begin
definition
let X be ( (
V41()
OrtAfPl-like ) (
V41()
OrtAfSp-like OrtAfPl-like )
OrtAfPl) ;
attr X is
satisfying_OPAP means
for
o,
a1,
a2,
a3,
b1,
b2,
b3 being ( ( ) ( )
Element of ( ( ) ( )
set ) )
for
M,
N being ( ( ) ( )
Subset of ) st
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) & not
b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Element of ( ( ) ( )
set ) ) & not
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
M : ( ( ) ( )
Element of ( ( ) ( )
set ) )
_|_ N : ( ( ) ( )
Subset of ) &
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
<> a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
<> a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
<> a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
<> b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
<> b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
<> b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) holds
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ;
attr X is
satisfying_PAP means
for
o,
a1,
a2,
a3,
b1,
b2,
b3 being ( ( ) ( )
Element of ( ( ) ( )
set ) )
for
M,
N being ( ( ) ( )
Subset of ) st
M : ( ( ) ( )
Element of ( ( ) ( )
set ) ) is
being_line &
N : ( ( ) ( )
Subset of ) is
being_line &
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) & not
b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Element of ( ( ) ( )
set ) ) & not
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
<> a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
<> a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
<> a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
<> b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
<> b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
<> b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) holds
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ;
attr X is
satisfying_MH1 means
for
a1,
a2,
a3,
a4,
b1,
b2,
b3,
b4 being ( ( ) ( )
Element of ( ( ) ( )
set ) )
for
M,
N being ( ( ) ( )
Subset of ) st
M : ( ( ) ( )
Subset of )
_|_ N : ( ( ) ( )
Subset of ) &
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) &
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) &
b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) &
b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) &
a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
a4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
b4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) & not
a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) & not
a4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) &
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
_|_ b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
_|_ b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
_|_ b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b4 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) holds
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
_|_ b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b4 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ;
attr X is
satisfying_MH2 means
for
a1,
a2,
a3,
a4,
b1,
b2,
b3,
b4 being ( ( ) ( )
Element of ( ( ) ( )
set ) )
for
M,
N being ( ( ) ( )
Subset of ) st
M : ( ( ) ( )
Subset of )
_|_ N : ( ( ) ( )
Subset of ) &
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) &
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) &
b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) &
b4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) &
a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
a4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) & not
a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) & not
a4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) &
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
_|_ b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
_|_ b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
_|_ b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b4 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) holds
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
_|_ b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b4 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ;
attr X is
satisfying_TDES means
for
o,
a,
a1,
b,
b1,
c,
c1 being ( ( ) ( )
Element of ( ( ) ( )
set ) ) st
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
<> a : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
<> a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
<> b : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
<> b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
<> c : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
o : ( ( ) ( )
Element of ( ( ) ( )
set ) )
<> c1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) & not
LIN b : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a : ( ( ) ( )
Element of ( ( ) ( )
set ) ) & not
LIN b : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
c : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
LIN o : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
LIN o : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
LIN o : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
c : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
c1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// o : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
c : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
b : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
c : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
c1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) holds
a : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
c : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
c1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ;
attr X is
satisfying_SCH means
for
a1,
a2,
a3,
a4,
b1,
b2,
b3,
b4 being ( ( ) ( )
Element of ( ( ) ( )
set ) )
for
M,
N being ( ( ) ( )
Subset of ) st
M : ( ( ) ( )
Subset of ) is
being_line &
N : ( ( ) ( )
Subset of ) is
being_line &
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) &
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) &
b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) &
b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) &
a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
a4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
b4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) & not
a4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) & not
a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) & not
b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) & not
b4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) & not
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) & not
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) & not
b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) & not
b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b4 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) holds
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b4 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ;
attr X is
satisfying_OSCH means
for
a1,
a2,
a3,
a4,
b1,
b2,
b3,
b4 being ( ( ) ( )
Element of ( ( ) ( )
set ) )
for
M,
N being ( ( ) ( )
Subset of ) st
M : ( ( ) ( )
Subset of )
_|_ N : ( ( ) ( )
Subset of ) &
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) &
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) &
b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) &
b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) &
a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
a4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
b4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) & not
a4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) & not
a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) & not
b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) & not
b4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in M : ( ( ) ( )
Subset of ) & not
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) & not
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) & not
b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) & not
b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
in N : ( ( ) ( )
Subset of ) &
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a2 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// b2 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b4 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) holds
a3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a4 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// b3 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b4 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ;
attr X is
satisfying_des means
for
a,
a1,
b,
b1,
c,
c1 being ( ( ) ( )
Element of ( ( ) ( )
set ) ) st not
LIN a : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b : ( ( ) ( )
Element of ( ( ) ( )
set ) ) & not
LIN a : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
c : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// b : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// c : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
c1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) &
a : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
c : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// a1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
c1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) holds
b : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
c : ( ( ) ( )
Element of ( ( ) ( )
set ) )
// b1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ,
c1 : ( ( ) ( )
Element of ( ( ) ( )
set ) ) ;
end;