& r1_boolealg(A,k1_boolealg(A,B,k4_lattices(A,C,B)),k1_boolealg(A,B,C)) ) ) ) ) ).
fof(t51_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_boolealg(A,k4_lattices(A,k1_boolealg(A,B,C),C),k5_lattices(A)) ) ) ) ).
fof(t52_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_boolealg(A,k3_lattices(A,B,k1_boolealg(A,C,B)),k3_lattices(A,B,C))
& r1_boolealg(A,k3_lattices(A,k1_boolealg(A,C,B),B),k3_lattices(A,C,B)) ) ) ) ) ).
fof(t53_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_boolealg(A,k3_lattices(A,k4_lattices(A,B,C),k1_boolealg(A,B,C)),B) ) ) ) ).
fof(t54_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(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_boolealg(A,k1_boolealg(A,B,k1_boolealg(A,C,D)),k3_lattices(A,k1_boolealg(A,B,C),k4_lattices(A,B,D))) ) ) ) ) ).
fof(t55_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_boolealg(A,k1_boolealg(A,B,k1_boolealg(A,B,C)),k4_lattices(A,B,C)) ) ) ) ).
fof(t56_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_boolealg(A,k1_boolealg(A,k3_lattices(A,B,C),C),k1_boolealg(A,B,C)) ) ) ) ).
fof(t57_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_boolealg(A,k4_lattices(A,B,C),k5_lattices(A))
<=> r1_boolealg(A,k1_boolealg(A,B,C),B) ) ) ) ) ).
fof(t58_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(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_boolealg(A,k1_boolealg(A,B,k3_lattices(A,C,D)),k4_lattices(A,k1_boolealg(A,B,C),k1_boolealg(A,B,D))) ) ) ) ) ).
fof(t59_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(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_boolealg(A,k1_boolealg(A,B,k4_lattices(A,C,D)),k3_lattices(A,k1_boolealg(A,B,C),k1_boolealg(A,B,D))) ) ) ) ) ).
fof(t60_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(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_boolealg(A,k4_lattices(A,B,k1_boolealg(A,C,D)),k1_boolealg(A,k4_lattices(A,B,C),k4_lattices(A,B,D)))
& r1_boolealg(A,k4_lattices(A,k1_boolealg(A,C,D),B),k1_boolealg(A,k4_lattices(A,C,B),k4_lattices(A,D,B))) ) ) ) ) ) ).
fof(t61_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_boolealg(A,k1_boolealg(A,k3_lattices(A,B,C),k4_lattices(A,B,C)),k3_lattices(A,k1_boolealg(A,B,C),k1_boolealg(A,C,B))) ) ) ) ).
fof(t62_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(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_boolealg(A,k1_boolealg(A,k1_boolealg(A,B,C),D),k1_boolealg(A,B,k3_lattices(A,C,D))) ) ) ) ) ).
fof(t63_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_boolealg(A,k1_boolealg(A,B,C),k1_boolealg(A,C,B))
=> r1_boolealg(A,B,C) ) ) ) ) ).
fof(t64_boolealg,axiom,
$true ).
fof(t65_boolealg,axiom,
$true ).
fof(t66_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r1_boolealg(A,k1_boolealg(A,B,B),k5_lattices(A)) ) ) ).
fof(t67_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r1_boolealg(A,k1_boolealg(A,B,k5_lattices(A)),B) ) ) ).
fof(t68_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_boolealg(A,k7_lattices(A,k1_boolealg(A,B,C)),k3_lattices(A,k7_lattices(A,B),C)) ) ) ) ).
fof(t69_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(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))
=> ( r3_boolealg(A,B,k3_lattices(A,C,D))
<=> ( r3_boolealg(A,B,C)
| r3_boolealg(A,B,D) ) ) ) ) ) ) ).
fof(t70_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ r2_boolealg(A,k4_lattices(A,B,C),k1_boolealg(A,B,C)) ) ) ) ).
fof(t71_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(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_boolealg(A,B,k3_lattices(A,C,D))
<=> ( ~ r2_boolealg(A,B,C)
& ~ r2_boolealg(A,B,D) ) ) ) ) ) ) ).
fof(t72_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ r2_boolealg(A,k1_boolealg(A,B,C),C) ) ) ) ).
fof(t73_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ~ r2_boolealg(A,B,C)
=> ( r1_boolealg(A,k1_boolealg(A,k3_lattices(A,B,C),C),B)
& r1_boolealg(A,k1_boolealg(A,k3_lattices(A,B,C),B),C) ) ) ) ) ) ).
fof(t74_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_boolealg(A,k3_lattices(A,k7_lattices(A,B),k7_lattices(A,C)),k3_lattices(A,B,C))
=> ( r2_boolealg(A,B,k7_lattices(A,B))
| r2_boolealg(A,C,k7_lattices(A,C))
| ( r1_boolealg(A,B,k7_lattices(A,C))
& r1_boolealg(A,C,k7_lattices(A,B)) ) ) ) ) ) ) ).
fof(t75_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_boolealg(A,k3_lattices(A,k7_lattices(A,B),k7_lattices(A,C)),k3_lattices(A,B,C))
=> ( r2_boolealg(A,C,k7_lattices(A,B))
| r2_boolealg(A,B,k7_lattices(A,C))
| ( r1_boolealg(A,B,k7_lattices(A,B))
& r1_boolealg(A,C,k7_lattices(A,C)) ) ) ) ) ) ) ).
fof(t76_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r1_boolealg(A,k3_boolealg(A,B,k5_lattices(A)),B) ) ) ).
fof(t77_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r1_boolealg(A,k3_boolealg(A,B,B),k5_lattices(A)) ) ) ).
fof(t78_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ r2_boolealg(A,k4_lattices(A,B,C),k3_boolealg(A,B,C)) ) ) ) ).
fof(t79_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_boolealg(A,k3_lattices(A,B,C),k3_boolealg(A,B,k1_boolealg(A,C,B))) ) ) ) ).
fof(t80_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_boolealg(A,k3_boolealg(A,B,k4_lattices(A,B,C)),k1_boolealg(A,B,C)) ) ) ) ).
fof(t81_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_boolealg(A,k3_lattices(A,B,C),k3_lattices(A,k3_boolealg(A,B,C),k4_lattices(A,B,C))) ) ) ) ).
fof(t82_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_boolealg(A,k3_boolealg(A,k3_boolealg(A,B,C),k4_lattices(A,B,C)),k3_lattices(A,B,C)) ) ) ) ).
fof(t83_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_boolealg(A,k3_boolealg(A,k3_boolealg(A,B,C),k3_lattices(A,B,C)),k4_lattices(A,B,C)) ) ) ) ).
fof(t84_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_boolealg(A,k3_boolealg(A,B,C),k1_boolealg(A,k3_lattices(A,B,C),k4_lattices(A,B,C))) ) ) ) ).
fof(t85_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(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_boolealg(A,k1_boolealg(A,k3_boolealg(A,B,C),D),k3_lattices(A,k1_boolealg(A,B,k3_lattices(A,C,D)),k1_boolealg(A,C,k3_lattices(A,B,D)))) ) ) ) ) ).
fof(t86_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(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_boolealg(A,k1_boolealg(A,B,k3_boolealg(A,C,D)),k3_lattices(A,k1_boolealg(A,B,k3_lattices(A,C,D)),k4_lattices(A,k4_lattices(A,B,C),D))) ) ) ) ) ).
fof(t87_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(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_boolealg(A,k3_boolealg(A,k3_boolealg(A,B,C),D),k3_boolealg(A,B,k3_boolealg(A,C,D))) ) ) ) ) ).
fof(t88_boolealg,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_boolealg(A,k7_lattices(A,k3_boolealg(A,B,C)),k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,k7_lattices(A,B),k7_lattices(A,C)))) ) ) ) ).
fof(symmetry_r1_boolealg,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( r1_boolealg(A,B,C)
=> r1_boolealg(A,C,B) ) ) ).
fof(reflexivity_r1_boolealg,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> r1_boolealg(A,B,B) ) ).
fof(redefinition_r1_boolealg,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( r1_boolealg(A,B,C)
<=> B = C ) ) ).
fof(symmetry_r3_boolealg,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( r3_boolealg(A,B,C)
=> r3_boolealg(A,C,B) ) ) ).
fof(redefinition_r3_boolealg,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( r3_boolealg(A,B,C)
<=> r2_boolealg(A,B,C) ) ) ).
fof(dt_k1_boolealg,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k1_boolealg(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k2_boolealg,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k2_boolealg(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k3_boolealg,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k3_boolealg(A,B,C),u1_struct_0(A)) ) ).
fof(commutativity_k3_boolealg,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k3_boolealg(A,B,C) = k3_boolealg(A,C,B) ) ).
fof(redefinition_k3_boolealg,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k3_boolealg(A,B,C) = k2_boolealg(A,B,C) ) ).
%------------------------------------------------------------------------------