:: SHEFFER2 semantic presentation
begin
definition
let
L
be ( ( non
empty
) ( non
empty
)
ShefferStr
) ;
attr
L
is
satisfying_Sh_1
means
:: SHEFFER2:def 1
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) ( )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
L
: ( ( ) ( )
ShefferOrthoLattStr
) : ( ( ) ( )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
L
: ( ( ) ( )
ShefferOrthoLattStr
) : ( ( ) ( )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
L
: ( ( ) ( )
ShefferOrthoLattStr
) : ( ( ) ( )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
L
: ( ( ) ( )
ShefferOrthoLattStr
) : ( ( ) ( )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
L
: ( ( ) ( )
ShefferOrthoLattStr
) : ( ( ) ( )
set
) )) : ( ( ) ( )
M2
( the
U1
of
L
: ( ( ) ( )
ShefferOrthoLattStr
) : ( ( ) ( )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
end;
registration
cluster
non
empty
trivial
->
non
empty
satisfying_Sh_1
for ( ( ) ( )
ShefferStr
) ;
end;
registration
cluster
non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
satisfying_Sh_1
for ( ( ) ( )
ShefferStr
) ;
end;
theorem
:: SHEFFER2:1
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
,
u
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
u
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:2
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:3
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:4
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:5
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:6
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:7
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:8
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:9
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:10
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:11
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:12
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:13
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:14
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:15
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:16
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:17
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:18
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:19
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:20
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:21
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:22
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:23
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:24
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:25
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:26
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:27
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:28
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:29
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
,
u
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
u
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:30
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:31
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
,
u
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
u
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:32
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:33
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:34
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:35
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:36
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:37
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:38
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:39
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:40
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
,
u
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
u
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
u
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:41
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:42
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:43
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:44
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:45
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:46
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:47
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:48
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:49
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:50
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:51
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:52
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:53
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:54
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:55
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:56
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
,
u
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
u
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:57
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:58
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:59
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:60
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:61
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:62
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:63
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:64
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:65
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:66
for
L
being ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sh_1
) ( non
empty
satisfying_Sh_1
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:67
for
L
being ( ( non
empty
) ( non
empty
)
ShefferStr
) st
L
: ( ( non
empty
) ( non
empty
)
ShefferStr
) is
satisfying_Sh_1
holds
L
: ( ( non
empty
) ( non
empty
)
ShefferStr
) is
satisfying_Sheffer_1
;
theorem
:: SHEFFER2:68
for
L
being ( ( non
empty
) ( non
empty
)
ShefferStr
) st
L
: ( ( non
empty
) ( non
empty
)
ShefferStr
) is
satisfying_Sh_1
holds
L
: ( ( non
empty
) ( non
empty
)
ShefferStr
) is
satisfying_Sheffer_2
;
theorem
:: SHEFFER2:69
for
L
being ( ( non
empty
) ( non
empty
)
ShefferStr
) st
L
: ( ( non
empty
) ( non
empty
)
ShefferStr
) is
satisfying_Sh_1
holds
L
: ( ( non
empty
) ( non
empty
)
ShefferStr
) is
satisfying_Sheffer_3
;
registration
cluster
non
empty
Lattice-like
Boolean
well-complemented
de_Morgan
properly_defined
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
satisfying_Sh_1
for ( ( ) ( )
ShefferOrthoLattStr
) ;
end;
registration
cluster
non
empty
properly_defined
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
->
non
empty
Lattice-like
Boolean
for ( ( ) ( )
ShefferOrthoLattStr
) ;
cluster
non
empty
Lattice-like
Boolean
well-complemented
properly_defined
->
non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
for ( ( ) ( )
ShefferOrthoLattStr
) ;
end;
begin
theorem
:: SHEFFER2:70
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
x
,
w
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:71
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
p
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
=
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:72
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
y
,
w
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:73
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
q
,
p
,
y
,
w
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:74
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
q
,
p
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:75
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
w
,
p
,
y
,
q
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:76
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
p
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
=
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:77
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
y
,
w
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:78
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
y
,
w
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:79
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
p
,
y
,
w
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:80
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
p
,
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:81
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:82
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
y
,
w
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:83
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
y
,
w
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:84
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
x
,
p
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:85
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
x
,
p
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:86
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
x
,
p
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:87
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
x
,
p
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:88
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
y
,
q
,
w
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:89
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
q
,
w
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:90
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
q
,
p
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:91
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
p
,
q
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
=
(
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:92
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
p
,
q
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
=
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:93
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
z
,
w
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:94
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
z
,
w
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:95
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
w
,
p
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:96
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
p
,
w
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
=
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:97
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
p
,
w
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
=
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:98
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
z
,
q
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:99
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
q
,
z
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:100
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
q
,
z
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:101
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
w
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:102
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
w
,
p
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:103
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
y
,
w
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:104
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
y
,
w
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:105
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
p
,
w
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:106
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
w
,
p
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:107
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
p
,
w
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:108
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:109
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
p
,
w
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:110
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
p
,
w
,
q
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:111
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
q
,
w
,
p
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:112
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
w
,
y
,
p
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:113
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
w
,
y
,
p
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:114
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
q
,
p
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:115
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
q
,
z
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:116
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
q
,
z
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:117
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
w
,
q
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:118
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
q
,
p
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:119
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
p
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:120
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
p
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:121
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
=
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:122
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:123
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
x
,
z
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:124
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
x
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:125
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
x
,
z
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:126
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
x
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:127
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
z
,
y
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
=
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:128
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
z
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:129
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
x
,
z
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:130
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
x
,
z
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:131
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
y
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:132
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
p
,
w
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:133
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
w
,
p
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:134
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
p
,
y
,
w
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:135
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
p
,
w
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:136
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
y
,
p
,
w
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:137
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
p
,
q
,
w
,
y
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:138
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
q
,
w
,
y
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:139
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
q
,
w
,
y
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:140
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
z
,
p
,
q
,
y
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:141
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
z
,
p
,
q
,
y
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:142
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
z
,
q
,
y
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:143
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
v
,
p
,
y
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
v
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
v
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:144
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
y
,
w
,
z
,
v
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
v
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
v
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
v
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
v
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:145
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
y
,
z
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:146
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
z
,
y
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:147
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
x
,
w
,
y
,
z
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:148
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
z
,
w
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:149
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
p
,
z
,
y
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
(
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:150
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
p
,
z
,
y
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
(
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:151
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
z
,
p
,
y
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:152
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
z
,
p
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:153
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
w
,
q
,
p
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:154
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
w
,
p
,
q
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
(
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
p
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:155
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
z
,
w
,
y
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:156
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
w
,
z
,
x
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
w
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:157
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
q
,
x
,
z
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
(
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:158
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
x
,
q
,
z
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
(
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:159
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
z
,
x
,
q
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
z
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) ;
theorem
:: SHEFFER2:160
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
)
for
x
,
q
,
y
being ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) holds
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
|
(
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
(
y
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
|
q
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) )
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
)
: ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) )) : ( ( ) ( )
M2
( the
U1
of
b
1
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) : ( ( ) (
V11
() )
set
) ))
=
x
: ( ( ) ( )
Element
of ( ( ) (
V11
() )
set
) ) ;
theorem
:: SHEFFER2:161
for
L
being ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) holds
L
: ( ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
) ( non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
)
ShefferStr
) is
satisfying_Sh_1
;
registration
cluster
non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
->
non
empty
satisfying_Sh_1
for ( ( ) ( )
ShefferStr
) ;
cluster
non
empty
satisfying_Sh_1
->
non
empty
satisfying_Sheffer_1
satisfying_Sheffer_2
satisfying_Sheffer_3
for ( ( ) ( )
ShefferStr
) ;
end;
registration
cluster
non
empty
properly_defined
satisfying_Sh_1
->
non
empty
Lattice-like
Boolean
for ( ( ) ( )
ShefferOrthoLattStr
) ;
cluster
non
empty
Lattice-like
Boolean
well-complemented
properly_defined
->
non
empty
satisfying_Sh_1
for ( ( ) ( )
ShefferOrthoLattStr
) ;
end;