:: LUKASI_1 semantic presentation
begin
theorem
:: LUKASI_1:1
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:2
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) holds
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:3
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) holds
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:4
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:5
for
A
being ( ( ) ( )
QC-alphabet
)
for
q
,
p
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:6
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:7
for
A
being ( ( ) ( )
QC-alphabet
)
for
q
,
p
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:8
for
A
being ( ( ) ( )
QC-alphabet
)
for
s
,
q
,
p
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
s
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
s
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:9
for
A
being ( ( ) ( )
QC-alphabet
)
for
q
,
r
,
p
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:10
for
A
being ( ( ) ( )
QC-alphabet
)
for
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:11
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:12
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
'not'
(
VERUM
A
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:13
for
A
being ( ( ) ( )
QC-alphabet
)
for
q
,
p
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) holds
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:14
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) holds
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:15
for
A
being ( ( ) ( )
QC-alphabet
)
for
s
,
q
,
p
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
s
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) holds
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
s
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:16
for
A
being ( ( ) ( )
QC-alphabet
)
for
s
,
q
,
p
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
s
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) holds
s
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:17
for
A
being ( ( ) ( )
QC-alphabet
)
for
s
,
q
,
p
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
s
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
s
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) holds
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:18
for
A
being ( ( ) ( )
QC-alphabet
)
for
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) holds
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:19
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) holds
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:20
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) holds
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:21
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) holds
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:22
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
,
s
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
s
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) holds
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
s
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:23
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
VERUM
A
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:24
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:25
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
'not'
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:26
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:27
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:28
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
(
(
'not'
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
(
'not'
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: LUKASI_1:29
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) &
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: LUKASI_1:30
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:31
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:32
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:33
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:34
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) iff
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: LUKASI_1:35
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) holds
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:36
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) iff
'not'
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: LUKASI_1:37
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) iff
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: LUKASI_1:38
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) iff
(
'not'
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: LUKASI_1:39
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) holds
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
theorem
:: LUKASI_1:40
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) holds
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
in
TAUT
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) ( )
Element
of
K6
(
(
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
set
) ) ;
registration
let
A
be ( ( ) ( )
QC-alphabet
) ;
let
p
,
q
,
r
be ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
cluster
K170
(
A
: ( ( ) ( )
QC-alphabet
) ,
(
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
(
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
QC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( (
V1
() ) (
V1
() )
set
) )
->
valid
;
end;
theorem
:: LUKASI_1:41
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
holds
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
;
theorem
:: LUKASI_1:42
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
&
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
holds
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
;
registration
let
A
be ( ( ) ( )
QC-alphabet
) ;
let
p
be ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
cluster
K170
(
A
: ( ( ) ( )
QC-alphabet
) ,
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
QC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( (
V1
() ) (
V1
() )
set
) )
->
valid
;
end;
registration
let
A
be ( ( ) ( )
QC-alphabet
) ;
let
p
,
q
be ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
cluster
K170
(
A
: ( ( ) ( )
QC-alphabet
) ,
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
QC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( (
V1
() ) (
V1
() )
set
) )
->
valid
;
end;
theorem
:: LUKASI_1:43
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
holds
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
;
registration
let
A
be ( ( ) ( )
QC-alphabet
) ;
let
p
,
q
,
s
be ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
cluster
K170
(
A
: ( ( ) ( )
QC-alphabet
) ,
(
s
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
s
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
QC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( (
V1
() ) (
V1
() )
set
) )
->
valid
;
end;
theorem
:: LUKASI_1:44
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
holds
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
;
theorem
:: LUKASI_1:45
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
&
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
holds
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
;
theorem
:: LUKASI_1:46
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
VERUM
A
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
&
(
'not'
(
VERUM
A
: ( ( ) ( )
QC-alphabet
)
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
) ;
registration
let
A
be ( ( ) ( )
QC-alphabet
) ;
let
p
,
q
be ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
cluster
K170
(
A
: ( ( ) ( )
QC-alphabet
) ,
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
(
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
QC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( (
V1
() ) (
V1
() )
set
) )
->
valid
;
end;
registration
let
A
be ( ( ) ( )
QC-alphabet
) ;
let
q
,
r
be ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
cluster
K170
(
A
: ( ( ) ( )
QC-alphabet
) ,
(
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
QC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( (
V1
() ) (
V1
() )
set
) )
->
valid
;
end;
theorem
:: LUKASI_1:47
for
A
being ( ( ) ( )
QC-alphabet
)
for
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
holds
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
;
registration
let
A
be ( ( ) ( )
QC-alphabet
) ;
let
p
,
q
,
r
be ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
cluster
K170
(
A
: ( ( ) ( )
QC-alphabet
) ,
(
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
(
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
QC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( (
V1
() ) (
V1
() )
set
) )
->
valid
;
end;
theorem
:: LUKASI_1:48
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
holds
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
;
theorem
:: LUKASI_1:49
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
&
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
holds
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
;
registration
let
A
be ( ( ) ( )
QC-alphabet
) ;
let
p
,
q
,
r
be ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
cluster
K170
(
A
: ( ( ) ( )
QC-alphabet
) ,
(
(
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
QC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( (
V1
() ) (
V1
() )
set
) )
->
valid
;
end;
theorem
:: LUKASI_1:50
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
holds
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
;
registration
let
A
be ( ( ) ( )
QC-alphabet
) ;
let
p
,
q
,
r
be ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
cluster
K170
(
A
: ( ( ) ( )
QC-alphabet
) ,
(
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
(
r
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
r
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
QC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( (
V1
() ) (
V1
() )
set
) )
->
valid
;
end;
theorem
:: LUKASI_1:51
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
holds
(
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
;
registration
let
A
be ( ( ) ( )
QC-alphabet
) ;
let
p
,
q
be ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
cluster
K170
(
A
: ( ( ) ( )
QC-alphabet
) ,
(
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
QC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( (
V1
() ) (
V1
() )
set
) )
->
valid
;
end;
registration
let
A
be ( ( ) ( )
QC-alphabet
) ;
let
p
,
q
be ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
cluster
K170
(
A
: ( ( ) ( )
QC-alphabet
) ,
(
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
QC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( (
V1
() ) (
V1
() )
set
) )
->
valid
;
end;
theorem
:: LUKASI_1:52
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
iff
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
) ;
registration
let
A
be ( ( ) ( )
QC-alphabet
) ;
let
p
be ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
cluster
K170
(
A
: ( ( ) ( )
QC-alphabet
) ,
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
'not'
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
QC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( (
V1
() ) (
V1
() )
set
) )
->
valid
;
end;
registration
let
A
be ( ( ) ( )
QC-alphabet
) ;
let
p
be ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
cluster
K170
(
A
: ( ( ) ( )
QC-alphabet
) ,
(
'not'
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
QC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( (
V1
() ) (
V1
() )
set
) )
->
valid
;
end;
theorem
:: LUKASI_1:53
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
'not'
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
iff
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
) ;
registration
let
A
be ( ( ) ( )
QC-alphabet
) ;
let
p
,
q
be ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
cluster
K170
(
A
: ( ( ) ( )
QC-alphabet
) ,
(
(
'not'
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
QC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( (
V1
() ) (
V1
() )
set
) )
->
valid
;
end;
theorem
:: LUKASI_1:54
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
(
'not'
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
iff
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
) ;
registration
let
A
be ( ( ) ( )
QC-alphabet
) ;
let
p
,
q
be ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
cluster
K170
(
A
: ( ( ) ( )
QC-alphabet
) ,
(
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
QC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( (
V1
() ) (
V1
() )
set
) )
->
valid
;
end;
theorem
:: LUKASI_1:55
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
iff
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
) ;
registration
let
A
be ( ( ) ( )
QC-alphabet
) ;
let
p
,
q
be ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
cluster
K170
(
A
: ( ( ) ( )
QC-alphabet
) ,
(
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
QC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( (
V1
() ) (
V1
() )
set
) )
->
valid
;
end;
theorem
:: LUKASI_1:56
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
holds
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
;
registration
let
A
be ( ( ) ( )
QC-alphabet
) ;
let
p
,
q
be ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
cluster
K170
(
A
: ( ( ) ( )
QC-alphabet
) ,
(
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ,
(
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
A
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ) : ( ( ) ( )
Element
of
QC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( (
V1
() ) (
V1
() )
set
) )
->
valid
;
end;
theorem
:: LUKASI_1:57
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) st
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
holds
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) is
valid
;
theorem
:: LUKASI_1:58
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
for
X
being ( ( ) ( )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: LUKASI_1:59
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
for
X
being ( ( ) ( )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) &
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: LUKASI_1:60
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
for
X
being ( ( ) ( )
Subset
of ( ( ) ( )
set
) ) holds
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) (
valid
)
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: LUKASI_1:61
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
for
X
being ( ( ) ( )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: LUKASI_1:62
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
for
X
being ( ( ) ( )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: LUKASI_1:63
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
for
X
being ( ( ) ( )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: LUKASI_1:64
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
for
X
being ( ( ) ( )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) &
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: LUKASI_1:65
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
for
X
being ( ( ) ( )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: LUKASI_1:66
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
for
X
being ( ( ) ( )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: LUKASI_1:67
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
for
X
being ( ( ) ( )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: LUKASI_1:68
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
,
r
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
for
X
being ( ( ) ( )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) &
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
r
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: LUKASI_1:69
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
for
X
being ( ( ) ( )
Subset
of ( ( ) ( )
set
) ) holds
(
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) iff
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ) ;
theorem
:: LUKASI_1:70
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
for
X
being ( ( ) ( )
Subset
of ( ( ) ( )
set
) ) holds
(
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
'not'
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) iff
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ) ;
theorem
:: LUKASI_1:71
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
for
X
being ( ( ) ( )
Subset
of ( ( ) ( )
set
) ) holds
(
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) iff
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ) ;
theorem
:: LUKASI_1:72
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
for
X
being ( ( ) ( )
Subset
of ( ( ) ( )
set
) ) holds
(
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
(
'not'
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) iff
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ) ;
theorem
:: LUKASI_1:73
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
for
X
being ( ( ) ( )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: LUKASI_1:74
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
for
X
being ( ( ) ( )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: LUKASI_1:75
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
for
X
being ( ( ) ( )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
(
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) &
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;
theorem
:: LUKASI_1:76
for
A
being ( ( ) ( )
QC-alphabet
)
for
p
,
q
being ( ( ) ( )
Element
of
CQC-WFF
A
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
for
X
being ( ( ) ( )
Subset
of ( ( ) ( )
set
) ) st
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
(
'not'
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
)
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) )
=>
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) &
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
'not'
q
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) : ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) holds
X
: ( ( ) ( )
Subset
of ( ( ) ( )
set
) )
|-
p
: ( ( ) ( )
Element
of
CQC-WFF
b
1
: ( ( ) ( )
QC-alphabet
) : ( ( ) (
V1
() )
Element
of
K6
(
(
QC-WFF
b
1
: ( ( ) ( )
QC-alphabet
)
)
: ( (
V1
() ) (
V1
() )
set
) ) : ( ( ) ( )
set
) ) ) ;