%------------------------------------------------------------------------------
% File : SET007+268 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Incidence Projective 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 : incproj [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 59 ( 6 unt; 0 def)
% Number of atoms : 850 ( 74 equ)
% Maximal formula atoms : 76 ( 14 avg)
% Number of connectives : 912 ( 121 ~; 22 |; 470 &)
% ( 25 <=>; 274 =>; 0 <=; 0 <~>)
% Maximal formula depth : 65 ( 15 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 34 ( 32 usr; 1 prp; 0-5 aty)
% Number of functors : 11 ( 11 usr; 0 con; 1-3 aty)
% Number of variables : 313 ( 277 !; 36 ?)
% 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(fc1_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(A) )
=> ~ v1_xboole_0(k1_incproj(A)) ) ).
fof(fc2_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(A) )
=> v1_incsp_1(k3_incproj(A)) ) ).
fof(fc3_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& l1_collsp(A) )
=> ( v1_incsp_1(k3_incproj(A))
& v1_incproj(k3_incproj(A))
& v2_incproj(k3_incproj(A))
& v3_incproj(k3_incproj(A))
& v4_incproj(k3_incproj(A))
& v5_incproj(k3_incproj(A)) ) ) ).
fof(rc1_incproj,axiom,
? [A] :
( l1_incsp_1(A)
& v1_incsp_1(A)
& v1_incproj(A)
& v2_incproj(A)
& v3_incproj(A)
& v4_incproj(A)
& v5_incproj(A) ) ).
fof(fc4_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& l1_collsp(A) )
=> ( v1_incsp_1(k3_incproj(A))
& v1_incproj(k3_incproj(A))
& v2_incproj(k3_incproj(A))
& v3_incproj(k3_incproj(A))
& v4_incproj(k3_incproj(A))
& v5_incproj(k3_incproj(A)) ) ) ).
fof(rc2_incproj,axiom,
? [A] :
( l1_incsp_1(A)
& v1_incproj(A)
& v2_incproj(A)
& v3_incproj(A)
& v4_incproj(A)
& v5_incproj(A)
& ~ v6_incproj(A)
& v7_incproj(A)
& v9_incproj(A)
& v10_incproj(A) ) ).
fof(rc3_incproj,axiom,
? [A] :
( l1_incsp_1(A)
& v1_incproj(A)
& v2_incproj(A)
& v3_incproj(A)
& v4_incproj(A)
& v5_incproj(A)
& ~ v6_incproj(A)
& v7_incproj(A)
& v9_incproj(A)
& v11_incproj(A) ) ).
fof(rc4_incproj,axiom,
? [A] :
( l1_incsp_1(A)
& v1_incproj(A)
& v2_incproj(A)
& v3_incproj(A)
& v4_incproj(A)
& v5_incproj(A)
& v6_incproj(A)
& v9_incproj(A)
& v10_incproj(A) ) ).
fof(rc5_incproj,axiom,
? [A] :
( l1_incsp_1(A)
& v1_incproj(A)
& v2_incproj(A)
& v3_incproj(A)
& v4_incproj(A)
& v5_incproj(A)
& v6_incproj(A)
& v9_incproj(A)
& v11_incproj(A) ) ).
fof(t1_incproj,axiom,
$true ).
fof(t2_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(A) )
=> ! [B] :
( m1_incproj(B,A)
<=> m1_subset_1(B,k1_incproj(A)) ) ) ).
fof(d2_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),k1_incproj(A))
=> ( B = k2_incproj(A)
<=> ! [C,D] :
( r2_hidden(k4_tarski(C,D),B)
<=> ( r2_hidden(C,u1_struct_0(A))
& r2_hidden(D,k1_incproj(A))
& ? [E] :
( D = E
& r2_hidden(C,E) ) ) ) ) ) ) ).
fof(d3_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(A) )
=> k3_incproj(A) = g1_incsp_1(u1_struct_0(A),k1_incproj(A),k2_incproj(A)) ) ).
fof(t3_incproj,axiom,
$true ).
fof(t4_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(A) )
=> ( u1_incsp_1(k3_incproj(A)) = u1_struct_0(A)
& u2_incsp_1(k3_incproj(A)) = k1_incproj(A)
& u3_incsp_1(k3_incproj(A)) = k2_incproj(A) ) ) ).
fof(t5_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
<=> m1_subset_1(B,u1_incsp_1(k3_incproj(A))) ) ) ).
fof(t6_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(A) )
=> ! [B] :
( m1_incproj(B,A)
<=> m1_subset_1(B,u2_incsp_1(k3_incproj(A))) ) ) ).
fof(t7_incproj,axiom,
$true ).
fof(t8_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(A) )
=> ! [B] :
( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
=> ! [C] :
( m1_subset_1(C,u2_incsp_1(k3_incproj(A)))
=> ( r1_incsp_1(k3_incproj(A),B,C)
<=> r2_hidden(k4_tarski(B,C),k2_incproj(A)) ) ) ) ) ).
fof(t9_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(A) )
=> ! [B] :
( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
=> ! [C] :
( m1_subset_1(C,u2_incsp_1(k3_incproj(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_incproj(E,A)
=> ( ( B = D
& C = E )
=> ( r1_incsp_1(k3_incproj(A),B,C)
<=> r2_hidden(D,E) ) ) ) ) ) ) ) ).
fof(t10_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(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))
& B != C
& C != D
& D != B ) ) ) ) ).
fof(t11_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ~ ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> B = C ) ) ) ).
fof(t12_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(A) )
=> ! [B] :
( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
=> ! [C] :
( m1_subset_1(C,u1_incsp_1(k3_incproj(A)))
=> ! [D] :
( m1_subset_1(D,u2_incsp_1(k3_incproj(A)))
=> ! [E] :
( m1_subset_1(E,u2_incsp_1(k3_incproj(A)))
=> ~ ( r1_incsp_1(k3_incproj(A),B,D)
& r1_incsp_1(k3_incproj(A),C,D)
& r1_incsp_1(k3_incproj(A),B,E)
& r1_incsp_1(k3_incproj(A),C,E)
& B != C
& D != E ) ) ) ) ) ) ).
fof(t13_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(A) )
=> ! [B] :
( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
=> ! [C] :
( m1_subset_1(C,u1_incsp_1(k3_incproj(A)))
=> ? [D] :
( m1_subset_1(D,u2_incsp_1(k3_incproj(A)))
& r1_incsp_1(k3_incproj(A),B,D)
& r1_incsp_1(k3_incproj(A),C,D) ) ) ) ) ).
fof(t14_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(A) )
=> ! [B] :
( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
=> ! [C] :
( m1_subset_1(C,u1_incsp_1(k3_incproj(A)))
=> ! [D] :
( m1_subset_1(D,u1_incsp_1(k3_incproj(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))
=> ( ( B = E
& C = F
& D = G )
=> ( r1_collsp(A,E,F,G)
<=> ? [H] :
( m1_subset_1(H,u2_incsp_1(k3_incproj(A)))
& r1_incsp_1(k3_incproj(A),B,H)
& r1_incsp_1(k3_incproj(A),C,H)
& r1_incsp_1(k3_incproj(A),D,H) ) ) ) ) ) ) ) ) ) ) ).
fof(t15_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(A) )
=> ~ ! [B] :
( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
=> ! [C] :
( m1_subset_1(C,u2_incsp_1(k3_incproj(A)))
=> r1_incsp_1(k3_incproj(A),B,C) ) ) ) ).
fof(t16_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& l1_collsp(A) )
=> ! [B] :
( m1_subset_1(B,u2_incsp_1(k3_incproj(A)))
=> ? [C] :
( m1_subset_1(C,u1_incsp_1(k3_incproj(A)))
& ? [D] :
( m1_subset_1(D,u1_incsp_1(k3_incproj(A)))
& ? [E] :
( m1_subset_1(E,u1_incsp_1(k3_incproj(A)))
& C != D
& D != E
& E != C
& r1_incsp_1(k3_incproj(A),C,B)
& r1_incsp_1(k3_incproj(A),D,B)
& r1_incsp_1(k3_incproj(A),E,B) ) ) ) ) ) ).
fof(t17_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& l1_collsp(A) )
=> ! [B] :
( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
=> ! [C] :
( m1_subset_1(C,u1_incsp_1(k3_incproj(A)))
=> ! [D] :
( m1_subset_1(D,u1_incsp_1(k3_incproj(A)))
=> ! [E] :
( m1_subset_1(E,u1_incsp_1(k3_incproj(A)))
=> ! [F] :
( m1_subset_1(F,u1_incsp_1(k3_incproj(A)))
=> ! [G] :
( m1_subset_1(G,u2_incsp_1(k3_incproj(A)))
=> ! [H] :
( m1_subset_1(H,u2_incsp_1(k3_incproj(A)))
=> ! [I] :
( m1_subset_1(I,u2_incsp_1(k3_incproj(A)))
=> ! [J] :
( m1_subset_1(J,u2_incsp_1(k3_incproj(A)))
=> ~ ( r1_incsp_1(k3_incproj(A),B,G)
& r1_incsp_1(k3_incproj(A),C,G)
& r1_incsp_1(k3_incproj(A),D,H)
& r1_incsp_1(k3_incproj(A),E,H)
& r1_incsp_1(k3_incproj(A),F,G)
& r1_incsp_1(k3_incproj(A),F,H)
& r1_incsp_1(k3_incproj(A),B,I)
& r1_incsp_1(k3_incproj(A),D,I)
& r1_incsp_1(k3_incproj(A),C,J)
& r1_incsp_1(k3_incproj(A),E,J)
& ~ r1_incsp_1(k3_incproj(A),F,I)
& ~ r1_incsp_1(k3_incproj(A),F,J)
& G != H
& ! [K] :
( m1_subset_1(K,u1_incsp_1(k3_incproj(A)))
=> ~ ( r1_incsp_1(k3_incproj(A),K,I)
& r1_incsp_1(k3_incproj(A),K,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t18_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& l1_collsp(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))
& r1_collsp(A,B,C,F)
& r1_collsp(A,D,E,F) ) ) ) ) )
=> ! [B] :
( m1_subset_1(B,u2_incsp_1(k3_incproj(A)))
=> ! [C] :
( m1_subset_1(C,u2_incsp_1(k3_incproj(A)))
=> ? [D] :
( m1_subset_1(D,u1_incsp_1(k3_incproj(A)))
& r1_incsp_1(k3_incproj(A),D,B)
& r1_incsp_1(k3_incproj(A),D,C) ) ) ) ) ) ).
fof(t19_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& l1_collsp(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))
=> ~ ( r1_collsp(A,B,C,F)
& r1_collsp(A,D,E,F) ) ) ) ) ) )
& ! [B] :
( m1_subset_1(B,u2_incsp_1(k3_incproj(A)))
=> ! [C] :
( m1_subset_1(C,u2_incsp_1(k3_incproj(A)))
=> ? [D] :
( m1_subset_1(D,u1_incsp_1(k3_incproj(A)))
& r1_incsp_1(k3_incproj(A),D,B)
& r1_incsp_1(k3_incproj(A),D,C) ) ) ) ) ) ).
fof(t20_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& l1_collsp(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))
& r1_collsp(A,B,D,G)
& r1_collsp(A,C,E,H)
& r1_collsp(A,F,G,H) ) ) ) ) ) ) )
=> ! [B] :
( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
=> ! [C] :
( m1_subset_1(C,u2_incsp_1(k3_incproj(A)))
=> ! [D] :
( m1_subset_1(D,u2_incsp_1(k3_incproj(A)))
=> ? [E] :
( m1_subset_1(E,u1_incsp_1(k3_incproj(A)))
& ? [F] :
( m1_subset_1(F,u1_incsp_1(k3_incproj(A)))
& ? [G] :
( m1_subset_1(G,u2_incsp_1(k3_incproj(A)))
& r1_incsp_1(k3_incproj(A),B,G)
& r1_incsp_1(k3_incproj(A),E,G)
& r1_incsp_1(k3_incproj(A),F,G)
& r1_incsp_1(k3_incproj(A),E,C)
& r1_incsp_1(k3_incproj(A),F,D) ) ) ) ) ) ) ) ) ).
fof(d4_incproj,axiom,
$true ).
fof(d5_incproj,axiom,
! [A,B,C] :
( r1_incproj(A,B,C)
<=> ( A != B
& B != C
& C != A ) ) ).
fof(d6_incproj,axiom,
! [A,B,C,D] :
( r2_incproj(A,B,C,D)
<=> ( A != B
& B != C
& C != A
& D != A
& D != B
& D != C ) ) ).
fof(d7_incproj,axiom,
! [A] :
( l1_incsp_1(A)
=> ! [B] :
( m1_subset_1(B,u1_incsp_1(A))
=> ! [C] :
( m1_subset_1(C,u1_incsp_1(A))
=> ! [D] :
( m1_subset_1(D,u2_incsp_1(A))
=> ( r3_incproj(A,B,C,D)
<=> ( r1_incsp_1(A,B,D)
& r1_incsp_1(A,C,D) ) ) ) ) ) ) ).
fof(d8_incproj,axiom,
! [A] :
( l1_incsp_1(A)
=> ! [B] :
( m1_subset_1(B,u1_incsp_1(A))
=> ! [C] :
( m1_subset_1(C,u1_incsp_1(A))
=> ! [D] :
( m1_subset_1(D,u2_incsp_1(A))
=> ! [E] :
( m1_subset_1(E,u1_incsp_1(A))
=> ( r4_incproj(A,B,C,D,E)
<=> ( r1_incsp_1(A,B,D)
& r1_incsp_1(A,C,D)
& r1_incsp_1(A,E,D) ) ) ) ) ) ) ) ).
fof(t21_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& l1_collsp(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))
=> ~ ( r1_collsp(A,B,C,D)
& r1_collsp(A,E,F,D)
& r1_collsp(A,B,E,G)
& r1_collsp(A,C,F,G)
& r1_collsp(A,B,F,H)
& r1_collsp(A,C,E,H)
& r1_collsp(A,G,D,H)
& ~ r1_collsp(A,B,C,F)
& ~ r1_collsp(A,B,C,E)
& ~ r1_collsp(A,B,E,F)
& ~ r1_collsp(A,C,E,F) ) ) ) ) ) ) ) )
=> ! [B] :
( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
=> ! [C] :
( m1_subset_1(C,u1_incsp_1(k3_incproj(A)))
=> ! [D] :
( m1_subset_1(D,u1_incsp_1(k3_incproj(A)))
=> ! [E] :
( m1_subset_1(E,u1_incsp_1(k3_incproj(A)))
=> ! [F] :
( m1_subset_1(F,u1_incsp_1(k3_incproj(A)))
=> ! [G] :
( m1_subset_1(G,u1_incsp_1(k3_incproj(A)))
=> ! [H] :
( m1_subset_1(H,u1_incsp_1(k3_incproj(A)))
=> ! [I] :
( m1_subset_1(I,u2_incsp_1(k3_incproj(A)))
=> ! [J] :
( m1_subset_1(J,u2_incsp_1(k3_incproj(A)))
=> ! [K] :
( m1_subset_1(K,u2_incsp_1(k3_incproj(A)))
=> ! [L] :
( m1_subset_1(L,u2_incsp_1(k3_incproj(A)))
=> ! [M] :
( m1_subset_1(M,u2_incsp_1(k3_incproj(A)))
=> ! [N] :
( m1_subset_1(N,u2_incsp_1(k3_incproj(A)))
=> ! [O] :
( m1_subset_1(O,u2_incsp_1(k3_incproj(A)))
=> ~ ( ~ r1_incsp_1(k3_incproj(A),C,I)
& ~ r1_incsp_1(k3_incproj(A),D,I)
& ~ r1_incsp_1(k3_incproj(A),B,J)
& ~ r1_incsp_1(k3_incproj(A),E,J)
& ~ r1_incsp_1(k3_incproj(A),B,K)
& ~ r1_incsp_1(k3_incproj(A),D,K)
& ~ r1_incsp_1(k3_incproj(A),C,L)
& ~ r1_incsp_1(k3_incproj(A),E,L)
& r4_incproj(k3_incproj(A),F,B,I,E)
& r4_incproj(k3_incproj(A),F,C,J,D)
& r4_incproj(k3_incproj(A),G,C,K,E)
& r4_incproj(k3_incproj(A),G,B,L,D)
& r4_incproj(k3_incproj(A),H,B,M,C)
& r4_incproj(k3_incproj(A),H,D,N,E)
& r3_incproj(k3_incproj(A),F,G,O)
& r1_incsp_1(k3_incproj(A),H,O) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t22_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& l1_collsp(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ( ( r1_collsp(A,C,D,K)
& r1_collsp(A,F,G,K)
& r1_collsp(A,D,E,I)
& r1_collsp(A,G,H,I)
& r1_collsp(A,C,E,J)
& r1_collsp(A,F,H,J)
& r1_collsp(A,B,C,F)
& r1_collsp(A,B,D,G)
& r1_collsp(A,B,E,H) )
=> ( B = F
| C = F
| B = G
| D = G
| B = H
| E = H
| r1_collsp(A,B,C,D)
| r1_collsp(A,B,C,E)
| r1_collsp(A,B,D,E)
| r1_collsp(A,I,J,K) ) ) ) ) ) ) ) ) ) ) ) )
=> ! [B] :
( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
=> ! [C] :
( m1_subset_1(C,u1_incsp_1(k3_incproj(A)))
=> ! [D] :
( m1_subset_1(D,u1_incsp_1(k3_incproj(A)))
=> ! [E] :
( m1_subset_1(E,u1_incsp_1(k3_incproj(A)))
=> ! [F] :
( m1_subset_1(F,u1_incsp_1(k3_incproj(A)))
=> ! [G] :
( m1_subset_1(G,u1_incsp_1(k3_incproj(A)))
=> ! [H] :
( m1_subset_1(H,u1_incsp_1(k3_incproj(A)))
=> ! [I] :
( m1_subset_1(I,u1_incsp_1(k3_incproj(A)))
=> ! [J] :
( m1_subset_1(J,u1_incsp_1(k3_incproj(A)))
=> ! [K] :
( m1_subset_1(K,u1_incsp_1(k3_incproj(A)))
=> ! [L] :
( m1_subset_1(L,u2_incsp_1(k3_incproj(A)))
=> ! [M] :
( m1_subset_1(M,u2_incsp_1(k3_incproj(A)))
=> ! [N] :
( m1_subset_1(N,u2_incsp_1(k3_incproj(A)))
=> ! [O] :
( m1_subset_1(O,u2_incsp_1(k3_incproj(A)))
=> ! [P] :
( m1_subset_1(P,u2_incsp_1(k3_incproj(A)))
=> ! [Q] :
( m1_subset_1(Q,u2_incsp_1(k3_incproj(A)))
=> ! [R] :
( m1_subset_1(R,u2_incsp_1(k3_incproj(A)))
=> ! [S] :
( m1_subset_1(S,u2_incsp_1(k3_incproj(A)))
=> ! [T] :
( m1_subset_1(T,u2_incsp_1(k3_incproj(A)))
=> ~ ( r4_incproj(k3_incproj(A),B,C,L,D)
& r4_incproj(k3_incproj(A),B,F,M,E)
& r4_incproj(k3_incproj(A),B,H,N,G)
& r4_incproj(k3_incproj(A),H,F,O,K)
& r4_incproj(k3_incproj(A),H,I,P,D)
& r4_incproj(k3_incproj(A),F,J,Q,D)
& r4_incproj(k3_incproj(A),K,E,R,G)
& r4_incproj(k3_incproj(A),C,I,S,G)
& r4_incproj(k3_incproj(A),C,J,T,E)
& r1_incproj(L,M,N)
& B != D
& B != F
& B != H
& B != C
& B != E
& B != G
& D != C
& F != E
& H != G
& ! [U] :
( m1_subset_1(U,u2_incsp_1(k3_incproj(A)))
=> ~ r4_incproj(k3_incproj(A),I,J,U,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t23_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& v2_anproj_2(A)
& v3_anproj_2(A)
& l1_collsp(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ! [H] :
( m1_subset_1(H,u1_struct_0(A))
=> ! [I] :
( m1_subset_1(I,u1_struct_0(A))
=> ! [J] :
( m1_subset_1(J,u1_struct_0(A))
=> ! [K] :
( m1_subset_1(K,u1_struct_0(A))
=> ( ( r1_collsp(A,B,C,D)
& r1_collsp(A,B,C,E)
& r1_collsp(A,B,F,G)
& r1_collsp(A,B,F,H)
& r1_collsp(A,C,G,K)
& r1_collsp(A,F,D,K)
& r1_collsp(A,C,H,J)
& r1_collsp(A,E,F,J)
& r1_collsp(A,D,H,I)
& r1_collsp(A,E,G,I) )
=> ( B = D
| B = E
| D = E
| C = D
| C = E
| B = G
| B = H
| G = H
| F = G
| F = H
| r1_collsp(A,B,C,F)
| r1_collsp(A,I,J,K) ) ) ) ) ) ) ) ) ) ) ) )
=> ! [B] :
( m1_subset_1(B,u1_incsp_1(k3_incproj(A)))
=> ! [C] :
( m1_subset_1(C,u1_incsp_1(k3_incproj(A)))
=> ! [D] :
( m1_subset_1(D,u1_incsp_1(k3_incproj(A)))
=> ! [E] :
( m1_subset_1(E,u1_incsp_1(k3_incproj(A)))
=> ! [F] :
( m1_subset_1(F,u1_incsp_1(k3_incproj(A)))
=> ! [G] :
( m1_subset_1(G,u1_incsp_1(k3_incproj(A)))
=> ! [H] :
( m1_subset_1(H,u1_incsp_1(k3_incproj(A)))
=> ! [I] :
( m1_subset_1(I,u1_incsp_1(k3_incproj(A)))
=> ! [J] :
( m1_subset_1(J,u1_incsp_1(k3_incproj(A)))
=> ! [K] :
( m1_subset_1(K,u1_incsp_1(k3_incproj(A)))
=> ! [L] :
( m1_subset_1(L,u2_incsp_1(k3_incproj(A)))
=> ! [M] :
( m1_subset_1(M,u2_incsp_1(k3_incproj(A)))
=> ! [N] :
( m1_subset_1(N,u2_incsp_1(k3_incproj(A)))
=> ! [O] :
( m1_subset_1(O,u2_incsp_1(k3_incproj(A)))
=> ! [P] :
( m1_subset_1(P,u2_incsp_1(k3_incproj(A)))
=> ! [Q] :
( m1_subset_1(Q,u2_incsp_1(k3_incproj(A)))
=> ! [R] :
( m1_subset_1(R,u2_incsp_1(k3_incproj(A)))
=> ! [S] :
( m1_subset_1(S,u2_incsp_1(k3_incproj(A)))
=> ! [T] :
( m1_subset_1(T,u2_incsp_1(k3_incproj(A)))
=> ( ( r2_incproj(B,C,D,E)
& r2_incproj(B,F,G,H)
& r1_incsp_1(k3_incproj(A),B,N)
& r1_incsp_1(k3_incproj(A),B,Q)
& r4_incproj(k3_incproj(A),D,H,L,I)
& r4_incproj(k3_incproj(A),E,F,O,J)
& r4_incproj(k3_incproj(A),C,G,R,K)
& r4_incproj(k3_incproj(A),C,H,M,J)
& r4_incproj(k3_incproj(A),E,G,P,I)
& r4_incproj(k3_incproj(A),D,F,S,K)
& r4_incproj(k3_incproj(A),F,G,N,H)
& r4_incproj(k3_incproj(A),C,D,Q,E)
& r3_incproj(k3_incproj(A),I,J,T) )
=> ( N = Q
| r1_incsp_1(k3_incproj(A),K,T) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d9_incproj,axiom,
! [A] :
( l1_incsp_1(A)
=> ( v1_incproj(A)
<=> ! [B] :
( m1_subset_1(B,u1_incsp_1(A))
=> ! [C] :
( m1_subset_1(C,u1_incsp_1(A))
=> ! [D] :
( m1_subset_1(D,u2_incsp_1(A))
=> ! [E] :
( m1_subset_1(E,u2_incsp_1(A))
=> ~ ( r1_incsp_1(A,B,D)
& r1_incsp_1(A,C,D)
& r1_incsp_1(A,B,E)
& r1_incsp_1(A,C,E)
& B != C
& D != E ) ) ) ) ) ) ) ).
fof(d10_incproj,axiom,
! [A] :
( l1_incsp_1(A)
=> ( v2_incproj(A)
<=> ! [B] :
( m1_subset_1(B,u1_incsp_1(A))
=> ! [C] :
( m1_subset_1(C,u1_incsp_1(A))
=> ? [D] :
( m1_subset_1(D,u2_incsp_1(A))
& r1_incsp_1(A,B,D)
& r1_incsp_1(A,C,D) ) ) ) ) ) ).
fof(d11_incproj,axiom,
! [A] :
( l1_incsp_1(A)
=> ( v3_incproj(A)
<=> ~ ! [B] :
( m1_subset_1(B,u1_incsp_1(A))
=> ! [C] :
( m1_subset_1(C,u2_incsp_1(A))
=> r1_incsp_1(A,B,C) ) ) ) ) ).
fof(d12_incproj,axiom,
! [A] :
( l1_incsp_1(A)
=> ( v4_incproj(A)
<=> ! [B] :
( m1_subset_1(B,u2_incsp_1(A))
=> ? [C] :
( m1_subset_1(C,u1_incsp_1(A))
& ? [D] :
( m1_subset_1(D,u1_incsp_1(A))
& ? [E] :
( m1_subset_1(E,u1_incsp_1(A))
& C != D
& D != E
& E != C
& r1_incsp_1(A,C,B)
& r1_incsp_1(A,D,B)
& r1_incsp_1(A,E,B) ) ) ) ) ) ) ).
fof(d13_incproj,axiom,
! [A] :
( l1_incsp_1(A)
=> ( v5_incproj(A)
<=> ! [B] :
( m1_subset_1(B,u1_incsp_1(A))
=> ! [C] :
( m1_subset_1(C,u1_incsp_1(A))
=> ! [D] :
( m1_subset_1(D,u1_incsp_1(A))
=> ! [E] :
( m1_subset_1(E,u1_incsp_1(A))
=> ! [F] :
( m1_subset_1(F,u1_incsp_1(A))
=> ! [G] :
( m1_subset_1(G,u1_incsp_1(A))
=> ! [H] :
( m1_subset_1(H,u2_incsp_1(A))
=> ! [I] :
( m1_subset_1(I,u2_incsp_1(A))
=> ! [J] :
( m1_subset_1(J,u2_incsp_1(A))
=> ! [K] :
( m1_subset_1(K,u2_incsp_1(A))
=> ~ ( r1_incsp_1(A,B,H)
& r1_incsp_1(A,C,H)
& r1_incsp_1(A,D,I)
& r1_incsp_1(A,E,I)
& r1_incsp_1(A,F,H)
& r1_incsp_1(A,F,I)
& r1_incsp_1(A,B,J)
& r1_incsp_1(A,D,J)
& r1_incsp_1(A,C,K)
& r1_incsp_1(A,E,K)
& ~ r1_incsp_1(A,F,J)
& ~ r1_incsp_1(A,F,K)
& H != I
& ! [L] :
( m1_subset_1(L,u1_incsp_1(A))
=> ~ ( r1_incsp_1(A,L,J)
& r1_incsp_1(A,L,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d14_incproj,axiom,
! [A] :
( ( v1_incproj(A)
& v2_incproj(A)
& v3_incproj(A)
& v4_incproj(A)
& v5_incproj(A)
& l1_incsp_1(A) )
=> ( v6_incproj(A)
<=> ! [B] :
( m1_subset_1(B,u2_incsp_1(A))
=> ! [C] :
( m1_subset_1(C,u2_incsp_1(A))
=> ? [D] :
( m1_subset_1(D,u1_incsp_1(A))
& r1_incsp_1(A,D,B)
& r1_incsp_1(A,D,C) ) ) ) ) ) ).
fof(d15_incproj,axiom,
$true ).
fof(d16_incproj,axiom,
! [A] :
( ( v1_incproj(A)
& v2_incproj(A)
& v3_incproj(A)
& v4_incproj(A)
& v5_incproj(A)
& l1_incsp_1(A) )
=> ( v7_incproj(A)
<=> ! [B] :
( m1_subset_1(B,u1_incsp_1(A))
=> ! [C] :
( m1_subset_1(C,u2_incsp_1(A))
=> ! [D] :
( m1_subset_1(D,u2_incsp_1(A))
=> ? [E] :
( m1_subset_1(E,u1_incsp_1(A))
& ? [F] :
( m1_subset_1(F,u1_incsp_1(A))
& ? [G] :
( m1_subset_1(G,u2_incsp_1(A))
& r1_incsp_1(A,B,G)
& r1_incsp_1(A,E,G)
& r1_incsp_1(A,F,G)
& r1_incsp_1(A,E,C)
& r1_incsp_1(A,F,D) ) ) ) ) ) ) ) ) ).
fof(d17_incproj,axiom,
! [A] :
( ( v1_incproj(A)
& v2_incproj(A)
& v3_incproj(A)
& v4_incproj(A)
& v5_incproj(A)
& l1_incsp_1(A) )
=> ( v8_incproj(A)
<=> ( v7_incproj(A)
& ~ v6_incproj(A) ) ) ) ).
fof(d18_incproj,axiom,
! [A] :
( ( v1_incproj(A)
& v2_incproj(A)
& v3_incproj(A)
& v4_incproj(A)
& v5_incproj(A)
& l1_incsp_1(A) )
=> ( v9_incproj(A)
<=> ! [B] :
( m1_subset_1(B,u1_incsp_1(A))
=> ! [C] :
( m1_subset_1(C,u1_incsp_1(A))
=> ! [D] :
( m1_subset_1(D,u1_incsp_1(A))
=> ! [E] :
( m1_subset_1(E,u1_incsp_1(A))
=> ! [F] :
( m1_subset_1(F,u1_incsp_1(A))
=> ! [G] :
( m1_subset_1(G,u1_incsp_1(A))
=> ! [H] :
( m1_subset_1(H,u1_incsp_1(A))
=> ! [I] :
( m1_subset_1(I,u2_incsp_1(A))
=> ! [J] :
( m1_subset_1(J,u2_incsp_1(A))
=> ! [K] :
( m1_subset_1(K,u2_incsp_1(A))
=> ! [L] :
( m1_subset_1(L,u2_incsp_1(A))
=> ! [M] :
( m1_subset_1(M,u2_incsp_1(A))
=> ! [N] :
( m1_subset_1(N,u2_incsp_1(A))
=> ! [O] :
( m1_subset_1(O,u2_incsp_1(A))
=> ~ ( ~ r1_incsp_1(A,C,I)
& ~ r1_incsp_1(A,D,I)
& ~ r1_incsp_1(A,B,J)
& ~ r1_incsp_1(A,E,J)
& ~ r1_incsp_1(A,B,K)
& ~ r1_incsp_1(A,D,K)
& ~ r1_incsp_1(A,C,L)
& ~ r1_incsp_1(A,E,L)
& r4_incproj(A,F,B,I,E)
& r4_incproj(A,F,C,J,D)
& r4_incproj(A,G,C,K,E)
& r4_incproj(A,G,B,L,D)
& r4_incproj(A,H,B,M,C)
& r4_incproj(A,H,D,N,E)
& r3_incproj(A,F,G,O)
& r1_incsp_1(A,H,O) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d19_incproj,axiom,
! [A] :
( ( v1_incproj(A)
& v2_incproj(A)
& v3_incproj(A)
& v4_incproj(A)
& v5_incproj(A)
& l1_incsp_1(A) )
=> ( v10_incproj(A)
<=> ! [B] :
( m1_subset_1(B,u1_incsp_1(A))
=> ! [C] :
( m1_subset_1(C,u1_incsp_1(A))
=> ! [D] :
( m1_subset_1(D,u1_incsp_1(A))
=> ! [E] :
( m1_subset_1(E,u1_incsp_1(A))
=> ! [F] :
( m1_subset_1(F,u1_incsp_1(A))
=> ! [G] :
( m1_subset_1(G,u1_incsp_1(A))
=> ! [H] :
( m1_subset_1(H,u1_incsp_1(A))
=> ! [I] :
( m1_subset_1(I,u1_incsp_1(A))
=> ! [J] :
( m1_subset_1(J,u1_incsp_1(A))
=> ! [K] :
( m1_subset_1(K,u1_incsp_1(A))
=> ! [L] :
( m1_subset_1(L,u2_incsp_1(A))
=> ! [M] :
( m1_subset_1(M,u2_incsp_1(A))
=> ! [N] :
( m1_subset_1(N,u2_incsp_1(A))
=> ! [O] :
( m1_subset_1(O,u2_incsp_1(A))
=> ! [P] :
( m1_subset_1(P,u2_incsp_1(A))
=> ! [Q] :
( m1_subset_1(Q,u2_incsp_1(A))
=> ! [R] :
( m1_subset_1(R,u2_incsp_1(A))
=> ! [S] :
( m1_subset_1(S,u2_incsp_1(A))
=> ! [T] :
( m1_subset_1(T,u2_incsp_1(A))
=> ~ ( r4_incproj(A,B,C,L,D)
& r4_incproj(A,B,F,M,E)
& r4_incproj(A,B,H,N,G)
& r4_incproj(A,H,F,O,K)
& r4_incproj(A,H,I,P,D)
& r4_incproj(A,F,J,Q,D)
& r4_incproj(A,K,E,R,G)
& r4_incproj(A,C,I,S,G)
& r4_incproj(A,C,J,T,E)
& r1_incproj(L,M,N)
& B != D
& B != F
& B != H
& B != C
& B != E
& B != G
& D != C
& F != E
& H != G
& ! [U] :
( m1_subset_1(U,u2_incsp_1(A))
=> ~ r4_incproj(A,I,J,U,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(d20_incproj,axiom,
! [A] :
( ( v1_incproj(A)
& v2_incproj(A)
& v3_incproj(A)
& v4_incproj(A)
& v5_incproj(A)
& l1_incsp_1(A) )
=> ( v11_incproj(A)
<=> ! [B] :
( m1_subset_1(B,u1_incsp_1(A))
=> ! [C] :
( m1_subset_1(C,u1_incsp_1(A))
=> ! [D] :
( m1_subset_1(D,u1_incsp_1(A))
=> ! [E] :
( m1_subset_1(E,u1_incsp_1(A))
=> ! [F] :
( m1_subset_1(F,u1_incsp_1(A))
=> ! [G] :
( m1_subset_1(G,u1_incsp_1(A))
=> ! [H] :
( m1_subset_1(H,u1_incsp_1(A))
=> ! [I] :
( m1_subset_1(I,u1_incsp_1(A))
=> ! [J] :
( m1_subset_1(J,u1_incsp_1(A))
=> ! [K] :
( m1_subset_1(K,u1_incsp_1(A))
=> ! [L] :
( m1_subset_1(L,u2_incsp_1(A))
=> ! [M] :
( m1_subset_1(M,u2_incsp_1(A))
=> ! [N] :
( m1_subset_1(N,u2_incsp_1(A))
=> ! [O] :
( m1_subset_1(O,u2_incsp_1(A))
=> ! [P] :
( m1_subset_1(P,u2_incsp_1(A))
=> ! [Q] :
( m1_subset_1(Q,u2_incsp_1(A))
=> ! [R] :
( m1_subset_1(R,u2_incsp_1(A))
=> ! [S] :
( m1_subset_1(S,u2_incsp_1(A))
=> ! [T] :
( m1_subset_1(T,u2_incsp_1(A))
=> ( ( r2_incproj(B,C,D,E)
& r2_incproj(B,F,G,H)
& r1_incsp_1(A,B,N)
& r1_incsp_1(A,B,Q)
& r4_incproj(A,D,H,L,I)
& r4_incproj(A,E,F,O,J)
& r4_incproj(A,C,G,R,K)
& r4_incproj(A,C,H,M,J)
& r4_incproj(A,E,G,P,I)
& r4_incproj(A,D,F,S,K)
& r4_incproj(A,F,G,N,H)
& r4_incproj(A,C,D,Q,E)
& r3_incproj(A,I,J,T) )
=> ( N = Q
| r1_incsp_1(A,K,T) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_m1_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(A) )
=> ! [B] :
( m1_incproj(B,A)
=> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ).
fof(existence_m1_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(A) )
=> ? [B] : m1_incproj(B,A) ) ).
fof(redefinition_m1_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(A) )
=> ! [B] :
( m1_incproj(B,A)
<=> m2_collsp(B,A) ) ) ).
fof(dt_k1_incproj,axiom,
$true ).
fof(dt_k2_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(A) )
=> m2_relset_1(k2_incproj(A),u1_struct_0(A),k1_incproj(A)) ) ).
fof(dt_k3_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(A) )
=> l1_incsp_1(k3_incproj(A)) ) ).
fof(d1_incproj,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_collsp(A)
& v3_collsp(A)
& v4_collsp(A)
& l1_collsp(A) )
=> k1_incproj(A) = a_1_0_incproj(A) ) ).
fof(fraenkel_a_1_0_incproj,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& v2_collsp(B)
& v3_collsp(B)
& v4_collsp(B)
& l1_collsp(B) )
=> ( r2_hidden(A,a_1_0_incproj(B))
<=> ? [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& A = C
& m1_incproj(C,B) ) ) ) ).
%------------------------------------------------------------------------------