SET007 Axioms: SET007+226.ax
%------------------------------------------------------------------------------
% File : SET007+226 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Analytical Ordered Affine Spaces
% 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 : analoaf [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 70 ( 23 unt; 0 def)
% Number of atoms : 767 ( 76 equ)
% Maximal formula atoms : 65 ( 10 avg)
% Number of connectives : 832 ( 135 ~; 16 |; 395 &)
% ( 9 <=>; 277 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 9 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-5 aty)
% Number of functors : 17 ( 17 usr; 2 con; 0-4 aty)
% Number of variables : 291 ( 243 !; 48 ?)
% 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_analoaf,axiom,
? [A] :
( l1_analoaf(A)
& v1_analoaf(A) ) ).
fof(rc2_analoaf,axiom,
? [A] :
( l1_analoaf(A)
& ~ v3_struct_0(A)
& v1_analoaf(A) ) ).
fof(fc1_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ( ~ v3_struct_0(k2_analoaf(A))
& v1_analoaf(k2_analoaf(A)) ) ) ).
fof(rc3_analoaf,axiom,
? [A] :
( l1_analoaf(A)
& ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_analoaf(A)
& v2_analoaf(A) ) ).
fof(rc4_analoaf,axiom,
? [A] :
( l1_analoaf(A)
& ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v1_analoaf(A)
& v2_analoaf(A)
& v3_analoaf(A) ) ).
fof(d1_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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_analoaf(A,B,C,D,E)
<=> ~ ( B != C
& D != E
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( ~ r1_xreal_0(F,np__0)
& ~ r1_xreal_0(G,np__0)
& k3_rlvect_1(A,k6_rlvect_1(A,C,B),F) = k3_rlvect_1(A,k6_rlvect_1(A,E,D),G) ) ) ) ) ) ) ) ) ) ) ).
fof(t1_analoaf,axiom,
$true ).
fof(t2_analoaf,axiom,
$true ).
fof(t3_analoaf,axiom,
$true ).
fof(t4_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> k4_rlvect_1(A,k6_rlvect_1(A,B,C),k6_rlvect_1(A,C,D)) = k6_rlvect_1(A,B,D) ) ) ) ) ).
fof(t5_analoaf,axiom,
$true ).
fof(t6_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> k6_rlvect_1(A,B,k6_rlvect_1(A,C,D)) = k4_rlvect_1(A,B,k6_rlvect_1(A,D,C)) ) ) ) ) ).
fof(t7_analoaf,axiom,
$true ).
fof(t8_analoaf,axiom,
$true ).
fof(t9_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ( k4_rlvect_1(A,B,C) = k4_rlvect_1(A,D,E)
=> k6_rlvect_1(A,B,E) = k6_rlvect_1(A,D,C) ) ) ) ) ) ) ).
fof(t10_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> k3_rlvect_1(A,k6_rlvect_1(A,B,C),D) = k5_rlvect_1(A,k3_rlvect_1(A,k6_rlvect_1(A,C,B),D)) ) ) ) ) ).
fof(t11_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> k3_rlvect_1(A,k6_rlvect_1(A,B,C),k5_real_1(D,E)) = k3_rlvect_1(A,k6_rlvect_1(A,C,B),k5_real_1(E,D)) ) ) ) ) ) ).
fof(t12_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( k3_rlvect_1(A,B,D) = C
=> ( D = np__0
| B = k3_rlvect_1(A,C,k2_real_1(D)) ) ) ) ) ) ) ).
fof(t13_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( ( k3_rlvect_1(A,B,D) = C
=> ( D = np__0
| B = k3_rlvect_1(A,C,k2_real_1(D)) ) )
& ( B = k3_rlvect_1(A,C,k2_real_1(D))
=> ( D = np__0
| k3_rlvect_1(A,B,D) = C ) ) ) ) ) ) ) ).
fof(t14_analoaf,axiom,
$true ).
fof(t15_analoaf,axiom,
$true ).
fof(t16_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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_analoaf(A,B,C,D,E)
& B != C
& D != E
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ~ ( k3_rlvect_1(A,k6_rlvect_1(A,C,B),F) = k3_rlvect_1(A,k6_rlvect_1(A,E,D),G)
& ~ r1_xreal_0(F,np__0)
& ~ r1_xreal_0(G,np__0) ) ) ) ) ) ) ) ) ) ).
fof(t17_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_analoaf(A,B,C,B,C) ) ) ) ).
fof(t18_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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_analoaf(A,B,C,D,D)
& r1_analoaf(A,B,B,C,D) ) ) ) ) ) ).
fof(t19_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_analoaf(A,B,C,C,B)
=> B = C ) ) ) ) ).
fof(t20_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ( ( r1_analoaf(A,B,C,D,E)
& r1_analoaf(A,B,C,F,G) )
=> ( B = C
| r1_analoaf(A,D,E,F,G) ) ) ) ) ) ) ) ) ) ).
fof(t21_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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_analoaf(A,B,C,D,E)
=> ( r1_analoaf(A,C,B,E,D)
& r1_analoaf(A,D,E,B,C) ) ) ) ) ) ) ) ).
fof(t22_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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_analoaf(A,B,C,C,D)
=> r1_analoaf(A,B,C,B,D) ) ) ) ) ) ).
fof(t23_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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_analoaf(A,B,C,B,D)
& ~ r1_analoaf(A,B,C,C,D)
& ~ r1_analoaf(A,B,D,D,C) ) ) ) ) ) ).
fof(t24_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ( k6_rlvect_1(A,B,C) = k6_rlvect_1(A,D,E)
=> r1_analoaf(A,C,B,E,D) ) ) ) ) ) ) ).
fof(t25_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ( B = k6_rlvect_1(A,k4_rlvect_1(A,C,D),E)
=> ( r1_analoaf(A,E,C,D,B)
& r1_analoaf(A,E,D,C,B) ) ) ) ) ) ) ) ).
fof(t26_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ( ~ ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> 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))
& r1_analoaf(A,B,C,D,E)
& r1_analoaf(A,B,D,C,E)
& C != E ) ) ) ) ) ) ).
fof(t27_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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))
=> ~ ( B != C
& r1_analoaf(A,C,B,B,D)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r1_analoaf(A,E,B,B,F)
& r1_analoaf(A,E,C,D,F) ) ) ) ) ) ) ) ) ).
fof(t28_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( k4_rlvect_1(A,k3_rlvect_1(A,B,D),k3_rlvect_1(A,C,E)) = k1_rlvect_1(A)
=> ( D = np__0
& E = np__0 ) ) ) )
=> ( B != C
& B != k1_rlvect_1(A)
& C != k1_rlvect_1(A) ) ) ) ) ) ).
fof(t29_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ~ ( ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( k4_rlvect_1(A,k3_rlvect_1(A,B,D),k3_rlvect_1(A,C,E)) = k1_rlvect_1(A)
=> ( D = np__0
& E = np__0 ) ) ) ) ) )
& ! [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_analoaf(A,B,C,D,E)
& ~ r1_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) ).
fof(t30_analoaf,axiom,
$true ).
fof(t31_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ( ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ? [E] :
( m1_subset_1(E,k1_numbers)
& ? [F] :
( m1_subset_1(F,k1_numbers)
& k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)) = D ) ) ) ) )
=> ! [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_analoaf(A,B,C,D,E)
& ~ r1_analoaf(A,B,C,E,D)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( ( r1_analoaf(A,B,C,B,F)
| r1_analoaf(A,B,C,F,B) )
& ( r1_analoaf(A,D,E,D,F)
| r1_analoaf(A,D,E,F,D) ) ) ) ) ) ) ) ) ) ) ).
fof(d2_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(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_hidden(k1_domain_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,E)),u1_analoaf(A)) ) ) ) ) ) ) ).
fof(d3_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ! [B] :
( m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
=> ( B = k1_analoaf(A)
<=> ! [C,D] :
( r2_hidden(k4_tarski(C,D),B)
<=> ? [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))
& C = k1_domain_1(u1_struct_0(A),u1_struct_0(A),E,F)
& D = k1_domain_1(u1_struct_0(A),u1_struct_0(A),G,H)
& r1_analoaf(A,E,F,G,H) ) ) ) ) ) ) ) ) ).
fof(t32_analoaf,axiom,
$true ).
fof(t33_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(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_hidden(k1_domain_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,E)),k1_analoaf(A))
<=> r1_analoaf(A,B,C,D,E) ) ) ) ) ) ) ).
fof(d4_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> k2_analoaf(A) = g1_analoaf(u1_struct_0(A),k1_analoaf(A)) ) ).
fof(t34_analoaf,axiom,
$true ).
fof(t35_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ( ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( k4_rlvect_1(A,k3_rlvect_1(A,B,D),k3_rlvect_1(A,C,E)) = k1_rlvect_1(A)
=> ( D = np__0
& E = np__0 ) ) ) ) ) )
=> ( ~ ! [B] :
( m1_subset_1(B,u1_struct_0(k2_analoaf(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_analoaf(A)))
=> B = C ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(k2_analoaf(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_analoaf(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k2_analoaf(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_analoaf(A)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k2_analoaf(A)))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(k2_analoaf(A)))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(k2_analoaf(A)))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(k2_analoaf(A)))
=> ( r2_analoaf(k2_analoaf(A),B,C,D,D)
& ( r2_analoaf(k2_analoaf(A),B,C,C,B)
=> B = C )
& ( ( r2_analoaf(k2_analoaf(A),B,C,F,G)
& r2_analoaf(k2_analoaf(A),B,C,H,I) )
=> ( B = C
| r2_analoaf(k2_analoaf(A),F,G,H,I) ) )
& ( r2_analoaf(k2_analoaf(A),B,C,D,E)
=> r2_analoaf(k2_analoaf(A),C,B,E,D) )
& ( r2_analoaf(k2_analoaf(A),B,C,C,D)
=> r2_analoaf(k2_analoaf(A),B,C,B,D) )
& ~ ( r2_analoaf(k2_analoaf(A),B,C,B,D)
& ~ r2_analoaf(k2_analoaf(A),B,C,C,D)
& ~ r2_analoaf(k2_analoaf(A),B,D,D,C) ) ) ) ) ) ) ) ) ) )
& ? [B] :
( m1_subset_1(B,u1_struct_0(k2_analoaf(A)))
& ? [C] :
( m1_subset_1(C,u1_struct_0(k2_analoaf(A)))
& ? [D] :
( m1_subset_1(D,u1_struct_0(k2_analoaf(A)))
& ? [E] :
( m1_subset_1(E,u1_struct_0(k2_analoaf(A)))
& ~ r2_analoaf(k2_analoaf(A),B,C,D,E)
& ~ r2_analoaf(k2_analoaf(A),B,C,E,D) ) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(k2_analoaf(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_analoaf(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k2_analoaf(A)))
=> ? [E] :
( m1_subset_1(E,u1_struct_0(k2_analoaf(A)))
& r2_analoaf(k2_analoaf(A),B,C,D,E)
& r2_analoaf(k2_analoaf(A),B,D,C,E)
& C != E ) ) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(k2_analoaf(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_analoaf(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k2_analoaf(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_analoaf(A)))
=> ~ ( B != D
& r2_analoaf(k2_analoaf(A),D,B,B,E)
& ! [F] :
( m1_subset_1(F,u1_struct_0(k2_analoaf(A)))
=> ~ ( r2_analoaf(k2_analoaf(A),C,B,B,F)
& r2_analoaf(k2_analoaf(A),C,D,E,F) ) ) ) ) ) ) ) ) ) ) ).
fof(t36_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ( ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ? [E] :
( m1_subset_1(E,k1_numbers)
& ? [F] :
( m1_subset_1(F,k1_numbers)
& k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)) = D ) ) ) ) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k2_analoaf(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k2_analoaf(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k2_analoaf(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k2_analoaf(A)))
=> ~ ( ~ r2_analoaf(k2_analoaf(A),B,C,D,E)
& ~ r2_analoaf(k2_analoaf(A),B,C,E,D)
& ! [F] :
( m1_subset_1(F,u1_struct_0(k2_analoaf(A)))
=> ~ ( ( r2_analoaf(k2_analoaf(A),B,C,B,F)
| r2_analoaf(k2_analoaf(A),B,C,F,B) )
& ( r2_analoaf(k2_analoaf(A),D,E,D,F)
| r2_analoaf(k2_analoaf(A),D,E,F,D) ) ) ) ) ) ) ) ) ) ) ).
fof(d5_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analoaf(A) )
=> ( v2_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))
=> ( r2_analoaf(A,B,C,D,D)
& ( r2_analoaf(A,B,C,C,B)
=> B = C )
& ( ( r2_analoaf(A,B,C,F,G)
& r2_analoaf(A,B,C,H,I) )
=> ( B = C
| r2_analoaf(A,F,G,H,I) ) )
& ( r2_analoaf(A,B,C,D,E)
=> r2_analoaf(A,C,B,E,D) )
& ( r2_analoaf(A,B,C,C,D)
=> r2_analoaf(A,B,C,B,D) )
& ~ ( r2_analoaf(A,B,C,B,D)
& ~ r2_analoaf(A,B,C,C,D)
& ~ 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,C,E,D) ) ) ) )
& ! [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)
& C != 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))
=> ~ ( B != D
& r2_analoaf(A,D,B,B,E)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r2_analoaf(A,C,B,B,F)
& r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) ) ) ) ).
fof(t37_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analoaf(A) )
=> ( ( ~ ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> 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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ( r2_analoaf(A,B,C,D,D)
& ( r2_analoaf(A,B,C,C,B)
=> B = C )
& ( ( r2_analoaf(A,B,C,F,G)
& r2_analoaf(A,B,C,H,I) )
=> ( B = C
| r2_analoaf(A,F,G,H,I) ) )
& ( r2_analoaf(A,B,C,D,E)
=> r2_analoaf(A,C,B,E,D) )
& ( r2_analoaf(A,B,C,C,D)
=> r2_analoaf(A,B,C,B,D) )
& ~ ( r2_analoaf(A,B,C,B,D)
& ~ r2_analoaf(A,B,C,C,D)
& ~ 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,C,E,D) ) ) ) )
& ! [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)
& C != 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))
=> ~ ( B != D
& r2_analoaf(A,D,B,B,E)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r2_analoaf(A,C,B,B,F)
& r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) )
<=> ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) ) ) ) ).
fof(t38_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ( ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( k4_rlvect_1(A,k3_rlvect_1(A,B,D),k3_rlvect_1(A,C,E)) = k1_rlvect_1(A)
=> ( D = np__0
& E = np__0 ) ) ) ) ) )
=> ( ~ v3_struct_0(k2_analoaf(A))
& ~ v3_realset2(k2_analoaf(A))
& v2_analoaf(k2_analoaf(A))
& l1_analoaf(k2_analoaf(A)) ) ) ) ).
fof(d6_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& l1_analoaf(A) )
=> ( v3_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,B,C,E,D)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( ( r2_analoaf(A,B,C,B,F)
| r2_analoaf(A,B,C,F,B) )
& ( r2_analoaf(A,D,E,D,F)
| r2_analoaf(A,D,E,F,D) ) ) ) ) ) ) ) ) ) ) ).
fof(t39_analoaf,axiom,
$true ).
fof(t40_analoaf,axiom,
$true ).
fof(t41_analoaf,axiom,
$true ).
fof(t42_analoaf,axiom,
$true ).
fof(t43_analoaf,axiom,
$true ).
fof(t44_analoaf,axiom,
$true ).
fof(t45_analoaf,axiom,
$true ).
fof(t46_analoaf,axiom,
$true ).
fof(t47_analoaf,axiom,
$true ).
fof(t48_analoaf,axiom,
$true ).
fof(t49_analoaf,axiom,
$true ).
fof(t50_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_analoaf(A) )
=> ( ( ~ ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> 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))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ( r2_analoaf(A,B,C,D,D)
& ( r2_analoaf(A,B,C,C,B)
=> B = C )
& ( ( r2_analoaf(A,B,C,F,G)
& r2_analoaf(A,B,C,H,I) )
=> ( B = C
| r2_analoaf(A,F,G,H,I) ) )
& ( r2_analoaf(A,B,C,D,E)
=> r2_analoaf(A,C,B,E,D) )
& ( r2_analoaf(A,B,C,C,D)
=> r2_analoaf(A,B,C,B,D) )
& ~ ( r2_analoaf(A,B,C,B,D)
& ~ r2_analoaf(A,B,C,C,D)
& ~ 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,C,E,D) ) ) ) )
& ! [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)
& C != 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))
=> ~ ( B != D
& r2_analoaf(A,D,B,B,E)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( r2_analoaf(A,C,B,B,F)
& r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) )
& ! [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,C,E,D)
& ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ~ ( ( r2_analoaf(A,B,C,B,F)
| r2_analoaf(A,B,C,F,B) )
& ( r2_analoaf(A,D,E,D,F)
| r2_analoaf(A,D,E,F,D) ) ) ) ) ) ) ) ) )
<=> ( ~ v3_struct_0(A)
& ~ v3_realset2(A)
& v2_analoaf(A)
& v3_analoaf(A)
& l1_analoaf(A) ) ) ) ).
fof(t51_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ( ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( k4_rlvect_1(A,k3_rlvect_1(A,B,D),k3_rlvect_1(A,C,E)) = k1_rlvect_1(A)
=> ( D = np__0
& E = np__0 ) ) ) )
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ? [E] :
( m1_subset_1(E,k1_numbers)
& ? [F] :
( m1_subset_1(F,k1_numbers)
& D = k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)) ) ) ) ) )
=> ( ~ v3_struct_0(k2_analoaf(A))
& ~ v3_realset2(k2_analoaf(A))
& v2_analoaf(k2_analoaf(A))
& v3_analoaf(k2_analoaf(A))
& l1_analoaf(k2_analoaf(A)) ) ) ) ).
fof(dt_l1_analoaf,axiom,
! [A] :
( l1_analoaf(A)
=> l1_struct_0(A) ) ).
fof(existence_l1_analoaf,axiom,
? [A] : l1_analoaf(A) ).
fof(abstractness_v1_analoaf,axiom,
! [A] :
( l1_analoaf(A)
=> ( v1_analoaf(A)
=> A = g1_analoaf(u1_struct_0(A),u1_analoaf(A)) ) ) ).
fof(dt_k1_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> m2_relset_1(k1_analoaf(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) ).
fof(dt_k2_analoaf,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v7_rlvect_1(A)
& l2_rlvect_1(A) )
=> ( v1_analoaf(k2_analoaf(A))
& l1_analoaf(k2_analoaf(A)) ) ) ).
fof(dt_u1_analoaf,axiom,
! [A] :
( l1_analoaf(A)
=> m2_relset_1(u1_analoaf(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) ).
fof(dt_g1_analoaf,axiom,
! [A,B] :
( m1_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
=> ( v1_analoaf(g1_analoaf(A,B))
& l1_analoaf(g1_analoaf(A,B)) ) ) ).
fof(free_g1_analoaf,axiom,
! [A,B] :
( m1_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
=> ! [C,D] :
( g1_analoaf(A,B) = g1_analoaf(C,D)
=> ( A = C
& B = D ) ) ) ).
%------------------------------------------------------------------------------