:: FOMODEL1 semantic presentation

REAL is non empty non trivial non finite set
NAT is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal countable denumerable Element of K10(REAL)
K10(REAL) is non empty non trivial non finite set
omega is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal countable denumerable set
K10(omega) is non empty non trivial non finite set
K135() is set
K10(NAT) is non empty non trivial non finite set
COMPLEX is non empty non trivial non finite set
RAT is non empty non trivial non finite set
INT is non empty non trivial non finite set
{} is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
{{}} is non empty trivial functional finite V36() 1 -element empty-membered with_common_domain countable set
1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable Element of NAT
{} * is non empty functional V36() FinSequence-membered FinSequenceSet of {}
the empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
K11({{}},NAT) is non empty non trivial Relation-like non finite set
[{},{}] is set
{[{},{}]} is non empty trivial Relation-like Function-like constant finite 1 -element countable finite-support set
K11({{}},NAT) \ {[{},{}]} is non empty non trivial Relation-like {{}} -defined NAT -valued non finite Element of K10(K11({{}},NAT))
K10(K11({{}},NAT)) is non empty non trivial non finite set
K11({{}},NAT) typed\ {[{},{}]} is Relation-like {{}} -defined NAT -valued Element of K10(K11({{}},NAT))
NAT \/ (K11({{}},NAT) \ {[{},{}]}) is non empty non trivial non finite set
K11(REAL,REAL) is non empty non trivial Relation-like non finite set
K10(K11(REAL,REAL)) is non empty non trivial non finite set
K293() is non empty V75() L8()
the carrier of K293() is non empty set
<REAL,+> is non empty L8()
K299() is non empty V75() SubStr of <REAL,+>
<NAT,+> is non empty V75() V97() uniquely-decomposable SubStr of K299()
<REAL,*> is non empty V75() V97() associative commutative L8()
<NAT,*> is non empty V75() V97() uniquely-decomposable SubStr of <REAL,*>
2 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable Element of NAT
{{},1} is non empty finite V36() countable set
K554() is set
K11(COMPLEX,COMPLEX) is non empty non trivial Relation-like non finite set
K10(K11(COMPLEX,COMPLEX)) is non empty non trivial non finite set
3 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable Element of NAT
0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of NAT
S is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
abs S is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
X is complex ext-real real integer set
- 1 is non empty complex ext-real non positive negative real integer set
S is complex ext-real real integer set
S is non empty non degenerated non trivial ZeroOneStr
the carrier of S is non empty non trivial set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable Element of K10( the carrier of S)
K10( the carrier of S) is non empty set
the carrier of S \ { the OneF of S} is Element of K10( the carrier of S)
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the ZeroF of S is Element of the carrier of S
0. S is zero Element of the carrier of S
1. S is non zero Element of the carrier of S
S is ()
the carrier of S is set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is Element of K10( the carrier of S)
K10( the carrier of S) is non empty set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is Relation-like set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty set
{0} is non empty trivial functional finite V36() 1 -element empty-membered with_common_domain countable Element of K10(NAT)
0 * is non empty functional V36() FinSequence-membered FinSequenceSet of 0
{0} is non empty trivial functional finite V36() 1 -element empty-membered with_common_domain countable set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty set
NAT \ {0} is non empty non trivial non finite with_non-empty_elements Element of K10(REAL)
NAT typed\ {0} is countable Element of K10(NAT)
NAT \ {0} is non empty non trivial non finite with_non-empty_elements countable denumerable Element of K10(NAT)
the of S " (NAT \ {0}) is Element of K10(( the carrier of S \ { the OneF of S}))
INT \ NAT is Element of K10(INT)
K10(INT) is non empty non trivial non finite set
INT typed\ NAT is Element of K10(INT)
the of S " (INT \ NAT) is Element of K10(( the carrier of S \ { the OneF of S}))
the of S " NAT is Element of K10(( the carrier of S \ { the OneF of S}))
INT \ {0} is non empty non trivial non finite with_non-empty_elements Element of K10(INT)
INT typed\ {0} is Element of K10(INT)
the of S " (INT \ {0}) is Element of K10(( the carrier of S \ { the OneF of S}))
the ZeroF of S is Element of the carrier of S
{ the ZeroF of S, the OneF of S} is non empty finite countable set
the carrier of S \ { the ZeroF of S, the OneF of S} is Element of K10( the carrier of S)
the carrier of S typed\ { the ZeroF of S, the OneF of S} is Element of K10( the carrier of S)
S is ()
(S) is set
the carrier of S is set
(S) is set
the OneF of S is Element of the carrier of S
{(S)} is non empty trivial finite 1 -element countable set
(S) \ {(S)} is Element of K10((S))
K10((S)) is non empty set
(S) typed\ {(S)} is Element of K10((S))
(S) is set
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is Element of K10( the carrier of S)
K10( the carrier of S) is non empty set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is Relation-like set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty set
1 -tuples_on (S) is functional V36() FinSequence-membered FinSequenceSet of (S)
S is ()
(S) is set
the carrier of S is set
S is ZeroOneStr
the carrier of S is set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is Element of K10( the carrier of S)
K10( the carrier of S) is non empty set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
X is Element of the carrier of S \ { the OneF of S}
the ZeroF of S is Element of the carrier of S
- 2 is non empty complex ext-real non positive negative real integer set
S is ZeroOneStr
the carrier of S is set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is Element of K10( the carrier of S)
K10( the carrier of S) is non empty set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
X is Element of the carrier of S \ { the OneF of S}
(S,X) is complex ext-real real integer set
S is non empty non degenerated non trivial ZeroOneStr
the carrier of S is non empty non trivial set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable Element of K10( the carrier of S)
K10( the carrier of S) is non empty set
the carrier of S \ { the OneF of S} is non empty Element of K10( the carrier of S)
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
S1 is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
SS1 is Element of the carrier of S \ { the OneF of S}
S1 . SS1 is complex ext-real real integer Element of INT
(S,SS1) is complex ext-real real integer Element of INT
S1 is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
SS1 is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
dom S1 is non empty Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty set
dom SS1 is non empty Element of K10(( the carrier of S \ { the OneF of S}))
SX is set
add is Element of the carrier of S \ { the OneF of S}
S1 . add is complex ext-real real integer Element of INT
(S,add) is complex ext-real real integer Element of INT
SS1 . add is complex ext-real real integer Element of INT
S1 . SX is set
SS1 . SX is set
the non empty non trivial non finite set is non empty non trivial non finite set
the Element of the non empty non trivial non finite set is Element of the non empty non trivial non finite set
{ the Element of the non empty non trivial non finite set } is non empty trivial finite 1 -element countable Element of K10( the non empty non trivial non finite set )
K10( the non empty non trivial non finite set ) is non empty non trivial non finite set
the non empty non trivial non finite set \ { the Element of the non empty non trivial non finite set } is non empty non trivial non finite Element of K10( the non empty non trivial non finite set )
the non empty non trivial non finite set typed\ { the Element of the non empty non trivial non finite set } is Element of K10( the non empty non trivial non finite set )
the Element of the non empty non trivial non finite set \ { the Element of the non empty non trivial non finite set } is Element of the non empty non trivial non finite set \ { the Element of the non empty non trivial non finite set }
SX is Element of the non empty non trivial non finite set
ZeroOneStr(# the non empty non trivial non finite set , the Element of the non empty non trivial non finite set ,SX #) is strict ZeroOneStr
1. ZeroOneStr(# the non empty non trivial non finite set , the Element of the non empty non trivial non finite set ,SX #) is Element of the carrier of ZeroOneStr(# the non empty non trivial non finite set , the Element of the non empty non trivial non finite set ,SX #)
the carrier of ZeroOneStr(# the non empty non trivial non finite set , the Element of the non empty non trivial non finite set ,SX #) is set
the OneF of ZeroOneStr(# the non empty non trivial non finite set , the Element of the non empty non trivial non finite set ,SX #) is Element of the carrier of ZeroOneStr(# the non empty non trivial non finite set , the Element of the non empty non trivial non finite set ,SX #)
0. ZeroOneStr(# the non empty non trivial non finite set , the Element of the non empty non trivial non finite set ,SX #) is zero Element of the carrier of ZeroOneStr(# the non empty non trivial non finite set , the Element of the non empty non trivial non finite set ,SX #)
the ZeroF of ZeroOneStr(# the non empty non trivial non finite set , the Element of the non empty non trivial non finite set ,SX #) is Element of the carrier of ZeroOneStr(# the non empty non trivial non finite set , the Element of the non empty non trivial non finite set ,SX #)
f is non empty non degenerated non trivial ZeroOneStr
S is non empty non degenerated non trivial non finite ZeroOneStr
the carrier of S is non empty non trivial non finite set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
(S) is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
(S) " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
the ZeroF of S is Element of the carrier of S
{ the ZeroF of S} is non empty trivial finite 1 -element countable Element of K10( the carrier of S)
( the carrier of S \ { the OneF of S}) \ { the ZeroF of S} is non empty non trivial non finite Element of K10( the carrier of S)
( the carrier of S \ { the OneF of S}) typed\ { the ZeroF of S} is Element of K10(( the carrier of S \ { the OneF of S}))
( the carrier of S \ { the OneF of S}) \ { the ZeroF of S} is non empty non trivial non finite Element of K10(( the carrier of S \ { the OneF of S}))
dom (S) is non empty Element of K10(( the carrier of S \ { the OneF of S}))
S2 is set
SS2 is Element of the carrier of S \ { the OneF of S}
(S,SS2) is complex ext-real real integer Element of INT
(S) . SS2 is complex ext-real real integer Element of INT
S is non empty non degenerated non trivial ZeroOneStr
(S) is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the carrier of S is non empty non trivial set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable Element of K10( the carrier of S)
K10( the carrier of S) is non empty set
the carrier of S \ { the OneF of S} is non empty Element of K10( the carrier of S)
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the ZeroF of S is Element of the carrier of S
(S) . the ZeroF of S is set
0. S is zero Element of the carrier of S
1. S is non zero Element of the carrier of S
SX is Element of the carrier of S \ { the OneF of S}
(S) . SX is complex ext-real real integer Element of INT
(S,SX) is complex ext-real real integer Element of INT
the non empty non degenerated non trivial non finite ZeroOneStr is non empty non degenerated non trivial non finite ZeroOneStr
0. the non empty non degenerated non trivial non finite ZeroOneStr is zero Element of the carrier of the non empty non degenerated non trivial non finite ZeroOneStr
the carrier of the non empty non degenerated non trivial non finite ZeroOneStr is non empty non trivial non finite set
the ZeroF of the non empty non degenerated non trivial non finite ZeroOneStr is Element of the carrier of the non empty non degenerated non trivial non finite ZeroOneStr
1. the non empty non degenerated non trivial non finite ZeroOneStr is non zero Element of the carrier of the non empty non degenerated non trivial non finite ZeroOneStr
the OneF of the non empty non degenerated non trivial non finite ZeroOneStr is Element of the carrier of the non empty non degenerated non trivial non finite ZeroOneStr
( the non empty non degenerated non trivial non finite ZeroOneStr ) is non empty Relation-like the carrier of the non empty non degenerated non trivial non finite ZeroOneStr \ { the OneF of the non empty non degenerated non trivial non finite ZeroOneStr } -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of the non empty non degenerated non trivial non finite ZeroOneStr \ { the OneF of the non empty non degenerated non trivial non finite ZeroOneStr }),INT))
{ the OneF of the non empty non degenerated non trivial non finite ZeroOneStr } is non empty trivial finite 1 -element countable Element of K10( the carrier of the non empty non degenerated non trivial non finite ZeroOneStr )
K10( the carrier of the non empty non degenerated non trivial non finite ZeroOneStr ) is non empty non trivial non finite set
the carrier of the non empty non degenerated non trivial non finite ZeroOneStr \ { the OneF of the non empty non degenerated non trivial non finite ZeroOneStr } is non empty non trivial non finite Element of K10( the carrier of the non empty non degenerated non trivial non finite ZeroOneStr )
the carrier of the non empty non degenerated non trivial non finite ZeroOneStr typed\ { the OneF of the non empty non degenerated non trivial non finite ZeroOneStr } is Element of K10( the carrier of the non empty non degenerated non trivial non finite ZeroOneStr )
K11(( the carrier of the non empty non degenerated non trivial non finite ZeroOneStr \ { the OneF of the non empty non degenerated non trivial non finite ZeroOneStr }),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of the non empty non degenerated non trivial non finite ZeroOneStr \ { the OneF of the non empty non degenerated non trivial non finite ZeroOneStr }),INT)) is non empty non trivial non finite set
( the carrier of the non empty non degenerated non trivial non finite ZeroOneStr , the ZeroF of the non empty non degenerated non trivial non finite ZeroOneStr , the OneF of the non empty non degenerated non trivial non finite ZeroOneStr ,( the non empty non degenerated non trivial non finite ZeroOneStr )) is () ()
S1 is () ()
0. S1 is zero Element of the carrier of S1
the carrier of S1 is set
the ZeroF of S1 is Element of the carrier of S1
1. S1 is Element of the carrier of S1
the OneF of S1 is Element of the carrier of S1
the of S1 is Relation-like the carrier of S1 \ { the OneF of S1} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S1 \ { the OneF of S1}),INT))
{ the OneF of S1} is non empty trivial finite 1 -element countable set
the carrier of S1 \ { the OneF of S1} is Element of K10( the carrier of S1)
K10( the carrier of S1) is non empty set
the carrier of S1 typed\ { the OneF of S1} is Element of K10( the carrier of S1)
K11(( the carrier of S1 \ { the OneF of S1}),INT) is Relation-like set
K10(K11(( the carrier of S1 \ { the OneF of S1}),INT)) is non empty set
(S1) is set
the of S1 " {0} is Element of K10(( the carrier of S1 \ { the OneF of S1}))
K10(( the carrier of S1 \ { the OneF of S1})) is non empty set
(S1) is set
the of S1 . (S1) is set
S is ()
S is ()
S is non empty ()
(S) is set
the carrier of S is non empty set
S is () ()
(S) is set
the carrier of S is set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is Element of K10( the carrier of S)
K10( the carrier of S) is non empty set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is Relation-like set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty set
S is non empty non degenerated non trivial () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty Element of K10( the carrier of S)
K10( the carrier of S) is non empty set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty set
(S) is non empty set
K10((S)) is non empty set
S is non empty non degenerated non trivial ()
(S) is set
the ZeroF of S is Element of the carrier of S
the carrier of S is non empty non trivial set
(S) is non empty set
(S) is set
the OneF of S is Element of the carrier of S
{(S)} is non empty trivial finite 1 -element countable set
(S) \ {(S)} is Element of K10((S))
K10((S)) is non empty set
(S) typed\ {(S)} is Element of K10((S))
1. S is non zero Element of the carrier of S
0. S is zero Element of the carrier of S
S is non empty non degenerated non trivial () ()
(S) is set
the carrier of S is non empty non trivial set
(S) is set
the ZeroF of S is Element of the carrier of S
(S) is set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty Element of K10( the carrier of S)
K10( the carrier of S) is non empty set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " (INT \ NAT) is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty set
(S) is non empty set
(S) is set
{(S)} is non empty trivial finite 1 -element countable set
(S) \ {(S)} is Element of K10((S))
K10((S)) is non empty set
(S) typed\ {(S)} is Element of K10((S))
dom the of S is non empty Element of K10(( the carrier of S \ { the OneF of S}))
the of S . (S) is set
add is Element of (S)
S is non empty non degenerated non trivial ()
(S) is set
(S) is set
the carrier of S is non empty non trivial set
(S) is set
the OneF of S is Element of the carrier of S
{(S)} is non empty trivial finite 1 -element countable set
(S) \ {(S)} is Element of K10((S))
K10((S)) is non empty set
(S) typed\ {(S)} is Element of K10((S))
(S) is non empty set
K10((S)) is non empty set
S is non empty non degenerated non trivial ()
(S) is set
the ZeroF of S is Element of the carrier of S
the carrier of S is non empty non trivial set
(S) is non empty set
(S) is non empty Element of K10((S))
K10((S)) is non empty set
(S) is set
(S) is set
the OneF of S is Element of the carrier of S
{(S)} is non empty trivial finite 1 -element countable set
(S) \ {(S)} is Element of K10((S))
K10((S)) is non empty set
(S) typed\ {(S)} is Element of K10((S))
S is non empty non degenerated non trivial () ()
(S) is non empty set
the carrier of S is non empty non trivial set
(S) is non empty non trivial non finite Element of K10((S))
K10((S)) is non empty set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty Element of K10( the carrier of S)
K10( the carrier of S) is non empty set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty set
(S) is set
the of S " (NAT \ {0}) is Element of K10(( the carrier of S \ { the OneF of S}))
(S) /\ (S) is Element of K10((S))
(S) typed/\ (S) is Element of K10((S))
K10((S)) is non empty non trivial non finite set
(S) /\ (S) is set
(S) /\typed (S) is Element of K10((S))
K10((S)) is non empty set
(S) is set
the of S " NAT is Element of K10(( the carrier of S \ { the OneF of S}))
(S) is set
the of S " (INT \ {0}) is Element of K10(( the carrier of S \ { the OneF of S}))
(S) /\ (S) is set
(S) typed/\ (S) is Element of K10((S))
K10((S)) is non empty set
(S) /\typed (S) is Element of K10((S))
K10((S)) is non empty set
(S) is set
the of S " (INT \ NAT) is Element of K10(( the carrier of S \ { the OneF of S}))
(S) is set
the ZeroF of S is Element of the carrier of S
{ the ZeroF of S, the OneF of S} is non empty finite countable set
the carrier of S \ { the ZeroF of S, the OneF of S} is Element of K10( the carrier of S)
the carrier of S typed\ { the ZeroF of S, the OneF of S} is Element of K10( the carrier of S)
(S) \ (S) is Element of K10((S))
K10((S)) is non empty set
(S) typed\ (S) is Element of K10((S))
(S) is non empty Element of K10((S))
(S) is set
(S) is set
{(S)} is non empty trivial finite 1 -element countable set
(S) \ {(S)} is Element of K10((S))
K10((S)) is non empty set
(S) typed\ {(S)} is Element of K10((S))
(S) is Element of (S)
{(S)} is non empty trivial finite 1 -element countable Element of K10((S))
K10((S)) is non empty set
{ the OneF of S} is non empty trivial finite 1 -element countable Element of K10( the carrier of S)
the carrier of S \ { the OneF of S} is non empty Element of K10( the carrier of S)
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
{0} /\ (NAT \ {0}) is finite countable Element of K10(REAL)
{0} typed/\ (NAT \ {0}) is trivial functional finite V36() empty-membered with_common_domain countable Element of K10({0})
K10({0}) is non empty finite V36() countable set
{0} /\ (NAT \ {0}) is finite countable set
{0} /\typed (NAT \ {0}) is with_non-empty_elements Element of K10((NAT \ {0}))
K10((NAT \ {0})) is non empty non trivial non finite set
the of S " ({0} /\ (NAT \ {0})) is Element of K10(( the carrier of S \ { the OneF of S}))
the of S " {} is empty proper epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of K10(( the carrier of S \ { the OneF of S}))
NAT /\ (INT \ {0}) is Element of K10(INT)
NAT typed/\ (INT \ {0}) is countable Element of K10(NAT)
NAT /\ (INT \ {0}) is set
NAT /\typed (INT \ {0}) is with_non-empty_elements Element of K10((INT \ {0}))
K10((INT \ {0})) is non empty non trivial non finite set
the of S " (NAT /\ (INT \ {0})) is Element of K10(( the carrier of S \ { the OneF of S}))
NAT /\ INT is Element of K10(REAL)
NAT typed/\ INT is countable Element of K10(NAT)
NAT /\ INT is set
NAT /\typed INT is Element of K10(INT)
(NAT /\ INT) \ {0} is with_non-empty_elements Element of K10(REAL)
(NAT /\ INT) typed\ {0} is Element of K10((NAT /\ INT))
K10((NAT /\ INT)) is non empty set
(NAT /\ INT) \ {0} is with_non-empty_elements Element of K10((NAT /\ INT))
the of S " ((NAT /\ INT) \ {0}) is Element of K10(( the carrier of S \ { the OneF of S}))
{ the ZeroF of S} is non empty trivial finite 1 -element countable Element of K10( the carrier of S)
{ the ZeroF of S} \/ { the OneF of S} is non empty finite countable Element of K10( the carrier of S)
(S) \ ({ the ZeroF of S} \/ { the OneF of S}) is Element of K10((S))
(S) typed\ ({ the ZeroF of S} \/ { the OneF of S}) is Element of K10((S))
( the carrier of S \ { the OneF of S}) \ { the ZeroF of S} is Element of K10( the carrier of S)
( the carrier of S \ { the OneF of S}) typed\ { the ZeroF of S} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty set
( the carrier of S \ { the OneF of S}) \ { the ZeroF of S} is Element of K10(( the carrier of S \ { the OneF of S}))
(S) \ ( the carrier of S \ { the OneF of S}) is Element of K10((S))
(S) typed\ ( the carrier of S \ { the OneF of S}) is Element of K10((S))
(S) /\ { the ZeroF of S} is finite countable Element of K10( the carrier of S)
(S) typed/\ { the ZeroF of S} is Element of K10((S))
(S) /\ { the ZeroF of S} is finite countable set
(S) /\typed { the ZeroF of S} is trivial finite countable Element of K10({ the ZeroF of S})
K10({ the ZeroF of S}) is non empty finite V36() countable set
((S) \ ( the carrier of S \ { the OneF of S})) \/ ((S) /\ { the ZeroF of S}) is set
{} \/ ((S) /\ { the ZeroF of S}) is finite countable set
the of S " INT is Element of K10(( the carrier of S \ { the OneF of S}))
( the of S " INT) \ ( the of S " NAT) is Element of K10(( the carrier of S \ { the OneF of S}))
( the of S " INT) typed\ ( the of S " NAT) is Element of K10(( the of S " INT))
K10(( the of S " INT)) is non empty set
( the of S " INT) \ ( the of S " NAT) is Element of K10(( the of S " INT))
( the of S " INT) \ ( the of S " {0}) is Element of K10(( the carrier of S \ { the OneF of S}))
( the of S " INT) typed\ ( the of S " {0}) is Element of K10(( the of S " INT))
( the of S " INT) \ ( the of S " {0}) is Element of K10(( the of S " INT))
( the of S " NAT) \ ( the of S " {0}) is Element of K10(( the carrier of S \ { the OneF of S}))
( the of S " NAT) typed\ ( the of S " {0}) is Element of K10(( the of S " NAT))
K10(( the of S " NAT)) is non empty set
( the of S " NAT) \ ( the of S " {0}) is Element of K10(( the of S " NAT))
the of S . (S) is set
the of S . the ZeroF of S is set
{ the OneF of S} \/ { the ZeroF of S} is non empty finite countable Element of K10( the carrier of S)
the carrier of S \ ({ the OneF of S} \/ { the ZeroF of S}) is Element of K10( the carrier of S)
the carrier of S typed\ ({ the OneF of S} \/ { the ZeroF of S}) is Element of K10( the carrier of S)
NN2 is set
S is non empty non degenerated non trivial () ()
(S) is set
the carrier of S is non empty non trivial set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty Element of K10( the carrier of S)
K10( the carrier of S) is non empty set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " NAT is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty set
(S) is non empty non trivial non finite Element of K10((S))
(S) is non empty set
K10((S)) is non empty set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
X is set
(S) is set
X is Element of (S)
(S) is set
the ZeroF of S is Element of the carrier of S
{ the ZeroF of S, the OneF of S} is non empty finite countable set
the carrier of S \ { the ZeroF of S, the OneF of S} is Element of K10( the carrier of S)
the carrier of S typed\ { the ZeroF of S, the OneF of S} is Element of K10( the carrier of S)
(S) is non empty Element of K10((S))
(S) is non empty set
K10((S)) is non empty set
(S) is set
{(S)} is non empty trivial finite 1 -element countable set
(S) \ {(S)} is Element of K10((S))
K10((S)) is non empty set
(S) typed\ {(S)} is Element of K10((S))
X is Element of (S)
(S) is set
the of S " (INT \ NAT) is Element of K10(( the carrier of S \ { the OneF of S}))
(S) is set
the of S " (INT \ {0}) is Element of K10(( the carrier of S \ { the OneF of S}))
X is Element of (S)
(S) is set
the of S " (NAT \ {0}) is Element of K10(( the carrier of S \ { the OneF of S}))
X is Element of (S)
(S) is non empty non trivial non finite Element of K10((S))
(S) is non empty set
K10((S)) is non empty set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
X is Element of (S)
(S) is set
the ZeroF of S is Element of the carrier of S
{ the ZeroF of S, the OneF of S} is non empty finite countable set
the carrier of S \ { the ZeroF of S, the OneF of S} is Element of K10( the carrier of S)
the carrier of S typed\ { the ZeroF of S, the OneF of S} is Element of K10( the carrier of S)
X is Element of (S)
(S) is set
the of S " (NAT \ {0}) is Element of K10(( the carrier of S \ { the OneF of S}))
(S) is set
the of S " (INT \ {0}) is Element of K10(( the carrier of S \ { the OneF of S}))
X is Element of (S)
(S) is set
the of S " (INT \ {0}) is Element of K10(( the carrier of S \ { the OneF of S}))
(S) is non empty Element of K10((S))
(S) is non empty set
K10((S)) is non empty set
(S) is set
{(S)} is non empty trivial finite 1 -element countable set
(S) \ {(S)} is Element of K10((S))
K10((S)) is non empty set
(S) typed\ {(S)} is Element of K10((S))
(S) is set
the of S " (INT \ NAT) is Element of K10(( the carrier of S \ { the OneF of S}))
(S) /\ (S) is set
(S) typed/\ (S) is Element of K10((S))
K10((S)) is non empty set
(S) /\typed (S) is Element of K10((S))
K10((S)) is non empty set
NAT /\ (INT \ NAT) is Element of K10(INT)
NAT typed/\ (INT \ NAT) is countable Element of K10(NAT)
NAT /\ (INT \ NAT) is set
NAT /\typed (INT \ NAT) is Element of K10((INT \ NAT))
K10((INT \ NAT)) is non empty set
the of S " (NAT /\ (INT \ NAT)) is Element of K10(( the carrier of S \ { the OneF of S}))
NAT /\ INT is Element of K10(REAL)
NAT typed/\ INT is countable Element of K10(NAT)
NAT /\ INT is set
NAT /\typed INT is Element of K10(INT)
NAT /\ NAT is Element of K10(REAL)
NAT typed/\ NAT is countable Element of K10(NAT)
NAT /\ NAT is set
NAT /\typed NAT is countable Element of K10(NAT)
(NAT /\ INT) \ (NAT /\ NAT) is Element of K10(REAL)
(NAT /\ INT) typed\ (NAT /\ NAT) is Element of K10((NAT /\ INT))
K10((NAT /\ INT)) is non empty set
(NAT /\ INT) \ (NAT /\ NAT) is Element of K10((NAT /\ INT))
the of S " ((NAT /\ INT) \ (NAT /\ NAT)) is Element of K10(( the carrier of S \ { the OneF of S}))
the of S " {} is empty proper epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of K10(( the carrier of S \ { the OneF of S}))
(S) \ (S) is Element of K10((S))
(S) typed\ (S) is Element of K10((S))
SX is Element of (S)
X is Element of (S)
(S) is non empty non trivial non finite Element of K10((S))
(S) is non empty set
K10((S)) is non empty set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
(S) is set
the of S " (NAT \ {0}) is Element of K10(( the carrier of S \ { the OneF of S}))
SS1 is Element of (S)
(S) /\ (S) is Element of K10((S))
(S) typed/\ (S) is Element of K10((S))
K10((S)) is non empty non trivial non finite set
(S) /\ (S) is set
(S) /\typed (S) is Element of K10((S))
K10((S)) is non empty set
S is non empty non degenerated non trivial () ()
(S) is set
the carrier of S is non empty non trivial set
(S) is non empty set
(S) is non empty Element of K10((S))
K10((S)) is non empty set
(S) is set
the OneF of S is Element of the carrier of S
{(S)} is non empty trivial finite 1 -element countable set
(S) \ {(S)} is Element of K10((S))
K10((S)) is non empty set
(S) typed\ {(S)} is Element of K10((S))
(S) is Element of (S)
the ZeroF of S is Element of the carrier of S
X is Element of (S)
(S) is non empty set
(S) is non empty non trivial non finite Element of K10((S))
K10((S)) is non empty set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty Element of K10( the carrier of S)
K10( the carrier of S) is non empty set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty set
the Element of (S) is Element of (S)
S is non empty non degenerated non trivial () ()
(S) is set
the carrier of S is non empty non trivial set
(S) is set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty Element of K10( the carrier of S)
K10( the carrier of S) is non empty set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " (INT \ {0}) is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty set
(S) is non empty set
the of S " NAT is Element of K10(( the carrier of S \ { the OneF of S}))
(S) is set
the of S " (NAT \ {0}) is Element of K10(( the carrier of S \ { the OneF of S}))
SX is (S) (S) Element of (S)
(S) /\ (S) is set
(S) typed/\ (S) is Element of K10((S))
K10((S)) is non empty set
(S) /\typed (S) is Element of K10((S))
K10((S)) is non empty set
S is non empty non degenerated non trivial () ()
(S) is set
the carrier of S is non empty non trivial set
the (S) (S) (S) (S) (S) (S) Element of (S) is (S) (S) (S) (S) (S) (S) Element of (S)
S is non empty non degenerated non trivial () ()
(S) is set
the carrier of S is non empty non trivial set
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty Element of K10( the carrier of S)
K10( the carrier of S) is non empty set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
X is (S) Element of (S)
the of S . X is set
(S) is non empty Element of K10((S))
(S) is non empty set
K10((S)) is non empty set
(S) is set
{(S)} is non empty trivial finite 1 -element countable set
(S) \ {(S)} is Element of K10((S))
K10((S)) is non empty set
(S) typed\ {(S)} is Element of K10((S))
K11((S),INT) is non empty non trivial Relation-like non finite set
K10(K11((S),INT)) is non empty non trivial non finite set
SS1 is non empty Relation-like (S) -defined INT -valued Function-like total quasi_total Element of K10(K11((S),INT))
SX is Element of (S)
SS1 . SX is complex ext-real real integer Element of INT
S is non empty non degenerated non trivial () ()
(S) is set
the carrier of S is non empty non trivial set
X is (S) (S) (S) (S) (S) (S) Element of (S)
(S,X) is complex ext-real real integer Element of INT
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty Element of K10( the carrier of S)
K10( the carrier of S) is non empty set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S . X is set
(S) is non empty non trivial non finite Element of K10((S))
(S) is non empty set
K10((S)) is non empty set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty set
SS1 is set
S is non empty non degenerated non trivial () ()
(S) is non empty set
the carrier of S is non empty non trivial set
(S) -concatenation is non empty Relation-like K11(((S) *),((S) *)) -defined (S) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((S) *),((S) *)),((S) *)))
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
K11(((S) *),((S) *)) is non empty non trivial Relation-like non finite set
K11(K11(((S) *),((S) *)),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((S) *),((S) *)),((S) *))) is non empty non trivial non finite set
S is non empty non degenerated non trivial () ()
(S) is non empty set
the carrier of S is non empty non trivial set
(S) -multiCat is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
K11((((S) *) *),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) *),((S) *))) is non empty non trivial non finite set
{} .--> {} is trivial Relation-like {{}} -defined Function-like one-to-one constant finite Function-yielding V160() Cardinal-yielding countable finite-support set
{{}} --> {} is non empty Relation-like empty-yielding {{}} -defined {{}} -valued Function-like constant total quasi_total finite Function-yielding V160() Cardinal-yielding countable finite-support Element of K10(K11({{}},{{}}))
K11({{}},{{}}) is non empty Relation-like finite countable set
K10(K11({{}},{{}})) is non empty finite V36() countable set
(S) -concatenation is non empty Relation-like K11(((S) *),((S) *)) -defined (S) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((S) *),((S) *)),((S) *)))
K11(((S) *),((S) *)) is non empty non trivial Relation-like non finite set
K11(K11(((S) *),((S) *)),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((S) *),((S) *)),((S) *))) is non empty non trivial non finite set
MultPlace ((S) -concatenation) is non empty Relation-like (((S) *) *) \ {{}} -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((S) *) *) \ {{}}),((S) *)))
(((S) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
(((S) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((S) *) *))
K11(((((S) *) *) \ {{}}),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((S) *) *) \ {{}}),((S) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((S) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
S is non empty non degenerated non trivial () ()
(S) is non empty set
the carrier of S is non empty non trivial set
(S) -firstChar is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
K11((((S) *) \ {{}}),(S)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) \ {{}}),(S))) is non empty non trivial non finite set
(S) -pr1 is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total associative Element of K10(K11(K11((S),(S)),(S)))
K11((S),(S)) is non empty Relation-like set
K11(K11((S),(S)),(S)) is non empty Relation-like set
K10(K11(K11((S),(S)),(S))) is non empty set
K530((S),(S)) is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total Element of K10(K11(K11((S),(S)),(S)))
MultPlace ((S) -pr1) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
S is non empty non degenerated non trivial () ()
(S) is non empty set
the carrier of S is non empty non trivial set
X is set
X is set
S is non empty non degenerated non trivial () ()
(S) is non empty set
the carrier of S is non empty non trivial set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
X is set
S is non empty non degenerated non trivial () ()
(S) is non empty set
the carrier of S is non empty non trivial set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
X is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of ((S) *) \ {{}}
S is non empty non degenerated non trivial () ()
(S) is non empty set
the carrier of S is non empty non trivial set
(S) is non empty non trivial non finite Element of K10((S))
K10((S)) is non empty set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty Element of K10( the carrier of S)
K10( the carrier of S) is non empty set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty set
(S) \/ (S) is non empty non trivial non finite set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty set
the carrier of S is non empty non trivial non finite set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
X is (S) Element of (S)
<*X*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
(S) is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
K11((((S) *) *),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) *),((S) *))) is non empty non trivial non finite set
(S) -multiCat is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
(S) -concatenation is non empty Relation-like K11(((S) *),((S) *)) -defined (S) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((S) *),((S) *)),((S) *)))
K11(((S) *),((S) *)) is non empty non trivial Relation-like non finite set
K11(K11(((S) *),((S) *)),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((S) *),((S) *)),((S) *))) is non empty non trivial non finite set
MultPlace ((S) -concatenation) is non empty Relation-like (((S) *) *) \ {{}} -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((S) *) *) \ {{}}),((S) *)))
(((S) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
(((S) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((S) *) *))
K11(((((S) *) *) \ {{}}),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((S) *) *) \ {{}}),((S) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((S) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
S1 is set
(S,X) is complex ext-real real integer Element of INT
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S . X is set
abs (S,X) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
{ (<*X*> ^ ((S) . b₁)) where b₁ is Relation-like NAT -defined (S) * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of ((S) *) * : ( rng b₁ c= S1 & b₁ is abs (S,X) -element ) } is set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
X is (S) Element of (S)
S1 is set
(S,X,S1) is set
(S) is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
<*X*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
(S) is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
K11((((S) *) *),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) *),((S) *))) is non empty non trivial non finite set
(S) -multiCat is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
(S) -concatenation is non empty Relation-like K11(((S) *),((S) *)) -defined (S) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((S) *),((S) *)),((S) *)))
K11(((S) *),((S) *)) is non empty non trivial Relation-like non finite set
K11(K11(((S) *),((S) *)),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((S) *),((S) *)),((S) *))) is non empty non trivial non finite set
MultPlace ((S) -concatenation) is non empty Relation-like (((S) *) *) \ {{}} -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((S) *) *) \ {{}}),((S) *)))
(((S) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
(((S) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((S) *) *))
K11(((((S) *) *) \ {{}}),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((S) *) *) \ {{}}),((S) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((S) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
(S,X) is complex ext-real real integer Element of INT
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S . X is set
abs (S,X) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
{ (<*X*> ^ ((S) . b₁)) where b₁ is Relation-like NAT -defined (S) * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of ((S) *) * : ( rng b₁ c= S1 & b₁ is abs (S,X) -element ) } is set
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
K10((((S) *) \ {{}})) is non empty non trivial non finite set
bool (((S) *) \ {{}}) is non empty non trivial non finite Element of K10(K10((((S) *) \ {{}})))
K10(K10((((S) *) \ {{}}))) is non empty non trivial non finite set
f is set
S2 is Relation-like NAT -defined (S) * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of ((S) *) *
(S) . S2 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
<*X*> ^ ((S) . S2) is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
rng S2 is functional finite V36() FinSequence-membered countable Element of K10(((S) *))
add is Element of (S)
<*add*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
SS2 is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of (S)
E1 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of (S)
SS2 ^ E1 is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
S is non empty non degenerated non trivial non finite () ()
(S) is set
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
(S) is non empty non trivial non finite set
{ (S,b₁,a₂) where b₁ is (S) Element of (S) : b₁ is (S) } is set
union { (S,b₁,a₂) where b₁ is (S) Element of (S) : b₁ is (S) } is set
X is Relation-like Function-like set
dom X is set
X . 0 is set
{ (S,b₁,a₂) where b₁ is (S) Element of (S) : b₁ is (S) } is set
union { (S,b₁,a₂) where b₁ is (S) Element of (S) : b₁ is (S) } is set
X is Relation-like Function-like set
dom X is set
X . 0 is set
S1 is Relation-like Function-like set
dom S1 is set
S1 . 0 is set
SS1 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
SS1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
X . (SS1 + 1) is set
X . SS1 is set
{ (S,b₁,(X . SS1)) where b₁ is (S) Element of (S) : b₁ is (S) } is set
union { (S,b₁,(X . SS1)) where b₁ is (S) Element of (S) : b₁ is (S) } is set
(union { (S,b₁,(X . SS1)) where b₁ is (S) Element of (S) : b₁ is (S) } ) \/ (X . SS1) is set
SS1 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
SS1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
S1 . (SS1 + 1) is set
S1 . SS1 is set
{ (S,b₁,(S1 . SS1)) where b₁ is (S) Element of (S) : b₁ is (S) } is set
union { (S,b₁,(S1 . SS1)) where b₁ is (S) Element of (S) : b₁ is (S) } is set
(union { (S,b₁,(S1 . SS1)) where b₁ is (S) Element of (S) : b₁ is (S) } ) \/ (S1 . SS1) is set
S is non empty non degenerated non trivial non finite () ()
(S) is set
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
(S) is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
K10(((S) *)) is non empty non trivial non finite set
K10((S)) is non empty non trivial non finite set
(S) is non empty non trivial non finite Element of K10((S))
SS1 is Element of K10((S))
SS1 * is non empty functional V36() FinSequence-membered Element of K10(((S) *))
S is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
X is non empty non degenerated non trivial non finite () ()
(X) is Relation-like Function-like set
(X) . S is set
(X) is non empty non trivial non finite set
the carrier of X is non empty non trivial non finite set
(X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X)
((X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((X) *))
K10(((X) *)) is non empty non trivial non finite set
((X) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((X) *))
(X) is non empty non trivial non finite Element of K10((X))
K10((X)) is non empty non trivial non finite set
the OneF of X is Element of the carrier of X
{ the OneF of X} is non empty trivial finite 1 -element countable set
the carrier of X \ { the OneF of X} is non empty non trivial non finite Element of K10( the carrier of X)
K10( the carrier of X) is non empty non trivial non finite set
the carrier of X typed\ { the OneF of X} is Element of K10( the carrier of X)
the of X is non empty Relation-like the carrier of X \ { the OneF of X} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of X \ { the OneF of X}),INT))
K11(( the carrier of X \ { the OneF of X}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of X \ { the OneF of X}),INT)) is non empty non trivial non finite set
the of X " {0} is Element of K10(( the carrier of X \ { the OneF of X}))
K10(( the carrier of X \ { the OneF of X})) is non empty non trivial non finite set
(X) . 0 is set
(X) is functional V36() FinSequence-membered Element of K10(((X) *))
(X) is non empty non trivial non finite set
1 -tuples_on (X) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (X)
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
(0 + 1) -tuples_on (X) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (X)
(X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10(((X) *))
((X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((X) *))
((X) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((X) *))
K10(((X) *)) is non empty non trivial non finite set
((X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((X) *))
add is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
(X) . add is set
add + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
(X) . (add + 1) is set
(X) is non empty non trivial non finite set
{ (X,b₁,((X) . add)) where b₁ is (X) Element of (X) : b₁ is (X) } is set
S2 is set
SS2 is (X) Element of (X)
(X,SS2,((X) . add)) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((X) *) \ {{}})
K10((((X) *) \ {{}})) is non empty non trivial non finite set
bool (((X) *) \ {{}}) is non empty non trivial non finite Element of K10(K10((((X) *) \ {{}})))
K10(K10((((X) *) \ {{}}))) is non empty non trivial non finite set
((X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X) *
<*SS2*> is non empty trivial Relation-like NAT -defined (X) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (X)
1 -tuples_on (X) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (X)
(X) is non empty Relation-like ((X) *) * -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((X) *) *),((X) *)))
K11((((X) *) *),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11((((X) *) *),((X) *))) is non empty non trivial non finite set
(X) -multiCat is non empty Relation-like ((X) *) * -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((X) *) *),((X) *)))
(X) -concatenation is non empty Relation-like K11(((X) *),((X) *)) -defined (X) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((X) *),((X) *)),((X) *)))
K11(((X) *),((X) *)) is non empty non trivial Relation-like non finite set
K11(K11(((X) *),((X) *)),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((X) *),((X) *)),((X) *))) is non empty non trivial non finite set
MultPlace ((X) -concatenation) is non empty Relation-like (((X) *) *) \ {{}} -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((X) *) *) \ {{}}),((X) *)))
(((X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((X) *) *))
K10((((X) *) *)) is non empty non trivial non finite set
(((X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((X) *) *))
K11(((((X) *) *) \ {{}}),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((X) *) *) \ {{}}),((X) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((X) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
(X,SS2) is complex ext-real real integer Element of INT
the of X . SS2 is set
abs (X,SS2) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
{ (<*SS2*> ^ ((X) . b₁)) where b₁ is Relation-like NAT -defined (X) * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of ((X) *) * : ( rng b₁ c= (X) . add & b₁ is abs (X,SS2) -element ) } is set
union { (X,b₁,((X) . add)) where b₁ is (X) Element of (X) : b₁ is (X) } is set
(union { (X,b₁,((X) . add)) where b₁ is (X) Element of (X) : b₁ is (X) } ) \/ ((X) . add) is set
S is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
X is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
S + X is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
S1 is non empty non degenerated non trivial non finite () ()
(S1) is Relation-like Function-like set
(S1) . S is set
(S1) . (S + X) is set
S + 0 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
(S1) . (S + 0) is set
SX is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
S + SX is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
(S1) . (S + SX) is set
SX + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
S + (SX + 1) is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
(S1) . (S + (SX + 1)) is set
(S + SX) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
(S1) . ((S + SX) + 1) is set
(S1) is non empty non trivial non finite set
the carrier of S1 is non empty non trivial non finite set
{ (S1,b₁,((S1) . (S + SX))) where b₁ is (S1) Element of (S1) : b₁ is (S1) } is set
union { (S1,b₁,((S1) . (S + SX))) where b₁ is (S1) Element of (S1) : b₁ is (S1) } is set
((S1) . (S + SX)) \/ (union { (S1,b₁,((S1) . (S + SX))) where b₁ is (S1) Element of (S1) : b₁ is (S1) } ) is set
S is non empty non degenerated non trivial non finite () ()
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
S is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
X is non empty non degenerated non trivial non finite () ()
(X) is Relation-like Function-like set
(X) . S is set
(X) is set
rng (X) is set
union (rng (X)) is set
dom (X) is set
S is set
X is non empty non degenerated non trivial non finite () ()
(X) is set
(X) is Relation-like Function-like set
rng (X) is set
union (rng (X)) is set
SS1 is set
dom (X) is set
SX is set
(X) . SX is set
add is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
f is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(X) . f is set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
X is non empty non degenerated non trivial non finite () ()
(X) is non empty non trivial non finite set
the carrier of X is non empty non trivial non finite set
(X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X)
((X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((X) *))
K10(((X) *)) is non empty non trivial non finite set
((X) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((X) *))
X is non empty non degenerated non trivial non finite () ()
(X) is non empty non trivial non finite set
the carrier of X is non empty non trivial non finite set
(X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X)
((X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((X) *))
K10(((X) *)) is non empty non trivial non finite set
((X) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((X) *))
S is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
SS1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of ((X) *) \ {{}}
(X) is Relation-like Function-like set
(X) . S is set
S1 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(X) . S1 is set
(X) is set
rng (X) is set
union (rng (X)) is set
S is non empty non degenerated non trivial non finite () ()
(S) is Relation-like Function-like set
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
bool ((S) *) is non empty non trivial non finite Element of K10(K10(((S) *)))
K10(((S) *)) is non empty non trivial non finite set
K10(K10(((S) *))) is non empty non trivial non finite set
K11(NAT,(bool ((S) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((S) *)))) is non empty non trivial non finite set
dom (S) is set
SS1 is set
rng (S) is set
SX is set
(S) . SX is set
add is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(S) . add is set
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
S is non empty non degenerated non trivial non finite () ()
(S) is set
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
K10(((S) *)) is non empty non trivial non finite set
(S) is non empty Relation-like NAT -defined bool ((S) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((S) *))))
bool ((S) *) is non empty non trivial non finite Element of K10(K10(((S) *)))
K10(K10(((S) *))) is non empty non trivial non finite set
K11(NAT,(bool ((S) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((S) *)))) is non empty non trivial non finite set
SX is set
add is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(S) . add is functional V36() FinSequence-membered Element of bool ((S) *)
(S) . 0 is functional V36() FinSequence-membered Element of bool ((S) *)
((S) . 0) \/ (S) is set
(S) is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty non trivial non finite set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
(S) \/ (S) is set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
K10(((S) *)) is non empty non trivial non finite set
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty Relation-like NAT -defined bool ((S) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((S) *))))
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
bool ((S) *) is non empty non trivial non finite Element of K10(K10(((S) *)))
K10(((S) *)) is non empty non trivial non finite set
K10(K10(((S) *))) is non empty non trivial non finite set
K11(NAT,(bool ((S) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((S) *)))) is non empty non trivial non finite set
X is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
(S) . X is set
(S) is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty non trivial non finite set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
the Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S)
(S) . 0 is functional V36() FinSequence-membered Element of bool ((S) *)
0 + X is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
(S) . (0 + X) is set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty Relation-like NAT -defined bool ((S) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((S) *))))
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
bool ((S) *) is non empty non trivial non finite Element of K10(K10(((S) *)))
K10(((S) *)) is non empty non trivial non finite set
K10(K10(((S) *))) is non empty non trivial non finite set
K11(NAT,(bool ((S) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((S) *)))) is non empty non trivial non finite set
X is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
(S) . X is non empty set
(S) is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty non trivial non finite set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
add is Element of (S) . X
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
(S) is non empty functional V36() FinSequence-membered Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
(S) is non empty Relation-like NAT -defined bool ((S) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((S) *))))
bool ((S) *) is non empty non trivial non finite Element of K10(K10(((S) *)))
K10(K10(((S) *))) is non empty non trivial non finite set
K11(NAT,(bool ((S) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((S) *)))) is non empty non trivial non finite set
(S) is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty non trivial non finite set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
add is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S)
f is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(S) . f is non empty functional V36() FinSequence-membered Element of bool ((S) *)
S2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) . f
X is non empty non degenerated non trivial non finite () ()
(X) is non empty non trivial non finite set
the carrier of X is non empty non trivial non finite set
(X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X)
((X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((X) *))
K10(((X) *)) is non empty non trivial non finite set
((X) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((X) *))
S is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
(X) is non empty Relation-like NAT -defined bool ((X) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((X) *))))
bool ((X) *) is non empty non trivial non finite Element of K10(K10(((X) *)))
K10(K10(((X) *))) is non empty non trivial non finite set
K11(NAT,(bool ((X) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((X) *)))) is non empty non trivial non finite set
(X) is functional V36() FinSequence-membered Element of K10(((X) *))
(X) is non empty non trivial non finite set
the OneF of X is Element of the carrier of X
{ the OneF of X} is non empty trivial finite 1 -element countable set
the carrier of X \ { the OneF of X} is non empty non trivial non finite Element of K10( the carrier of X)
K10( the carrier of X) is non empty non trivial non finite set
the carrier of X typed\ { the OneF of X} is Element of K10( the carrier of X)
the of X is non empty Relation-like the carrier of X \ { the OneF of X} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of X \ { the OneF of X}),INT))
K11(( the carrier of X \ { the OneF of X}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of X \ { the OneF of X}),INT)) is non empty non trivial non finite set
the of X " {0} is Element of K10(( the carrier of X \ { the OneF of X}))
K10(( the carrier of X \ { the OneF of X})) is non empty non trivial non finite set
1 -tuples_on (X) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (X)
the Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X)
(X) . 0 is non empty functional V36() FinSequence-membered Element of bool ((X) *)
f is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of ((X) *) \ {{}}
0 + S is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
(X) . (0 + S) is non empty set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty non trivial non finite set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
(S) is non empty non trivial non finite Element of K10((S))
K10((S)) is non empty non trivial non finite set
(S) is non empty Relation-like NAT -defined bool ((S) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((S) *))))
bool ((S) *) is non empty non trivial non finite Element of K10(K10(((S) *)))
K10(K10(((S) *))) is non empty non trivial non finite set
K11(NAT,(bool ((S) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((S) *)))) is non empty non trivial non finite set
SX is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of ((S) *) \ {{}}
(S) . 0 is non empty functional V36() FinSequence-membered Element of bool ((S) *)
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
add is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty non trivial non finite set
(S) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
K11((((S) *) \ {{}}),(S)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) \ {{}}),(S))) is non empty non trivial non finite set
(S) -firstChar is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) -pr1 is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total associative Element of K10(K11(K11((S),(S)),(S)))
K11((S),(S)) is non empty non trivial Relation-like non finite set
K11(K11((S),(S)),(S)) is non empty non trivial Relation-like non finite set
K10(K11(K11((S),(S)),(S))) is non empty non trivial non finite set
K530((S),(S)) is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total Element of K10(K11(K11((S),(S)),(S)))
MultPlace ((S) -pr1) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
X is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support (S) ( 0 ,S) Element of ((S) *) \ {{}}
(S) . X is Element of (S)
(S) is non empty functional V36() FinSequence-membered Element of K10(((S) *))
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
(S) is non empty Relation-like NAT -defined bool ((S) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((S) *))))
bool ((S) *) is non empty non trivial non finite Element of K10(K10(((S) *)))
K10(K10(((S) *))) is non empty non trivial non finite set
K11(NAT,(bool ((S) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((S) *)))) is non empty non trivial non finite set
(S) is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty non trivial non finite set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
((S) -firstChar) . X is Element of (S)
(S) is non empty non trivial non finite Element of K10((S))
K10((S)) is non empty non trivial non finite set
E1 is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of (S)
E1 . 1 is set
(S) . 0 is non empty functional V36() FinSequence-membered Element of bool ((S) *)
N1 is set
<*N1*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support set
<*N1*> ^ {} is non empty Relation-like NAT -defined Function-like finite 1 + {} -element FinSequence-like FinSubsequence-like countable finite-support set
1 + {} is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
<*N1*> null {} is Relation-like NAT -defined {} \/ (dom <*N1*>) -defined Seg (1 + {}) -defined {} \/ (rng <*N1*>) -valued Function-like total finite len <*N1*> -element FinSequence-like FinSubsequence-like countable finite-support set
dom <*N1*> is non empty trivial finite 1 -element countable set
{} \/ (dom <*N1*>) is non empty finite countable set
Seg (1 + {}) is non empty finite 1 + {} -element countable Element of K10(NAT)
rng <*N1*> is non empty trivial finite 1 -element countable set
{} \/ (rng <*N1*>) is non empty finite countable set
len <*N1*> is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable Element of NAT
<*N1*> \typed/ {} is Relation-like NAT -defined finite countable Element of K10((<*N1*> \/ {}))
<*N1*> \/ {} is non empty Relation-like NAT -defined finite countable set
K10((<*N1*> \/ {})) is non empty finite V36() countable set
{} ^ <*N1*> is non empty Relation-like NAT -defined Function-like finite {} + 1 -element {} + 1 -element FinSequence-like FinSubsequence-like countable finite-support set
{} + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
{} + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable Element of NAT
E2 is Element of (S)
S is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
S + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
X is non empty non degenerated non trivial non finite () ()
(X) is non empty non trivial non finite set
the carrier of X is non empty non trivial non finite set
(X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X)
((X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((X) *))
K10(((X) *)) is non empty non trivial non finite set
((X) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((X) *))
(X) is non empty non trivial non finite set
bool ((X) *) is non empty non trivial non finite Element of K10(K10(((X) *)))
K10(K10(((X) *))) is non empty non trivial non finite set
(X) is non empty Relation-like NAT -defined bool ((X) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((X) *))))
K11(NAT,(bool ((X) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((X) *)))) is non empty non trivial non finite set
(X) . S is non empty functional V36() FinSequence-membered Element of bool ((X) *)
((X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X) *
((X) . S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((X) *) *))
K10((((X) *) *)) is non empty non trivial non finite set
(X) is non empty Relation-like ((X) *) * -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((X) *) *),((X) *)))
K11((((X) *) *),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11((((X) *) *),((X) *))) is non empty non trivial non finite set
(X) -multiCat is non empty Relation-like ((X) *) * -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((X) *) *),((X) *)))
(X) -concatenation is non empty Relation-like K11(((X) *),((X) *)) -defined (X) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((X) *),((X) *)),((X) *)))
K11(((X) *),((X) *)) is non empty non trivial Relation-like non finite set
K11(K11(((X) *),((X) *)),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((X) *),((X) *)),((X) *))) is non empty non trivial non finite set
MultPlace ((X) -concatenation) is non empty Relation-like (((X) *) *) \ {{}} -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((X) *) *) \ {{}}),((X) *)))
(((X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((X) *) *))
(((X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((X) *) *))
K11(((((X) *) *) \ {{}}),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((X) *) *) \ {{}}),((X) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((X) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
{ (X,b₁,((X) . S)) where b₁ is (X) Element of (X) : b₁ is (X) } is set
SS1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (X) (S + 1,X) Element of ((X) *) \ {{}}
(X) . (S + 1) is non empty set
union { (X,b₁,((X) . S)) where b₁ is (X) Element of (X) : b₁ is (X) } is set
(union { (X,b₁,((X) . S)) where b₁ is (X) Element of (X) : b₁ is (X) } ) \/ ((X) . S) is non empty set
SX is set
add is (X) Element of (X)
(X,add,((X) . S)) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((X) *) \ {{}})
K10((((X) *) \ {{}})) is non empty non trivial non finite set
bool (((X) *) \ {{}}) is non empty non trivial non finite Element of K10(K10((((X) *) \ {{}})))
K10(K10((((X) *) \ {{}}))) is non empty non trivial non finite set
<*add*> is non empty trivial Relation-like NAT -defined (X) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (X)
1 -tuples_on (X) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (X)
(X,add) is complex ext-real real integer Element of INT
the of X is non empty Relation-like the carrier of X \ { the OneF of X} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of X \ { the OneF of X}),INT))
the OneF of X is Element of the carrier of X
{ the OneF of X} is non empty trivial finite 1 -element countable set
the carrier of X \ { the OneF of X} is non empty non trivial non finite Element of K10( the carrier of X)
K10( the carrier of X) is non empty non trivial non finite set
the carrier of X typed\ { the OneF of X} is Element of K10( the carrier of X)
K11(( the carrier of X \ { the OneF of X}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of X \ { the OneF of X}),INT)) is non empty non trivial non finite set
the of X . add is set
abs (X,add) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
{ (<*add*> ^ ((X) . b₁)) where b₁ is Relation-like NAT -defined (X) * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of ((X) *) * : ( rng b₁ c= (X) . S & b₁ is abs (X,add) -element ) } is set
f is (X) (X) (X) (X) Element of (X)
S2 is (X) (X) (X) (X) Element of (X)
(X,S2) is complex ext-real real integer Element of INT
the of X . S2 is set
abs (X,S2) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
<*S2*> is non empty trivial Relation-like NAT -defined (X) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (X)
(X,f) is complex ext-real real integer Element of INT
the of X . f is set
abs (X,f) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
SS2 is Relation-like NAT -defined (X) * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of ((X) *) *
(X) . SS2 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
<*S2*> ^ ((X) . SS2) is non empty Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
rng SS2 is functional finite V36() FinSequence-membered countable Element of K10(((X) *))
E1 is Relation-like NAT -defined (X) . S -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support FinSequence of (X) . S
N1 is Relation-like NAT -defined (X) . S -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of ((X) . S) *
E2 is Relation-like NAT -defined (X) . S -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of ((X) . S) *
(X) . E2 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
<*S2*> ^ ((X) . E2) is non empty Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
S is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
S + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
X is non empty non degenerated non trivial non finite () ()
(X) is non empty non trivial non finite set
the carrier of X is non empty non trivial non finite set
(X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X)
((X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((X) *))
K10(((X) *)) is non empty non trivial non finite set
((X) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((X) *))
(X) is non empty non trivial non finite set
bool ((X) *) is non empty non trivial non finite Element of K10(K10(((X) *)))
K10(K10(((X) *))) is non empty non trivial non finite set
(X) is non empty Relation-like NAT -defined bool ((X) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((X) *))))
K11(NAT,(bool ((X) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((X) *)))) is non empty non trivial non finite set
(X) . S is non empty functional V36() FinSequence-membered Element of bool ((X) *)
((X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X) *
((X) . S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((X) *) *))
K10((((X) *) *)) is non empty non trivial non finite set
(X) is non empty Relation-like ((X) *) * -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((X) *) *),((X) *)))
K11((((X) *) *),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11((((X) *) *),((X) *))) is non empty non trivial non finite set
(X) -multiCat is non empty Relation-like ((X) *) * -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((X) *) *),((X) *)))
(X) -concatenation is non empty Relation-like K11(((X) *),((X) *)) -defined (X) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((X) *),((X) *)),((X) *)))
K11(((X) *),((X) *)) is non empty non trivial Relation-like non finite set
K11(K11(((X) *),((X) *)),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((X) *),((X) *)),((X) *))) is non empty non trivial non finite set
MultPlace ((X) -concatenation) is non empty Relation-like (((X) *) *) \ {{}} -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((X) *) *) \ {{}}),((X) *)))
(((X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((X) *) *))
(((X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((X) *) *))
K11(((((X) *) *) \ {{}}),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((X) *) *) \ {{}}),((X) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((X) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
(X) is non empty set
the OneF of X is Element of the carrier of X
{ the OneF of X} is non empty trivial finite 1 -element countable set
the carrier of X \ { the OneF of X} is non empty non trivial non finite Element of K10( the carrier of X)
K10( the carrier of X) is non empty non trivial non finite set
the carrier of X typed\ { the OneF of X} is Element of K10( the carrier of X)
the of X is non empty Relation-like the carrier of X \ { the OneF of X} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of X \ { the OneF of X}),INT))
K11(( the carrier of X \ { the OneF of X}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of X \ { the OneF of X}),INT)) is non empty non trivial non finite set
the of X " NAT is Element of K10(( the carrier of X \ { the OneF of X}))
K10(( the carrier of X \ { the OneF of X})) is non empty non trivial non finite set
(X) is non empty non trivial non finite Element of K10((X))
K10((X)) is non empty non trivial non finite set
the of X " {0} is Element of K10(( the carrier of X \ { the OneF of X}))
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
(X) . 0 is non empty functional V36() FinSequence-membered Element of bool ((X) *)
((X) . 0) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((X) *) *))
f is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (X) (0 + 1,X) Element of ((X) *) \ {{}}
(X) is functional V36() FinSequence-membered Element of K10(((X) *))
(X) is non empty non trivial non finite set
1 -tuples_on (X) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (X)
{ <*b₁*> where b₁ is Element of (X) : verum } is set
S2 is Element of (X)
<*S2*> is non empty trivial Relation-like NAT -defined (X) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (X)
1 -tuples_on (X) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (X)
E1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
rng E1 is finite countable set
N1 is Relation-like NAT -defined (X) . 0 -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support FinSequence of (X) . 0
SS2 is (X) (X) (X) (X) (X) (X) Element of (X)
N2 is (X) (X) (X) (X) (X) (X) Element of (X)
(X,N2) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of INT
the of X . N2 is set
abs (X,N2) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of NAT
<*N2*> is non empty trivial Relation-like NAT -defined (X) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (X)
1 -tuples_on (X) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (X)
E2 is Relation-like NAT -defined (X) . 0 -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of ((X) . 0) *
Y is Relation-like NAT -defined (X) . 0 -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of ((X) . 0) *
(X) . Y is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
<*N2*> ^ ((X) . Y) is non empty Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(X) . {} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
<*SS2*> is non empty trivial Relation-like NAT -defined (X) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (X)
<*SS2*> ^ {} is non empty Relation-like NAT -defined Function-like finite 1 + {} -element FinSequence-like FinSubsequence-like countable finite-support set
1 + {} is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
<*SS2*> null {} is Relation-like NAT -defined {} \/ (dom <*SS2*>) -defined Seg (1 + {}) -defined {} \/ (rng <*SS2*>) -valued Function-like total finite len <*SS2*> -element FinSequence-like FinSubsequence-like countable finite-support set
dom <*SS2*> is non empty trivial finite 1 -element countable set
{} \/ (dom <*SS2*>) is non empty finite countable set
Seg (1 + {}) is non empty finite 1 + {} -element countable Element of K10(NAT)
rng <*SS2*> is non empty trivial finite 1 -element countable set
{} \/ (rng <*SS2*>) is non empty finite countable set
len <*SS2*> is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable Element of NAT
<*SS2*> \typed/ {} is Relation-like NAT -defined finite countable Element of K10((<*SS2*> \/ {}))
<*SS2*> \/ {} is non empty Relation-like NAT -defined finite countable set
K10((<*SS2*> \/ {})) is non empty finite V36() countable set
{} ^ <*SS2*> is non empty Relation-like NAT -defined Function-like finite {} + 1 -element {} + 1 -element FinSequence-like FinSubsequence-like countable finite-support set
{} + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
{} + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable Element of NAT
f is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
f + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
SS2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
SS2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
(X) . SS2 is non empty functional V36() FinSequence-membered Element of bool ((X) *)
((X) . SS2) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((X) *) *))
E1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (X) (SS2 + 1,X) Element of ((X) *) \ {{}}
S2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(X) . S2 is non empty functional V36() FinSequence-membered Element of bool ((X) *)
((X) . S2) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((X) *) *))
N1 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
N1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
(X) . N1 is non empty functional V36() FinSequence-membered Element of bool ((X) *)
((X) . N1) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((X) *) *))
N1 is (X) (X) (X) (X) Element of (X)
(X,N1) is complex ext-real real integer Element of INT
the of X . N1 is set
abs (X,N1) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
E2 is Relation-like NAT -defined (X) . S2 -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of ((X) . S2) *
<*N1*> is non empty trivial Relation-like NAT -defined (X) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (X)
1 -tuples_on (X) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (X)
(X) . E2 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
<*N1*> ^ ((X) . E2) is non empty Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
K10(((X) . SS2)) is non empty set
Y is functional V36() FinSequence-membered Element of K10(((X) . SS2))
Y * is non empty functional V36() FinSequence-membered Element of K10((((X) . SS2) *))
((X) . SS2) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X) . SS2
K10((((X) . SS2) *)) is non empty non trivial non finite set
K10((((X) . SS2) *)) is non empty non trivial non finite set
NN1 is Relation-like NAT -defined (X) . SS2 -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of ((X) . SS2) *
(X) . NN1 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
<*N1*> ^ ((X) . NN1) is non empty Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
S2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
SS2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
SS2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
(X) . SS2 is non empty functional V36() FinSequence-membered Element of bool ((X) *)
((X) . SS2) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((X) *) *))
f + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
(X) . f is non empty functional V36() FinSequence-membered Element of bool ((X) *)
((X) . f) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((X) *) *))
E1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (X) (f + 1,X) Element of ((X) *) \ {{}}
f is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (X) (S + 1,X) Element of ((X) *) \ {{}}
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty non trivial non finite set
(S) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
K11((((S) *) \ {{}}),(S)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) \ {{}}),(S))) is non empty non trivial non finite set
(S) -firstChar is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) -pr1 is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total associative Element of K10(K11(K11((S),(S)),(S)))
K11((S),(S)) is non empty non trivial Relation-like non finite set
K11(K11((S),(S)),(S)) is non empty non trivial Relation-like non finite set
K10(K11(K11((S),(S)),(S))) is non empty non trivial non finite set
K530((S),(S)) is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total Element of K10(K11(K11((S),(S)),(S)))
MultPlace ((S) -pr1) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) Element of ((S) *) \ {{}}
(S) . X is Element of (S)
(S) is non empty functional V36() FinSequence-membered Element of K10(((S) *))
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
(S) is non empty Relation-like NAT -defined bool ((S) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((S) *))))
bool ((S) *) is non empty non trivial non finite Element of K10(K10(((S) *)))
K10(K10(((S) *))) is non empty non trivial non finite set
K11(NAT,(bool ((S) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((S) *)))) is non empty non trivial non finite set
(S) is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty non trivial non finite set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
((S) -firstChar) . X is Element of (S)
(S) is non empty non trivial non finite Element of K10((S))
K10((S)) is non empty non trivial non finite set
E1 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(S) . E1 is non empty functional V36() FinSequence-membered Element of bool ((S) *)
N1 is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of (S)
N1 . 1 is set
E2 is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support (S) ( 0 ,S) Element of ((S) *) \ {{}}
(S) . E2 is (S) (S) (S) (S) (S) (S) Element of (S)
N2 is Element of (S)
E2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
E2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
N2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
N2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
(S) . N2 is non empty functional V36() FinSequence-membered Element of bool ((S) *)
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
((S) . N2) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
Y is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) (N2 + 1,S) Element of ((S) *) \ {{}}
(S) is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
K11((((S) *) *),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) *),((S) *))) is non empty non trivial non finite set
(S) -multiCat is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
(S) -concatenation is non empty Relation-like K11(((S) *),((S) *)) -defined (S) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((S) *),((S) *)),((S) *)))
K11(((S) *),((S) *)) is non empty non trivial Relation-like non finite set
K11(K11(((S) *),((S) *)),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((S) *),((S) *)),((S) *))) is non empty non trivial non finite set
MultPlace ((S) -concatenation) is non empty Relation-like (((S) *) *) \ {{}} -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((S) *) *) \ {{}}),((S) *)))
(((S) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) *))
(((S) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((S) *) *))
K11(((((S) *) *) \ {{}}),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((S) *) *) \ {{}}),((S) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((S) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
NN1 is (S) (S) (S) (S) Element of (S)
(S,NN1) is complex ext-real real integer Element of INT
the of S . NN1 is set
abs (S,NN1) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
NN2 is Relation-like NAT -defined (S) . N2 -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of ((S) . N2) *
<*NN1*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
(S) . NN2 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
<*NN1*> ^ ((S) . NN2) is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
NN11 is Element of (S)
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
K11((((S) *) \ {{}}),(S)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) \ {{}}),(S))) is non empty non trivial non finite set
(S) -firstChar is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) -pr1 is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total associative Element of K10(K11(K11((S),(S)),(S)))
K11((S),(S)) is non empty non trivial Relation-like non finite set
K11(K11((S),(S)),(S)) is non empty non trivial Relation-like non finite set
K10(K11(K11((S),(S)),(S))) is non empty non trivial non finite set
K530((S),(S)) is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total Element of K10(K11(K11((S),(S)),(S)))
MultPlace ((S) -pr1) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) Element of ((S) *) \ {{}}
(S) . X is (S) (S) (S) (S) Element of (S)
(S,((S) . X)) is complex ext-real real integer Element of INT
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S . ((S) . X) is set
S is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
S + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
X is non empty non degenerated non trivial non finite () ()
(X) is non empty non trivial non finite set
the carrier of X is non empty non trivial non finite set
(X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X)
((X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((X) *))
K10(((X) *)) is non empty non trivial non finite set
((X) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((X) *))
bool ((X) *) is non empty non trivial non finite Element of K10(K10(((X) *)))
K10(K10(((X) *))) is non empty non trivial non finite set
(X) is non empty Relation-like NAT -defined bool ((X) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((X) *))))
K11(NAT,(bool ((X) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((X) *)))) is non empty non trivial non finite set
(X) . S is non empty functional V36() FinSequence-membered Element of bool ((X) *)
((X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X) *
((X) . S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((X) *) *))
K10((((X) *) *)) is non empty non trivial non finite set
(X) is non empty Relation-like ((X) *) \ {{}} -defined (X) -valued Function-like total quasi_total Element of K10(K11((((X) *) \ {{}}),(X)))
K11((((X) *) \ {{}}),(X)) is non empty non trivial Relation-like non finite set
K10(K11((((X) *) \ {{}}),(X))) is non empty non trivial non finite set
(X) -firstChar is non empty Relation-like ((X) *) \ {{}} -defined (X) -valued Function-like total quasi_total Element of K10(K11((((X) *) \ {{}}),(X)))
(X) -pr1 is non empty Relation-like K11((X),(X)) -defined (X) -valued Function-like total quasi_total associative Element of K10(K11(K11((X),(X)),(X)))
K11((X),(X)) is non empty non trivial Relation-like non finite set
K11(K11((X),(X)),(X)) is non empty non trivial Relation-like non finite set
K10(K11(K11((X),(X)),(X))) is non empty non trivial non finite set
K530((X),(X)) is non empty Relation-like K11((X),(X)) -defined (X) -valued Function-like total quasi_total Element of K10(K11(K11((X),(X)),(X)))
MultPlace ((X) -pr1) is non empty Relation-like ((X) *) \ {{}} -defined (X) -valued Function-like total quasi_total Element of K10(K11((((X) *) \ {{}}),(X)))
(X) is non empty Relation-like ((X) *) * -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((X) *) *),((X) *)))
K11((((X) *) *),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11((((X) *) *),((X) *))) is non empty non trivial non finite set
(X) -multiCat is non empty Relation-like ((X) *) * -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((X) *) *),((X) *)))
(X) -concatenation is non empty Relation-like K11(((X) *),((X) *)) -defined (X) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((X) *),((X) *)),((X) *)))
K11(((X) *),((X) *)) is non empty non trivial Relation-like non finite set
K11(K11(((X) *),((X) *)),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((X) *),((X) *)),((X) *))) is non empty non trivial non finite set
MultPlace ((X) -concatenation) is non empty Relation-like (((X) *) *) \ {{}} -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((X) *) *) \ {{}}),((X) *)))
(((X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((X) *) *))
(((X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((X) *) *))
K11(((((X) *) *) \ {{}}),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((X) *) *) \ {{}}),((X) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((X) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
S1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (X) (S + 1,X) Element of ((X) *) \ {{}}
(X) . S1 is (X) (X) (X) (X) Element of (X)
(X,((X) . S1)) is complex ext-real real integer Element of INT
the of X is non empty Relation-like the carrier of X \ { the OneF of X} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of X \ { the OneF of X}),INT))
the OneF of X is Element of the carrier of X
{ the OneF of X} is non empty trivial finite 1 -element countable set
the carrier of X \ { the OneF of X} is non empty non trivial non finite Element of K10( the carrier of X)
K10( the carrier of X) is non empty non trivial non finite set
the carrier of X typed\ { the OneF of X} is Element of K10( the carrier of X)
K11(( the carrier of X \ { the OneF of X}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of X \ { the OneF of X}),INT)) is non empty non trivial non finite set
the of X . ((X) . S1) is set
abs (X,((X) . S1)) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
<*((X) . S1)*> is non empty trivial Relation-like NAT -defined (X) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (X)
1 -tuples_on (X) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (X)
(X) is non empty non trivial non finite set
SS1 is (X) (X) (X) (X) Element of (X)
(X,SS1) is complex ext-real real integer Element of INT
the of X . SS1 is set
abs (X,SS1) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
SX is Relation-like NAT -defined (X) . S -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of ((X) . S) *
<*SS1*> is non empty trivial Relation-like NAT -defined (X) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (X)
1 -tuples_on (X) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (X)
(X) . SX is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
<*SS1*> ^ ((X) . SX) is non empty Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
S1 . 1 is set
S is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
X is non empty non degenerated non trivial non finite () ()
(X) is non empty Relation-like NAT -defined bool ((X) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((X) *))))
(X) is non empty non trivial non finite set
the carrier of X is non empty non trivial non finite set
(X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X)
bool ((X) *) is non empty non trivial non finite Element of K10(K10(((X) *)))
K10(((X) *)) is non empty non trivial non finite set
K10(K10(((X) *))) is non empty non trivial non finite set
K11(NAT,(bool ((X) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((X) *)))) is non empty non trivial non finite set
(X) . S is non empty set
(X) is non empty non trivial non finite Element of K10((X))
K10((X)) is non empty non trivial non finite set
the OneF of X is Element of the carrier of X
{ the OneF of X} is non empty trivial finite 1 -element countable set
the carrier of X \ { the OneF of X} is non empty non trivial non finite Element of K10( the carrier of X)
K10( the carrier of X) is non empty non trivial non finite set
the carrier of X typed\ { the OneF of X} is Element of K10( the carrier of X)
the of X is non empty Relation-like the carrier of X \ { the OneF of X} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of X \ { the OneF of X}),INT))
K11(( the carrier of X \ { the OneF of X}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of X \ { the OneF of X}),INT)) is non empty non trivial non finite set
the of X " {0} is Element of K10(( the carrier of X \ { the OneF of X}))
K10(( the carrier of X \ { the OneF of X})) is non empty non trivial non finite set
1 -tuples_on (X) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (X)
(X) is non empty Relation-like K11(((X) *),((X) *)) -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((X) *),((X) *)),((X) *)))
K11(((X) *),((X) *)) is non empty non trivial Relation-like non finite set
K11(K11(((X) *),((X) *)),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((X) *),((X) *)),((X) *))) is non empty non trivial non finite set
(X) -concatenation is non empty Relation-like K11(((X) *),((X) *)) -defined (X) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((X) *),((X) *)),((X) *)))
(X) is non empty Relation-like ((X) *) * -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((X) *) *),((X) *)))
((X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X) *
K11((((X) *) *),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11((((X) *) *),((X) *))) is non empty non trivial non finite set
(X) -multiCat is non empty Relation-like ((X) *) * -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((X) *) *),((X) *)))
MultPlace ((X) -concatenation) is non empty Relation-like (((X) *) *) \ {{}} -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((X) *) *) \ {{}}),((X) *)))
(((X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((X) *) *))
K10((((X) *) *)) is non empty non trivial non finite set
(((X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((X) *) *))
K11(((((X) *) *) \ {{}}),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((X) *) *) \ {{}}),((X) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((X) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
dom ((X) -multiCat) is non empty functional V36() FinSequence-membered Element of K10((((X) *) *))
N1 is non empty Element of K10((X))
1 -tuples_on N1 is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of N1
(X) . 0 is non empty set
(1 -tuples_on N1) /\ (1 -tuples_on (X)) is set
(1 -tuples_on N1) typed/\ (1 -tuples_on (X)) is functional V36() FinSequence-membered with_non-empty_elements N1 -prefix Element of K10((1 -tuples_on N1))
K10((1 -tuples_on N1)) is non empty set
(1 -tuples_on N1) /\typed (1 -tuples_on (X)) is functional V36() FinSequence-membered with_non-empty_elements (X) -prefix (X) Element of K10((1 -tuples_on (X)))
K10((1 -tuples_on (X))) is non empty set
N1 /\ (X) is Element of K10((X))
N1 typed/\ (X) is Element of K10(N1)
K10(N1) is non empty set
N1 /\ (X) is set
N1 /\typed (X) is Element of K10((X))
1 -tuples_on (N1 /\ (X)) is functional V36() FinSequence-membered FinSequenceSet of N1 /\ (X)
(X) . 0 is non empty functional V36() FinSequence-membered Element of bool ((X) *)
(X) is functional V36() FinSequence-membered Element of K10(((X) *))
(X) is non empty non trivial non finite set
1 -tuples_on (X) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (X)
N2 is functional V36() FinSequence-membered with_non-empty_elements (X) -prefix (X) Element of K10((1 -tuples_on (X)))
N2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
(X) . N2 is non empty set
N2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
(X) . (N2 + 1) is non empty set
NN2 is set
((X) . (N2 + 1)) /\ ((X) *) is set
((X) . (N2 + 1)) typed/\ ((X) *) is Element of K10(((X) . (N2 + 1)))
K10(((X) . (N2 + 1))) is non empty set
((X) . (N2 + 1)) /\typed ((X) *) is functional V36() FinSequence-membered Element of K10(((X) *))
NN11 is set
z2 is set
o2 is set
NN1 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(X) . NN1 is non empty functional V36() FinSequence-membered Element of bool ((X) *)
Y is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
Y + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
((X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((X) *))
((X) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((X) *))
a2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (X) (Y + 1,X) Element of ((X) *) \ {{}}
ITT1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (X) (Y + 1,X) Element of ((X) *) \ {{}}
(X) . Y is non empty functional V36() FinSequence-membered Element of bool ((X) *)
((X) . Y) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((X) *) *))
(X) is non empty Relation-like ((X) *) \ {{}} -defined (X) -valued Function-like total quasi_total Element of K10(K11((((X) *) \ {{}}),(X)))
K11((((X) *) \ {{}}),(X)) is non empty non trivial Relation-like non finite set
K10(K11((((X) *) \ {{}}),(X))) is non empty non trivial non finite set
(X) -firstChar is non empty Relation-like ((X) *) \ {{}} -defined (X) -valued Function-like total quasi_total Element of K10(K11((((X) *) \ {{}}),(X)))
(X) -pr1 is non empty Relation-like K11((X),(X)) -defined (X) -valued Function-like total quasi_total associative Element of K10(K11(K11((X),(X)),(X)))
K11((X),(X)) is non empty non trivial Relation-like non finite set
K11(K11((X),(X)),(X)) is non empty non trivial Relation-like non finite set
K10(K11(K11((X),(X)),(X))) is non empty non trivial non finite set
K530((X),(X)) is non empty Relation-like K11((X),(X)) -defined (X) -valued Function-like total quasi_total Element of K10(K11(K11((X),(X)),(X)))
MultPlace ((X) -pr1) is non empty Relation-like ((X) *) \ {{}} -defined (X) -valued Function-like total quasi_total Element of K10(K11((((X) *) \ {{}}),(X)))
(X) . a2 is (X) (X) (X) (X) Element of (X)
(X,((X) . a2)) is complex ext-real real integer Element of INT
the of X . ((X) . a2) is set
abs (X,((X) . a2)) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
<*((X) . a2)*> is non empty trivial Relation-like NAT -defined (X) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (X)
ITT2 is Relation-like NAT -defined (X) . Y -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of ((X) . Y) *
(X) . ITT2 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
<*((X) . a2)*> ^ ((X) . ITT2) is non empty Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(X) . ITT1 is (X) (X) (X) (X) Element of (X)
(X,((X) . ITT1)) is complex ext-real real integer Element of INT
the of X . ((X) . ITT1) is set
abs (X,((X) . ITT1)) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
<*((X) . ITT1)*> is non empty trivial Relation-like NAT -defined (X) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (X)
T2 is Relation-like NAT -defined (X) . Y -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of ((X) . Y) *
(X) . T2 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
<*((X) . ITT1)*> ^ ((X) . T2) is non empty Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
w11 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
w22 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
(X) . (NN2,z2) is set
(X) . (NN11,o2) is set
ITT2 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of (X)
ITT2 ^ w11 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
ITT1 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of (X)
(X) . (ITT1,w22) is set
(<*((X) . a2)*> ^ ((X) . ITT2)) ^ w11 is non empty Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
ITT1 ^ w22 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
((X) . ITT2) ^ w11 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
<*((X) . a2)*> ^ (((X) . ITT2) ^ w11) is non empty Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(<*((X) . ITT1)*> ^ ((X) . T2)) ^ w22 is non empty Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
head1 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of (X)
tail1 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of (X)
head1 ^ tail1 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
<*((X) . a2)*> ^ (head1 ^ tail1) is non empty Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
head2 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of (X)
tail2 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of (X)
head2 ^ tail2 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
<*((X) . ITT1)*> ^ (head2 ^ tail2) is non empty Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
(X) . (<*((X) . a2)*>,(head1 ^ tail1)) is set
K10((1 -tuples_on (X))) is non empty set
S1 is functional V36() FinSequence-membered with_non-empty_elements (X) -prefix (X) Element of K10((1 -tuples_on (X)))
S1 /\ ((X) *) is functional V36() FinSequence-membered with_non-empty_elements (X) -prefix (X) Element of K10((1 -tuples_on (X)))
S1 typed/\ ((X) *) is functional V36() FinSequence-membered with_non-empty_elements Element of K10(S1)
K10(S1) is non empty set
S1 /\ ((X) *) is set
S1 /\typed ((X) *) is functional V36() FinSequence-membered Element of K10(((X) *))
(X) . (<*((X) . ITT1)*>,(head2 ^ tail2)) is set
((X) -concatenation) . (head1,tail1) is set
T11 is Relation-like NAT -defined (X) . Y -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support FinSequence of (X) . Y
len T11 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
T22 is Relation-like NAT -defined (X) . Y -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support FinSequence of (X) . Y
len T22 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(abs (X,((X) . a2))) -tuples_on ((X) . N2) is non empty functional V36() FinSequence-membered FinSequenceSet of (X) . N2
((X) -multiCat) . T11 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((X) -multiCat) .: ((abs (X,((X) . a2))) -tuples_on ((X) . N2)) is functional V36() FinSequence-membered Element of K10(((X) *))
((X) -multiCat) . T22 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((X) -multiCat) . ITT2 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
((X) -multiCat) . T2 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
(((X) -multiCat) .: ((abs (X,((X) . a2))) -tuples_on ((X) . N2))) /\ ((X) *) is functional V36() FinSequence-membered Element of K10(((X) *))
(((X) -multiCat) .: ((abs (X,((X) . a2))) -tuples_on ((X) . N2))) typed/\ ((X) *) is functional V36() FinSequence-membered Element of K10((((X) -multiCat) .: ((abs (X,((X) . a2))) -tuples_on ((X) . N2))))
K10((((X) -multiCat) .: ((abs (X,((X) . a2))) -tuples_on ((X) . N2)))) is non empty set
(((X) -multiCat) .: ((abs (X,((X) . a2))) -tuples_on ((X) . N2))) /\ ((X) *) is set
(((X) -multiCat) .: ((abs (X,((X) . a2))) -tuples_on ((X) . N2))) /\typed ((X) *) is functional V36() FinSequence-membered Element of K10(((X) *))
((X) -concatenation) . ((((X) -multiCat) . ITT2),w11) is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
((X) -concatenation) . ((((X) -multiCat) . T2),w22) is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
S is non empty non degenerated non trivial non finite () ()
(S) is non empty Relation-like NAT -defined bool ((S) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((S) *))))
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
bool ((S) *) is non empty non trivial non finite Element of K10(K10(((S) *)))
K10(((S) *)) is non empty non trivial non finite set
K10(K10(((S) *))) is non empty non trivial non finite set
K11(NAT,(bool ((S) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((S) *)))) is non empty non trivial non finite set
X is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
(S) . X is non empty set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
K10(((S) *)) is non empty non trivial non finite set
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
(S) is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
K11((((S) *) *),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) *),((S) *))) is non empty non trivial non finite set
(S) -multiCat is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
(S) -concatenation is non empty Relation-like K11(((S) *),((S) *)) -defined (S) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((S) *),((S) *)),((S) *)))
K11(((S) *),((S) *)) is non empty non trivial Relation-like non finite set
K11(K11(((S) *),((S) *)),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((S) *),((S) *)),((S) *))) is non empty non trivial non finite set
MultPlace ((S) -concatenation) is non empty Relation-like (((S) *) *) \ {{}} -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((S) *) *) \ {{}}),((S) *)))
(((S) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) *))
(((S) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((S) *) *))
K11(((((S) *) *) \ {{}}),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((S) *) *) \ {{}}),((S) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((S) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
X is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S) . X is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
S is non empty non degenerated non trivial non finite () ()
(S) is non empty functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
K10(((S) *)) is non empty non trivial non finite set
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
(S) is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
K11((((S) *) *),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) *),((S) *))) is non empty non trivial non finite set
(S) -multiCat is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
(S) -concatenation is non empty Relation-like K11(((S) *),((S) *)) -defined (S) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((S) *),((S) *)),((S) *)))
K11(((S) *),((S) *)) is non empty non trivial Relation-like non finite set
K11(K11(((S) *),((S) *)),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((S) *),((S) *)),((S) *))) is non empty non trivial non finite set
MultPlace ((S) -concatenation) is non empty Relation-like (((S) *) *) \ {{}} -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((S) *) *) \ {{}}),((S) *)))
(((S) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) *))
(((S) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((S) *) *))
K11(((((S) *) *) \ {{}}),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((S) *) *) \ {{}}),((S) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((S) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
X is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S) . X is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
S1 is Relation-like set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty non trivial non finite set
the (S) (S) (S) Element of (S) is (S) (S) (S) Element of (S)
(S, the (S) (S) (S) Element of (S)) is complex ext-real real integer Element of INT
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S . the (S) (S) (S) Element of (S) is set
abs (S, the (S) (S) (S) Element of (S)) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(S) is non empty functional V36() FinSequence-membered Element of K10(((S) *))
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
the Relation-like NAT -defined (S) -valued Function-like finite abs (S, the (S) (S) (S) Element of (S)) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) * is Relation-like NAT -defined (S) -valued Function-like finite abs (S, the (S) (S) (S) Element of (S)) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S) is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
K11((((S) *) *),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) *),((S) *))) is non empty non trivial non finite set
(S) -multiCat is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
(S) -concatenation is non empty Relation-like K11(((S) *),((S) *)) -defined (S) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((S) *),((S) *)),((S) *)))
K11(((S) *),((S) *)) is non empty non trivial Relation-like non finite set
K11(K11(((S) *),((S) *)),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((S) *),((S) *)),((S) *))) is non empty non trivial non finite set
MultPlace ((S) -concatenation) is non empty Relation-like (((S) *) *) \ {{}} -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((S) *) *) \ {{}}),((S) *)))
(((S) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) *))
(((S) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((S) *) *))
K11(((((S) *) *) \ {{}}),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((S) *) *) \ {{}}),((S) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((S) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
(S) . the Relation-like NAT -defined (S) -valued Function-like finite abs (S, the (S) (S) (S) Element of (S)) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) * is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
SX is Element of (S)
<*SX*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
add is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of (S)
<*SX*> ^ add is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
f is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of ((S) *) \ {{}}
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty non trivial non finite set
(S) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
K11((((S) *) \ {{}}),(S)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) \ {{}}),(S))) is non empty non trivial non finite set
(S) -firstChar is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) -pr1 is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total associative Element of K10(K11(K11((S),(S)),(S)))
K11((S),(S)) is non empty non trivial Relation-like non finite set
K11(K11((S),(S)),(S)) is non empty non trivial Relation-like non finite set
K10(K11(K11((S),(S)),(S))) is non empty non trivial non finite set
K530((S),(S)) is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total Element of K10(K11(K11((S),(S)),(S)))
MultPlace ((S) -pr1) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) Element of ((S) *) \ {{}}
(S) . X is Element of (S)
(S) is non empty functional V36() FinSequence-membered Element of K10(((S) *))
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
(S) is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
K11((((S) *) *),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) *),((S) *))) is non empty non trivial non finite set
(S) -multiCat is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
(S) -concatenation is non empty Relation-like K11(((S) *),((S) *)) -defined (S) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((S) *),((S) *)),((S) *)))
K11(((S) *),((S) *)) is non empty non trivial Relation-like non finite set
K11(K11(((S) *),((S) *)),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((S) *),((S) *)),((S) *))) is non empty non trivial non finite set
MultPlace ((S) -concatenation) is non empty Relation-like (((S) *) *) \ {{}} -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((S) *) *) \ {{}}),((S) *)))
(((S) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
(((S) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((S) *) *))
K11(((((S) *) *) \ {{}}),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((S) *) *) \ {{}}),((S) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((S) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((S) *) *))
f is (S) (S) (S) Element of (S)
(S,f) is complex ext-real real integer Element of INT
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S . f is set
abs (S,f) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
<*f*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
S2 is Relation-like NAT -defined (S) -valued Function-like finite abs (S,f) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S) . S2 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
<*f*> ^ ((S) . S2) is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
SS2 is Element of (S)
<*SS2*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
E1 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of (S)
N1 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of (S)
E1 ^ N1 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
(E1 ^ N1) . 1 is set
E2 is Element of (S)
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of ((S) *) \ {{}} : b₁ is (S) } is set
S is non empty non degenerated non trivial non finite () ()
(S) is set
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of ((S) *) \ {{}} : b₁ is (S) } is set
K10((((S) *) \ {{}})) is non empty non trivial non finite set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of ((S) *) \ {{}} : S₁[b₁] } is set
S is non empty non degenerated non trivial non finite () ()
(S) is functional V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) \ {{}}))
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
K10((((S) *) \ {{}})) is non empty non trivial non finite set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of ((S) *) \ {{}} : b₁ is (S) } is set
the non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) Element of ((S) *) \ {{}} is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) Element of ((S) *) \ {{}}
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty functional V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) \ {{}}))
K10((((S) *) \ {{}})) is non empty non trivial non finite set
{ b₁ where b₁ is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of ((S) *) \ {{}} : b₁ is (S) } is set
S1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S)
SS1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of ((S) *) \ {{}}
S is non empty non degenerated non trivial non finite () ()
(S) is non empty functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
K10(((S) *)) is non empty non trivial non finite set
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
(S) -concatenation is non empty Relation-like K11(((S) *),((S) *)) -defined (S) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((S) *),((S) *)),((S) *)))
K11(((S) *),((S) *)) is non empty non trivial Relation-like non finite set
K11(K11(((S) *),((S) *)),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((S) *),((S) *)),((S) *))) is non empty non trivial non finite set
(S) -multiCat is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
K11((((S) *) *),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) *),((S) *))) is non empty non trivial non finite set
MultPlace ((S) -concatenation) is non empty Relation-like (((S) *) *) \ {{}} -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((S) *) *) \ {{}}),((S) *)))
(((S) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
(((S) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((S) *) *))
K11(((((S) *) *) \ {{}}),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((S) *) *) \ {{}}),((S) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((S) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
(S) is non empty Relation-like NAT -defined bool ((S) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((S) *))))
bool ((S) *) is non empty non trivial non finite Element of K10(K10(((S) *)))
K10(K10(((S) *))) is non empty non trivial non finite set
K11(NAT,(bool ((S) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((S) *)))) is non empty non trivial non finite set
f is set
(S) /\ ((S) *) is functional V36() FinSequence-membered Element of K10(((S) *))
(S) typed/\ ((S) *) is functional V36() FinSequence-membered Element of K10((S))
K10((S)) is non empty set
(S) /\ ((S) *) is set
(S) /\typed ((S) *) is functional V36() FinSequence-membered Element of K10(((S) *))
S2 is set
SS2 is set
E1 is set
((S) -concatenation) . (f,SS2) is set
((S) -concatenation) . (S2,E1) is set
N1 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(S) . N1 is non empty functional V36() FinSequence-membered (S) -prefix (S) Element of bool ((S) *)
E2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(S) . E2 is non empty functional V36() FinSequence-membered (S) -prefix (S) Element of bool ((S) *)
N1 + E2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
(S) . (N1 + E2) is non empty (S) -prefix (S) set
((S) . (N1 + E2)) /\ ((S) *) is set
((S) . (N1 + E2)) typed/\ ((S) *) is Element of K10(((S) . (N1 + E2)))
K10(((S) . (N1 + E2))) is non empty set
((S) . (N1 + E2)) /\typed ((S) *) is functional V36() FinSequence-membered Element of K10(((S) *))
S is non empty non degenerated non trivial non finite () ()
(S) is non empty functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
K10(((S) *)) is non empty non trivial non finite set
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty functional V36() FinSequence-membered (S) -prefix (S) Element of K10(((S) *))
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
(S) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
K11((((S) *) \ {{}}),(S)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) \ {{}}),(S))) is non empty non trivial non finite set
(S) -firstChar is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) -pr1 is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total associative Element of K10(K11(K11((S),(S)),(S)))
K11((S),(S)) is non empty non trivial Relation-like non finite set
K11(K11((S),(S)),(S)) is non empty non trivial Relation-like non finite set
K10(K11(K11((S),(S)),(S))) is non empty non trivial non finite set
K530((S),(S)) is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total Element of K10(K11(K11((S),(S)),(S)))
MultPlace ((S) -pr1) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) Element of ((S) *) \ {{}}
(S) . X is (S) (S) (S) (S) Element of (S)
(S,((S) . X)) is complex ext-real real integer Element of INT
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S . ((S) . X) is set
abs (S,((S) . X)) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
<*((S) . X)*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
(S) is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
K11((((S) *) *),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) *),((S) *))) is non empty non trivial non finite set
(S) -multiCat is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
(S) -concatenation is non empty Relation-like K11(((S) *),((S) *)) -defined (S) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((S) *),((S) *)),((S) *)))
K11(((S) *),((S) *)) is non empty non trivial Relation-like non finite set
K11(K11(((S) *),((S) *)),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((S) *),((S) *)),((S) *))) is non empty non trivial non finite set
MultPlace ((S) -concatenation) is non empty Relation-like (((S) *) *) \ {{}} -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((S) *) *) \ {{}}),((S) *)))
(((S) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) *))
(((S) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((S) *) *))
K11(((((S) *) *) \ {{}}),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((S) *) *) \ {{}}),((S) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((S) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
(S) is non empty Relation-like NAT -defined bool ((S) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((S) *))))
bool ((S) *) is non empty non trivial non finite Element of K10(K10(((S) *)))
K10(K10(((S) *))) is non empty non trivial non finite set
K11(NAT,(bool ((S) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((S) *)))) is non empty non trivial non finite set
S2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(S) . S2 is non empty functional V36() FinSequence-membered (S) -prefix (S) Element of bool ((S) *)
SS2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) (S2,S) Element of ((S) *) \ {{}}
E2 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S) . E2 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
<*((S) . X)*> ^ ((S) . E2) is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
N1 is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support (S) ( 0 ,S) Element of ((S) *) \ {{}}
(S) . N1 is (S) (S) (S) (S) (S) (S) Element of (S)
(S,((S) . N1)) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of INT
the of S . ((S) . N1) is set
abs (S,((S) . N1)) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of NAT
len N1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable Element of NAT
E1 is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of (S)
E1 /. 1 is Element of (S)
<*(E1 /. 1)*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
E1 . 1 is set
<*(E1 . 1)*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support set
((S) -firstChar) . X is Element of (S)
<*(((S) -firstChar) . X)*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
<*(((S) -firstChar) . X)*> ^ {} is non empty Relation-like NAT -defined Function-like finite 1 + {} -element FinSequence-like FinSubsequence-like countable finite-support set
1 + {} is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
<*(((S) -firstChar) . X)*> null {} is Relation-like NAT -defined {} \/ (dom <*(((S) -firstChar) . X)*>) -defined Seg (1 + {}) -defined {} \/ (rng <*(((S) -firstChar) . X)*>) -valued Function-like total finite len <*(((S) -firstChar) . X)*> -element FinSequence-like FinSubsequence-like countable finite-support set
dom <*(((S) -firstChar) . X)*> is non empty trivial finite 1 -element countable set
{} \/ (dom <*(((S) -firstChar) . X)*>) is non empty finite countable set
Seg (1 + {}) is non empty finite 1 + {} -element countable Element of K10(NAT)
rng <*(((S) -firstChar) . X)*> is non empty trivial finite 1 -element countable set
{} \/ (rng <*(((S) -firstChar) . X)*>) is non empty finite countable set
len <*(((S) -firstChar) . X)*> is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable Element of NAT
<*(((S) -firstChar) . X)*> \typed/ {} is Relation-like NAT -defined finite countable Element of K10((<*(((S) -firstChar) . X)*> \/ {}))
<*(((S) -firstChar) . X)*> \/ {} is non empty Relation-like NAT -defined finite countable set
K10((<*(((S) -firstChar) . X)*> \/ {})) is non empty finite V36() countable set
{} ^ <*(((S) -firstChar) . X)*> is non empty Relation-like NAT -defined Function-like finite {} + 1 -element {} + 1 -element FinSequence-like FinSubsequence-like countable finite-support set
{} + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
{} + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable Element of NAT
<*(((S) -firstChar) . X)*> ^ ((S) . E2) is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
N1 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
N1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
E2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
E2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
SS2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) (S2,S) Element of ((S) *) \ {{}}
(S) . E2 is non empty functional V36() FinSequence-membered (S) -prefix (S) Element of bool ((S) *)
((S) . E2) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((S) *) *))
N2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) (E2 + 1,S) Element of ((S) *) \ {{}}
(S) . N2 is (S) (S) (S) (S) Element of (S)
<*((S) . N2)*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
Y is Relation-like NAT -defined (S) . E2 -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of ((S) . E2) *
(S) . Y is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
<*((S) . N2)*> ^ ((S) . Y) is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
K10((S)) is non empty set
NN1 is functional V36() FinSequence-membered Element of K10((S))
NN1 * is non empty functional V36() FinSequence-membered Element of K10(((S) *))
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
K10(((S) *)) is non empty non trivial non finite set
NN2 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S) . NN2 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
<*((S) . X)*> ^ ((S) . NN2) is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(S) is non empty Relation-like NAT -defined bool ((S) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((S) *))))
bool ((S) *) is non empty non trivial non finite Element of K10(K10(((S) *)))
K10(K10(((S) *))) is non empty non trivial non finite set
K11(NAT,(bool ((S) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((S) *)))) is non empty non trivial non finite set
(abs (S,((S) . X))) -tuples_on (S) is non empty functional V36() FinSequence-membered FinSequenceSet of (S)
dom ((S) -multiCat) is non empty functional V36() FinSequence-membered Element of K10((((S) *) *))
S2 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S) . S2 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
<*((S) . X)*> ^ ((S) . S2) is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
SS2 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S) . SS2 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
<*((S) . X)*> ^ ((S) . SS2) is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
E1 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support FinSequence of (S)
len E1 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
N1 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support FinSequence of (S)
len N1 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
E2 is Relation-like NAT -defined (S) -valued Function-like finite abs (S,((S) . X)) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (abs (S,((S) . X))) -tuples_on (S)
((S) -multiCat) . E2 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
N2 is Relation-like NAT -defined (S) -valued Function-like finite abs (S,((S) . X)) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (abs (S,((S) . X))) -tuples_on (S)
((S) -multiCat) . N2 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((abs (S,((S) . X))) -tuples_on (S)) /\ (dom ((S) -multiCat)) is functional V36() FinSequence-membered Element of K10((((S) *) *))
((abs (S,((S) . X))) -tuples_on (S)) typed/\ (dom ((S) -multiCat)) is functional V36() FinSequence-membered Element of K10(((abs (S,((S) . X))) -tuples_on (S)))
K10(((abs (S,((S) . X))) -tuples_on (S))) is non empty set
((abs (S,((S) . X))) -tuples_on (S)) /\ (dom ((S) -multiCat)) is set
((abs (S,((S) . X))) -tuples_on (S)) /\typed (dom ((S) -multiCat)) is functional V36() FinSequence-membered Element of K10((dom ((S) -multiCat)))
K10((dom ((S) -multiCat))) is non empty set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty functional V36() FinSequence-membered (S) -prefix (S) Element of K10(((S) *))
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) Element of ((S) *) \ {{}}
(S,X) is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S,X) is complex ext-real real integer Element of INT
(S) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
K11((((S) *) \ {{}}),(S)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) \ {{}}),(S))) is non empty non trivial non finite set
(S) -firstChar is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) -pr1 is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total associative Element of K10(K11(K11((S),(S)),(S)))
K11((S),(S)) is non empty non trivial Relation-like non finite set
K11(K11((S),(S)),(S)) is non empty non trivial Relation-like non finite set
K10(K11(K11((S),(S)),(S))) is non empty non trivial non finite set
K530((S),(S)) is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total Element of K10(K11(K11((S),(S)),(S)))
MultPlace ((S) -pr1) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) . X is (S) (S) (S) (S) Element of (S)
(S,((S) . X)) is complex ext-real real integer Element of INT
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S . ((S) . X) is set
abs (S,X) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
S1 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty functional V36() FinSequence-membered (S) -prefix (S) Element of K10(((S) *))
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
X is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support (S) ( 0 ,S) Element of ((S) *) \ {{}}
(S,X) is Relation-like NAT -defined (S) -valued Function-like finite abs (S,X) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S,X) is complex ext-real real integer Element of INT
(S) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
K11((((S) *) \ {{}}),(S)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) \ {{}}),(S))) is non empty non trivial non finite set
(S) -firstChar is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) -pr1 is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total associative Element of K10(K11(K11((S),(S)),(S)))
K11((S),(S)) is non empty non trivial Relation-like non finite set
K11(K11((S),(S)),(S)) is non empty non trivial Relation-like non finite set
K10(K11(K11((S),(S)),(S))) is non empty non trivial non finite set
K530((S),(S)) is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total Element of K10(K11(K11((S),(S)),(S)))
MultPlace ((S) -pr1) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) . X is (S) (S) (S) (S) (S) (S) Element of (S)
(S,((S) . X)) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of INT
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S . ((S) . X) is set
abs (S,X) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
S1 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
S is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
S + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
X is non empty non degenerated non trivial non finite () ()
(X) is non empty non trivial non finite set
the carrier of X is non empty non trivial non finite set
(X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X)
((X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((X) *))
K10(((X) *)) is non empty non trivial non finite set
((X) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((X) *))
(X) is non empty functional V36() FinSequence-membered (X) -prefix (X) Element of K10(((X) *))
(X) is Relation-like Function-like set
rng (X) is set
union (rng (X)) is set
((X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X) *
(X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((X) *) *))
K10((((X) *) *)) is non empty non trivial non finite set
S1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (X) (S + 1,X) Element of ((X) *) \ {{}}
(X,S1) is Relation-like NAT -defined (X) -valued Function-like finite abs (X,S1) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (X) *
(X,S1) is complex ext-real real integer Element of INT
(X) is non empty Relation-like ((X) *) \ {{}} -defined (X) -valued Function-like total quasi_total Element of K10(K11((((X) *) \ {{}}),(X)))
K11((((X) *) \ {{}}),(X)) is non empty non trivial Relation-like non finite set
K10(K11((((X) *) \ {{}}),(X))) is non empty non trivial non finite set
(X) -firstChar is non empty Relation-like ((X) *) \ {{}} -defined (X) -valued Function-like total quasi_total Element of K10(K11((((X) *) \ {{}}),(X)))
(X) -pr1 is non empty Relation-like K11((X),(X)) -defined (X) -valued Function-like total quasi_total associative Element of K10(K11(K11((X),(X)),(X)))
K11((X),(X)) is non empty non trivial Relation-like non finite set
K11(K11((X),(X)),(X)) is non empty non trivial Relation-like non finite set
K10(K11(K11((X),(X)),(X))) is non empty non trivial non finite set
K530((X),(X)) is non empty Relation-like K11((X),(X)) -defined (X) -valued Function-like total quasi_total Element of K10(K11(K11((X),(X)),(X)))
MultPlace ((X) -pr1) is non empty Relation-like ((X) *) \ {{}} -defined (X) -valued Function-like total quasi_total Element of K10(K11((((X) *) \ {{}}),(X)))
(X) . S1 is (X) (X) (X) (X) Element of (X)
(X,((X) . S1)) is complex ext-real real integer Element of INT
the of X is non empty Relation-like the carrier of X \ { the OneF of X} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of X \ { the OneF of X}),INT))
the OneF of X is Element of the carrier of X
{ the OneF of X} is non empty trivial finite 1 -element countable set
the carrier of X \ { the OneF of X} is non empty non trivial non finite Element of K10( the carrier of X)
K10( the carrier of X) is non empty non trivial non finite set
the carrier of X typed\ { the OneF of X} is Element of K10( the carrier of X)
K11(( the carrier of X \ { the OneF of X}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of X \ { the OneF of X}),INT)) is non empty non trivial non finite set
the of X . ((X) . S1) is set
abs (X,S1) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
bool ((X) *) is non empty non trivial non finite Element of K10(K10(((X) *)))
K10(K10(((X) *))) is non empty non trivial non finite set
(X) is non empty Relation-like NAT -defined bool ((X) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((X) *))))
K11(NAT,(bool ((X) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((X) *)))) is non empty non trivial non finite set
(X) . S is non empty functional V36() FinSequence-membered (X) -prefix (X) Element of bool ((X) *)
(X) is non empty Relation-like ((X) *) * -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((X) *) *),((X) *)))
K11((((X) *) *),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11((((X) *) *),((X) *))) is non empty non trivial non finite set
(X) -multiCat is non empty Relation-like ((X) *) * -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((X) *) *),((X) *)))
(X) -concatenation is non empty Relation-like K11(((X) *),((X) *)) -defined (X) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((X) *),((X) *)),((X) *)))
K11(((X) *),((X) *)) is non empty non trivial Relation-like non finite set
K11(K11(((X) *),((X) *)),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((X) *),((X) *)),((X) *))) is non empty non trivial non finite set
MultPlace ((X) -concatenation) is non empty Relation-like (((X) *) *) \ {{}} -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((X) *) *) \ {{}}),((X) *)))
(((X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((X) *) *))
(((X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((X) *) *))
K11(((((X) *) *) \ {{}}),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((X) *) *) \ {{}}),((X) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((X) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
((X) . S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((X) *) *))
<*((X) . S1)*> is non empty trivial Relation-like NAT -defined (X) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (X)
1 -tuples_on (X) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (X)
SS2 is Relation-like NAT -defined (X) . S -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of ((X) . S) *
(X) . SS2 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
<*((X) . S1)*> ^ ((X) . SS2) is non empty Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
K10((X)) is non empty set
K10(((X) *)) is non empty non trivial non finite set
E1 is functional V36() FinSequence-membered Element of K10((X))
E1 * is non empty functional V36() FinSequence-membered Element of K10(((X) *))
(X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X)
K10(((X) *)) is non empty non trivial non finite set
N1 is non empty functional V36() FinSequence-membered Element of K10(((X) *))
E2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of N1
N2 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (X) *
Y is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (X) *
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
K11((((S) *) \ {{}}),(S)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) \ {{}}),(S))) is non empty non trivial non finite set
(S) -firstChar is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) -pr1 is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total associative Element of K10(K11(K11((S),(S)),(S)))
K11((S),(S)) is non empty non trivial Relation-like non finite set
K11(K11((S),(S)),(S)) is non empty non trivial Relation-like non finite set
K10(K11(K11((S),(S)),(S))) is non empty non trivial non finite set
K530((S),(S)) is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total Element of K10(K11(K11((S),(S)),(S)))
MultPlace ((S) -pr1) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) Element of ((S) *) \ {{}}
(S) . X is (S) (S) (S) Element of (S)
(S,((S) . X)) is complex ext-real real integer Element of INT
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S . ((S) . X) is set
abs (S,((S) . X)) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(S) is non empty functional V36() FinSequence-membered (S) -prefix (S) Element of K10(((S) *))
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
<*((S) . X)*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
(S) is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
K11((((S) *) *),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) *),((S) *))) is non empty non trivial non finite set
(S) -multiCat is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
(S) -concatenation is non empty Relation-like K11(((S) *),((S) *)) -defined (S) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((S) *),((S) *)),((S) *)))
K11(((S) *),((S) *)) is non empty non trivial Relation-like non finite set
K11(K11(((S) *),((S) *)),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((S) *),((S) *)),((S) *))) is non empty non trivial non finite set
MultPlace ((S) -concatenation) is non empty Relation-like (((S) *) *) \ {{}} -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((S) *) *) \ {{}}),((S) *)))
(((S) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) *))
(((S) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((S) *) *))
K11(((((S) *) *) \ {{}}),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((S) *) *) \ {{}}),((S) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((S) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
(S) is non empty non trivial non finite set
f is (S) (S) (S) Element of (S)
(S,f) is complex ext-real real integer Element of INT
the of S . f is set
abs (S,f) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
<*f*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
S2 is Relation-like NAT -defined (S) -valued Function-like finite abs (S,f) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S) . S2 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
<*f*> ^ ((S) . S2) is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
SS2 is Element of (S)
<*SS2*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
E1 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of (S)
N1 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of (S)
E1 ^ N1 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
(E1 ^ N1) . 1 is set
E2 is Relation-like NAT -defined (S) -valued Function-like finite abs (S,((S) . X)) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S) . E2 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
<*((S) . X)*> ^ ((S) . E2) is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
dom (S) is non empty functional V36() FinSequence-membered Element of K10((((S) *) *))
S2 is Element of (S)
<*S2*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
E1 is Relation-like NAT -defined (S) -valued Function-like finite abs (S,((S) . X)) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S) . E1 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
<*((S) . X)*> ^ ((S) . E1) is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
N1 is Relation-like NAT -defined (S) -valued Function-like finite abs (S,((S) . X)) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S) . N1 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
<*((S) . X)*> ^ ((S) . N1) is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
len E1 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
len N1 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(abs (S,((S) . X))) -tuples_on (S) is non empty functional V36() FinSequence-membered FinSequenceSet of (S)
E2 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support FinSequence of (S)
N2 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support FinSequence of (S)
Y is Relation-like NAT -defined (S) -valued Function-like finite abs (S,((S) . X)) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (abs (S,((S) . X))) -tuples_on (S)
NN1 is Relation-like NAT -defined (S) -valued Function-like finite abs (S,((S) . X)) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (abs (S,((S) . X))) -tuples_on (S)
((abs (S,((S) . X))) -tuples_on (S)) /\ (dom (S)) is functional V36() FinSequence-membered Element of K10((((S) *) *))
((abs (S,((S) . X))) -tuples_on (S)) typed/\ (dom (S)) is functional V36() FinSequence-membered Element of K10(((abs (S,((S) . X))) -tuples_on (S)))
K10(((abs (S,((S) . X))) -tuples_on (S))) is non empty set
((abs (S,((S) . X))) -tuples_on (S)) /\ (dom (S)) is set
((abs (S,((S) . X))) -tuples_on (S)) /\typed (dom (S)) is functional V36() FinSequence-membered Element of K10((dom (S)))
K10((dom (S))) is non empty set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) Element of ((S) *) \ {{}}
(S,X) is Relation-like NAT -defined (S) -valued Function-like finite abs (S,((S) . X)) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
K11((((S) *) \ {{}}),(S)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) \ {{}}),(S))) is non empty non trivial non finite set
(S) -firstChar is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) -pr1 is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total associative Element of K10(K11(K11((S),(S)),(S)))
K11((S),(S)) is non empty non trivial Relation-like non finite set
K11(K11((S),(S)),(S)) is non empty non trivial Relation-like non finite set
K10(K11(K11((S),(S)),(S))) is non empty non trivial non finite set
K530((S),(S)) is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total Element of K10(K11(K11((S),(S)),(S)))
MultPlace ((S) -pr1) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) . X is (S) (S) (S) Element of (S)
(S,((S) . X)) is complex ext-real real integer Element of INT
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S . ((S) . X) is set
abs (S,((S) . X)) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(S) is non empty functional V36() FinSequence-membered (S) -prefix (S) Element of K10(((S) *))
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
S1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty (S) -prefix (S) set
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
K10((((S) *) \ {{}})) is non empty non trivial non finite set
bool (((S) *) \ {{}}) is non empty non trivial non finite Element of K10(K10((((S) *) \ {{}})))
K10(K10((((S) *) \ {{}}))) is non empty non trivial non finite set
(S) is non empty functional V36() FinSequence-membered (S) -prefix (S) Element of K10(((S) *))
SS1 is set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty functional V36() FinSequence-membered with_non-empty_elements (S) -prefix (S) Element of bool (((S) *) \ {{}})
K10((((S) *) \ {{}})) is non empty non trivial non finite set
bool (((S) *) \ {{}}) is non empty non trivial non finite Element of K10(K10((((S) *) \ {{}})))
K10(K10((((S) *) \ {{}}))) is non empty non trivial non finite set
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S)
S is non empty non degenerated non trivial non finite () ()
(S) is non empty functional V36() FinSequence-membered with_non-empty_elements (S) -prefix (S) Element of bool (((S) *) \ {{}})
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
K10((((S) *) \ {{}})) is non empty non trivial non finite set
bool (((S) *) \ {{}}) is non empty non trivial non finite Element of K10(K10((((S) *) \ {{}})))
K10(K10((((S) *) \ {{}}))) is non empty non trivial non finite set
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10(((((S) *) \ {{}}) *))
(((S) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of ((S) *) \ {{}}
K10(((((S) *) \ {{}}) *)) is non empty non trivial non finite set
K11((S),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11((S),((S) *))) is non empty non trivial non finite set
(S) is non empty functional V36() FinSequence-membered (S) -prefix (S) Element of K10(((S) *))
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
SS1 is non empty Relation-like (S) -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((S),((S) *)))
SX is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) Element of (S)
SS1 . SX is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S,SX) is Relation-like NAT -defined (S) -valued Function-like finite abs (S,SX) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S,SX) is complex ext-real real integer Element of INT
(S) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
K11((((S) *) \ {{}}),(S)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) \ {{}}),(S))) is non empty non trivial non finite set
(S) -firstChar is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) -pr1 is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total associative Element of K10(K11(K11((S),(S)),(S)))
K11((S),(S)) is non empty non trivial Relation-like non finite set
K11(K11((S),(S)),(S)) is non empty non trivial Relation-like non finite set
K10(K11(K11((S),(S)),(S))) is non empty non trivial non finite set
K530((S),(S)) is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total Element of K10(K11(K11((S),(S)),(S)))
MultPlace ((S) -pr1) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) . SX is (S) (S) (S) (S) Element of (S)
(S,((S) . SX)) is complex ext-real real integer Element of INT
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S . ((S) . SX) is set
abs (S,SX) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
S1 is non empty Relation-like (S) -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((S),((S) *)))
SS1 is non empty Relation-like (S) -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((S),((S) *)))
SX is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) Element of (S)
S1 . SX is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S,SX) is Relation-like NAT -defined (S) -valued Function-like finite abs (S,SX) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S) is non empty functional V36() FinSequence-membered (S) -prefix (S) Element of K10(((S) *))
(S,SX) is complex ext-real real integer Element of INT
(S) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
K11((((S) *) \ {{}}),(S)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) \ {{}}),(S))) is non empty non trivial non finite set
(S) -firstChar is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) -pr1 is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total associative Element of K10(K11(K11((S),(S)),(S)))
K11((S),(S)) is non empty non trivial Relation-like non finite set
K11(K11((S),(S)),(S)) is non empty non trivial Relation-like non finite set
K10(K11(K11((S),(S)),(S))) is non empty non trivial non finite set
K530((S),(S)) is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total Element of K10(K11(K11((S),(S)),(S)))
MultPlace ((S) -pr1) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) . SX is (S) (S) (S) (S) Element of (S)
(S,((S) . SX)) is complex ext-real real integer Element of INT
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S . ((S) . SX) is set
abs (S,SX) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
SS1 . SX is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
S1 is non empty non degenerated non trivial non finite () ()
(S1) is non empty Relation-like NAT -defined bool ((S1) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((S1) *))))
(S1) is non empty non trivial non finite set
the carrier of S1 is non empty non trivial non finite set
(S1) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S1)
bool ((S1) *) is non empty non trivial non finite Element of K10(K10(((S1) *)))
K10(((S1) *)) is non empty non trivial non finite set
K10(K10(((S1) *))) is non empty non trivial non finite set
K11(NAT,(bool ((S1) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((S1) *)))) is non empty non trivial non finite set
S is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
(S1) . S is non empty (S1) -prefix (S1) set
X is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
S + X is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
(S1) . (S + X) is non empty (S1) -prefix (S1) set
S is set
X is non empty non degenerated non trivial non finite () ()
(X) is non empty functional V36() FinSequence-membered with_non-empty_elements (X) -prefix (X) Element of bool (((X) *) \ {{}})
(X) is non empty non trivial non finite set
the carrier of X is non empty non trivial non finite set
(X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X)
((X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((X) *))
K10(((X) *)) is non empty non trivial non finite set
((X) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((X) *))
K10((((X) *) \ {{}})) is non empty non trivial non finite set
bool (((X) *) \ {{}}) is non empty non trivial non finite Element of K10(K10((((X) *) \ {{}})))
K10(K10((((X) *) \ {{}}))) is non empty non trivial non finite set
(X) is Relation-like Function-like set
rng (X) is set
union (rng (X)) is set
bool ((X) *) is non empty non trivial non finite Element of K10(K10(((X) *)))
K10(K10(((X) *))) is non empty non trivial non finite set
(X) is non empty Relation-like NAT -defined bool ((X) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((X) *))))
K11(NAT,(bool ((X) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((X) *)))) is non empty non trivial non finite set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty functional V36() FinSequence-membered with_non-empty_elements (S) -prefix (S) Element of bool (((S) *) \ {{}})
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
K10((((S) *) \ {{}})) is non empty non trivial non finite set
bool (((S) *) \ {{}}) is non empty non trivial non finite Element of K10(K10((((S) *) \ {{}})))
K10(K10((((S) *) \ {{}}))) is non empty non trivial non finite set
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty functional V36() FinSequence-membered with_non-empty_elements (S) -prefix (S) Element of bool (((S) *) \ {{}})
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
K10((((S) *) \ {{}})) is non empty non trivial non finite set
bool (((S) *) \ {{}}) is non empty non trivial non finite Element of K10(K10((((S) *) \ {{}})))
K10(K10((((S) *) \ {{}}))) is non empty non trivial non finite set
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
S is set
X is non empty non degenerated non trivial non finite () ()
(X) is non empty functional V36() FinSequence-membered with_non-empty_elements (X) -prefix (X) Element of bool (((X) *) \ {{}})
(X) is non empty non trivial non finite set
the carrier of X is non empty non trivial non finite set
(X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X)
((X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((X) *))
K10(((X) *)) is non empty non trivial non finite set
((X) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((X) *))
K10((((X) *) \ {{}})) is non empty non trivial non finite set
bool (((X) *) \ {{}}) is non empty non trivial non finite Element of K10(K10((((X) *) \ {{}})))
K10(K10((((X) *) \ {{}}))) is non empty non trivial non finite set
(X) is Relation-like Function-like set
rng (X) is set
union (rng (X)) is set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) is non empty Element of K10((S))
K10((S)) is non empty non trivial non finite set
(S) is non empty non trivial non finite set
(S) is set
the OneF of S is Element of the carrier of S
{(S)} is non empty trivial finite 1 -element countable set
(S) \ {(S)} is non empty non trivial non finite Element of K10((S))
K10((S)) is non empty non trivial non finite set
(S) typed\ {(S)} is Element of K10((S))
(S) is set
the ZeroF of S is Element of the carrier of S
{ the ZeroF of S, the OneF of S} is non empty finite countable set
the carrier of S \ { the ZeroF of S, the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the ZeroF of S, the OneF of S} is Element of K10( the carrier of S)
(S) \ (S) is Element of K10((S))
(S) typed\ (S) is Element of K10((S))
K10((S)) is non empty set
(S) \ (S) is Element of K10((S))
(S) is Element of (S)
{(S)} is non empty trivial finite 1 -element countable Element of K10((S))
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
(S) is set
the of S " (INT \ NAT) is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
{ the OneF of S} is non empty trivial finite 1 -element countable Element of K10( the carrier of S)
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
{ the ZeroF of S} is non empty trivial finite 1 -element countable Element of K10( the carrier of S)
{ the ZeroF of S} \/ { the OneF of S} is non empty finite countable Element of K10( the carrier of S)
(S) \ ({ the ZeroF of S} \/ { the OneF of S}) is non empty non trivial non finite Element of K10((S))
(S) typed\ ({ the ZeroF of S} \/ { the OneF of S}) is Element of K10((S))
(S) \ ((S) \ ({ the ZeroF of S} \/ { the OneF of S})) is Element of K10((S))
(S) typed\ ((S) \ ({ the ZeroF of S} \/ { the OneF of S})) is Element of K10((S))
(S) \ ((S) \ ({ the ZeroF of S} \/ { the OneF of S})) is Element of K10((S))
(S) \ { the ZeroF of S} is Element of K10((S))
(S) typed\ { the ZeroF of S} is Element of K10((S))
(S) \ { the ZeroF of S} is Element of K10((S))
(S) \ ((S) \ { the ZeroF of S}) is Element of K10((S))
(S) typed\ ((S) \ { the ZeroF of S}) is Element of K10((S))
(S) \ ((S) \ { the ZeroF of S}) is Element of K10((S))
(S) \ (S) is empty proper epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of K10((S))
(S) typed\ (S) is Element of K10((S))
(S) \ (S) is empty proper epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of K10((S))
(S) /\ { the ZeroF of S} is finite countable Element of K10( the carrier of S)
(S) typed/\ { the ZeroF of S} is Element of K10((S))
(S) /\ { the ZeroF of S} is finite countable set
(S) /\typed { the ZeroF of S} is trivial finite countable Element of K10({ the ZeroF of S})
K10({ the ZeroF of S}) is non empty finite V36() countable set
((S) \ (S)) \/ ((S) /\ { the ZeroF of S}) is finite countable set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty set
the carrier of S is non empty non trivial non finite set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " NAT is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
(S) is non empty non trivial non finite Element of K10((S))
(S) is non empty non trivial non finite set
K10((S)) is non empty non trivial non finite set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
(S) \ (S) is Element of K10((S))
K10((S)) is non empty set
(S) typed\ (S) is Element of K10((S))
(S) is set
the of S " (NAT \ {0}) is Element of K10(( the carrier of S \ { the OneF of S}))
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) is non empty Element of K10((S))
K10((S)) is non empty non trivial non finite set
(S) is non empty non trivial non finite set
(S) is set
the OneF of S is Element of the carrier of S
{(S)} is non empty trivial finite 1 -element countable set
(S) \ {(S)} is non empty non trivial non finite Element of K10((S))
K10((S)) is non empty non trivial non finite set
(S) typed\ {(S)} is Element of K10((S))
(S) is set
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " (INT \ NAT) is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
(S) \ (S) is Element of K10((S))
(S) typed\ (S) is Element of K10((S))
K10((S)) is non empty set
(S) \ (S) is Element of K10((S))
(S) is non empty set
the of S " NAT is Element of K10(( the carrier of S \ { the OneF of S}))
the of S " INT is Element of K10(( the carrier of S \ { the OneF of S}))
INT \ (INT \ NAT) is Element of K10(INT)
INT typed\ (INT \ NAT) is Element of K10(INT)
the of S " (INT \ (INT \ NAT)) is Element of K10(( the carrier of S \ { the OneF of S}))
INT \ INT is empty proper epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of K10(INT)
INT typed\ INT is Element of K10(INT)
INT /\ NAT is Element of K10(REAL)
INT typed/\ NAT is Element of K10(INT)
INT /\ NAT is set
INT /\typed NAT is countable Element of K10(NAT)
(INT \ INT) \/ (INT /\ NAT) is set
the of S " ((INT \ INT) \/ (INT /\ NAT)) is Element of K10(( the carrier of S \ { the OneF of S}))
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) is set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " (INT \ NAT) is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
(S) is non empty Element of K10((S))
(S) is non empty non trivial non finite set
K10((S)) is non empty non trivial non finite set
(S) is set
{(S)} is non empty trivial finite 1 -element countable set
(S) \ {(S)} is non empty non trivial non finite Element of K10((S))
K10((S)) is non empty non trivial non finite set
(S) typed\ {(S)} is Element of K10((S))
(S) is non empty set
the of S " NAT is Element of K10(( the carrier of S \ { the OneF of S}))
SX is (S) Element of (S)
(S) \ (S) is Element of K10((S))
(S) typed\ (S) is Element of K10((S))
K10((S)) is non empty set
(S) \ (S) is Element of K10((S))
S is non empty non degenerated non trivial non finite () ()
(S) is set
the carrier of S is non empty non trivial non finite set
the ZeroF of S is Element of the carrier of S
the OneF of S is Element of the carrier of S
{ the ZeroF of S, the OneF of S} is non empty finite countable set
the carrier of S \ { the ZeroF of S, the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the ZeroF of S, the OneF of S} is Element of K10( the carrier of S)
(S) is non empty non trivial non finite set
K10((S)) is non empty non trivial non finite set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) is non empty non trivial non finite Element of K10((S))
(S) is non empty non trivial non finite set
K10((S)) is non empty non trivial non finite set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
(S) is set
the of S " (NAT \ {0}) is Element of K10(( the carrier of S \ { the OneF of S}))
(S) is non empty set
the of S " NAT is Element of K10(( the carrier of S \ { the OneF of S}))
add is (S) (S) (S) (S) Element of (S)
(S) \ (S) is Element of K10((S))
K10((S)) is non empty set
(S) typed\ (S) is Element of K10((S))
S is set
X is non empty non degenerated non trivial non finite () ()
(X) is non empty non trivial non finite set
the carrier of X is non empty non trivial non finite set
(X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X)
((X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((X) *))
K10(((X) *)) is non empty non trivial non finite set
((X) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((X) *))
S is set
X is non empty non degenerated non trivial non finite () ()
(X) is non empty non trivial non finite set
the carrier of X is non empty non trivial non finite set
(X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X)
((X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((X) *))
K10(((X) *)) is non empty non trivial non finite set
((X) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((X) *))
S is non empty non degenerated non trivial non finite () ()
(S) is non empty Relation-like NAT -defined bool ((S) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((S) *))))
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
bool ((S) *) is non empty non trivial non finite Element of K10(K10(((S) *)))
K10(((S) *)) is non empty non trivial non finite set
K10(K10(((S) *))) is non empty non trivial non finite set
K11(NAT,(bool ((S) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((S) *)))) is non empty non trivial non finite set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) is non empty non trivial non finite Element of K10((S))
K10((S)) is non empty non trivial non finite set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
X is Element of (S)
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) is set
the OneF of S is Element of the carrier of S
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
(S) is set
the of S " (INT \ {0}) is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
(S) is non empty non trivial non finite set
dom the of S is non empty Element of K10(( the carrier of S \ { the OneF of S}))
{(S)} is non empty trivial finite 1 -element countable set
(S) \ {(S)} is non empty non trivial non finite Element of K10((S))
K10((S)) is non empty non trivial non finite set
(S) typed\ {(S)} is Element of K10((S))
add is Element of (S)
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) is set
the OneF of S is Element of the carrier of S
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
(S) is Element of K10((S))
(S) is non empty non trivial non finite set
K10((S)) is non empty non trivial non finite set
the ZeroF of S is Element of the carrier of S
{ the ZeroF of S, the OneF of S} is non empty finite countable set
the carrier of S \ { the ZeroF of S, the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
the carrier of S typed\ { the ZeroF of S, the OneF of S} is Element of K10( the carrier of S)
{ the ZeroF of S,(S)} is non empty finite countable set
add is Element of (S)
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) is set
the OneF of S is Element of the carrier of S
(S) is Element of (S)
(S) is non empty non trivial non finite set
(S) is non empty Element of K10((S))
K10((S)) is non empty non trivial non finite set
{(S)} is non empty trivial finite 1 -element countable set
(S) \ {(S)} is non empty non trivial non finite Element of K10((S))
K10((S)) is non empty non trivial non finite set
(S) typed\ {(S)} is Element of K10((S))
the ZeroF of S is Element of the carrier of S
(S) is Element of K10((S))
{ the ZeroF of S, the OneF of S} is non empty finite countable set
the carrier of S \ { the ZeroF of S, the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the ZeroF of S, the OneF of S} is Element of K10( the carrier of S)
X is Element of (S)
(S) is set
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " (INT \ NAT) is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
(S) \ (S) is Element of K10((S))
K10((S)) is non empty set
(S) typed\ (S) is Element of K10((S))
{(S)} is non empty trivial finite 1 -element countable Element of K10((S))
K10((S)) is non empty set
{(S)} \/ {(S)} is non empty finite countable set
{(S),(S)} is non empty finite countable set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) Element of ((S) *) \ {{}}
(S) is non empty functional V36() FinSequence-membered with_non-empty_elements (S) -prefix (S) Element of bool (((S) *) \ {{}})
K10((((S) *) \ {{}})) is non empty non trivial non finite set
bool (((S) *) \ {{}}) is non empty non trivial non finite Element of K10(K10((((S) *) \ {{}})))
K10(K10((((S) *) \ {{}}))) is non empty non trivial non finite set
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
(S) is non empty Relation-like NAT -defined bool ((S) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((S) *))))
bool ((S) *) is non empty non trivial non finite Element of K10(K10(((S) *)))
K10(K10(((S) *))) is non empty non trivial non finite set
K11(NAT,(bool ((S) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((S) *)))) is non empty non trivial non finite set
SX is Relation-like Function-like set
add is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
SX . add is set
f is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
S2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
S1 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
SS1 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
X is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
S1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) (X,S) Element of ((S) *) \ {{}}
(S,S1) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
SS1 is set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
X is (S) (S) Element of (S)
(S,X) is complex ext-real real integer Element of INT
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S . X is set
(S) is non empty non trivial non finite set
(S) is set
(S) is set
the of S " (INT \ {0}) is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
dom the of S is non empty Element of K10(( the carrier of S \ { the OneF of S}))
add is set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
X is (S) (S) (S) (S) Element of (S)
(S,X) is complex ext-real real integer Element of INT
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S . X is set
(S) is non empty set
the of S " NAT is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
SX is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
X is (S) (S) (S) Element of (S)
(S,X) is non empty complex ext-real real integer Element of INT
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S . X is set
(S) is set
the of S " (INT \ NAT) is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
dom the of S is non empty Element of K10(( the carrier of S \ { the OneF of S}))
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
K11((((S) *) \ {{}}),(S)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) \ {{}}),(S))) is non empty non trivial non finite set
(S) -firstChar is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) -pr1 is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total associative Element of K10(K11(K11((S),(S)),(S)))
K11((S),(S)) is non empty non trivial Relation-like non finite set
K11(K11((S),(S)),(S)) is non empty non trivial Relation-like non finite set
K10(K11(K11((S),(S)),(S))) is non empty non trivial non finite set
K530((S),(S)) is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total Element of K10(K11(K11((S),(S)),(S)))
MultPlace ((S) -pr1) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) Element of ((S) *) \ {{}}
(S) . X is (S) (S) (S) (S) Element of (S)
(S,X) is Relation-like NAT -defined (S) -valued Function-like finite abs (S,X) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S) is non empty functional V36() FinSequence-membered (S) -prefix (S) Element of K10(((S) *))
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
(S,X) is complex ext-real real integer Element of INT
(S,((S) . X)) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of INT
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S . ((S) . X) is set
abs (S,X) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
(S) is non empty Relation-like NAT -defined bool ((S) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((S) *))))
bool ((S) *) is non empty non trivial non finite Element of K10(K10(((S) *)))
K10(K10(((S) *))) is non empty non trivial non finite set
K11(NAT,(bool ((S) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((S) *)))) is non empty non trivial non finite set
(S,X) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
(S) is non empty functional V36() FinSequence-membered with_non-empty_elements (S) -prefix (S) Element of bool (((S) *) \ {{}})
K10((((S) *) \ {{}})) is non empty non trivial non finite set
bool (((S) *) \ {{}}) is non empty non trivial non finite Element of K10(K10((((S) *) \ {{}})))
K10(K10((((S) *) \ {{}}))) is non empty non trivial non finite set
f is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
f + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
(S) is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
K11((((S) *) *),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) *),((S) *))) is non empty non trivial non finite set
(S) -multiCat is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
(S) -concatenation is non empty Relation-like K11(((S) *),((S) *)) -defined (S) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((S) *),((S) *)),((S) *)))
K11(((S) *),((S) *)) is non empty non trivial Relation-like non finite set
K11(K11(((S) *),((S) *)),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((S) *),((S) *)),((S) *))) is non empty non trivial non finite set
MultPlace ((S) -concatenation) is non empty Relation-like (((S) *) *) \ {{}} -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((S) *) *) \ {{}}),((S) *)))
(((S) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) *))
(((S) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((S) *) *))
K11(((((S) *) *) \ {{}}),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((S) *) *) \ {{}}),((S) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((S) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
(S) is non empty non trivial non finite set
(S) . f is non empty (S) -prefix (S) set
{ (S,b₁,((S) . f)) where b₁ is (S) Element of (S) : b₁ is (S) } is set
(S) . (f + 1) is non empty (S) -prefix (S) set
union { (S,b₁,((S) . f)) where b₁ is (S) Element of (S) : b₁ is (S) } is set
(union { (S,b₁,((S) . f)) where b₁ is (S) Element of (S) : b₁ is (S) } ) \/ ((S) . f) is non empty set
N1 is set
E2 is (S) Element of (S)
(S,E2,((S) . f)) is functional V36() FinSequence-membered with_non-empty_elements Element of bool (((S) *) \ {{}})
<*E2*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
(S,E2) is complex ext-real real integer Element of INT
the of S . E2 is set
abs (S,E2) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
{ (<*E2*> ^ ((S) . b₁)) where b₁ is Relation-like NAT -defined (S) * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of ((S) *) * : ( rng b₁ c= (S) . f & b₁ is abs (S,E2) -element ) } is set
Y is Relation-like NAT -defined (S) * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of ((S) *) *
(S) . Y is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
<*E2*> ^ ((S) . Y) is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
rng Y is functional finite V36() FinSequence-membered countable Element of K10(((S) *))
(<*E2*> ^ ((S) . Y)) . 1 is set
<*E2*> . 1 is set
NN1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
NN1 + 0 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
(((S) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of ((S) *) \ {{}}
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10(((((S) *) \ {{}}) *))
K10(((((S) *) \ {{}}) *)) is non empty non trivial non finite set
NN2 is non empty Relation-like non empty-yielding NAT -defined (S) -valued Function-like finite NN1 + 0 -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
S is non empty non degenerated non trivial non finite () ()
(S) is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
K11((((S) *) *),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) *),((S) *))) is non empty non trivial non finite set
(S) -multiCat is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
(S) -concatenation is non empty Relation-like K11(((S) *),((S) *)) -defined (S) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((S) *),((S) *)),((S) *)))
K11(((S) *),((S) *)) is non empty non trivial Relation-like non finite set
K11(K11(((S) *),((S) *)),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((S) *),((S) *)),((S) *))) is non empty non trivial non finite set
MultPlace ((S) -concatenation) is non empty Relation-like (((S) *) *) \ {{}} -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((S) *) *) \ {{}}),((S) *)))
(((S) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
(((S) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((S) *) *))
K11(((((S) *) *) \ {{}}),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((S) *) *) \ {{}}),((S) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((S) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
X is Relation-like Function-like set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
K11((((S) *) *),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) *),((S) *))) is non empty non trivial non finite set
(S) -multiCat is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
(S) -concatenation is non empty Relation-like K11(((S) *),((S) *)) -defined (S) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((S) *),((S) *)),((S) *)))
K11(((S) *),((S) *)) is non empty non trivial Relation-like non finite set
K11(K11(((S) *),((S) *)),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((S) *),((S) *)),((S) *))) is non empty non trivial non finite set
MultPlace ((S) -concatenation) is non empty Relation-like (((S) *) *) \ {{}} -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((S) *) *) \ {{}}),((S) *)))
(((S) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
(((S) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((S) *) *))
K11(((((S) *) *) \ {{}}),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((S) *) *) \ {{}}),((S) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((S) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
X is non empty Relation-like non empty-yielding NAT -defined ((S) *) \ {{}} -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support set
(S) . X is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
len X is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable Element of NAT
f is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
f + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
(f + 1) + 0 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
S2 is non empty Relation-like NAT -defined Function-like finite (f + 1) + 0 -element FinSequence-like FinSubsequence-like countable finite-support set
S2 . (f + 1) is set
{(S2 . (f + 1))} is non empty trivial finite 1 -element countable set
{(S2 . (f + 1))} \ (((S) *) \ {{}}) is trivial finite countable Element of K10({(S2 . (f + 1))})
K10({(S2 . (f + 1))}) is non empty finite V36() countable set
{(S2 . (f + 1))} typed\ (((S) *) \ {{}}) is trivial finite countable Element of K10({(S2 . (f + 1))})
Seg f is finite f -element countable Element of K10(NAT)
S2 | (Seg f) is Relation-like Seg f -defined NAT -defined Seg f -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
<*(S2 . (f + 1))*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support set
(S2 | (Seg f)) ^ <*(S2 . (f + 1))*> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((S2 | (Seg f)) ^ <*(S2 . (f + 1))*>) \+\ S2 is Relation-like finite countable set
((S2 | (Seg f)) ^ <*(S2 . (f + 1))*>) \ S2 is Relation-like NAT -defined finite countable set
((S2 | (Seg f)) ^ <*(S2 . (f + 1))*>) typed\ S2 is Relation-like NAT -defined Function-like finite countable finite-support Element of K10(((S2 | (Seg f)) ^ <*(S2 . (f + 1))*>))
K10(((S2 | (Seg f)) ^ <*(S2 . (f + 1))*>)) is non empty finite V36() countable set
((S2 | (Seg f)) ^ <*(S2 . (f + 1))*>) \ S2 is Relation-like NAT -defined Function-like finite countable finite-support Element of K10(((S2 | (Seg f)) ^ <*(S2 . (f + 1))*>))
S2 \ ((S2 | (Seg f)) ^ <*(S2 . (f + 1))*>) is Relation-like NAT -defined finite countable set
S2 typed\ ((S2 | (Seg f)) ^ <*(S2 . (f + 1))*>) is Relation-like NAT -defined Function-like finite countable finite-support Element of K10(S2)
K10(S2) is non empty finite V36() countable set
S2 \ ((S2 | (Seg f)) ^ <*(S2 . (f + 1))*>) is Relation-like NAT -defined Function-like finite countable finite-support Element of K10(S2)
(((S2 | (Seg f)) ^ <*(S2 . (f + 1))*>) \ S2) \/ (S2 \ ((S2 | (Seg f)) ^ <*(S2 . (f + 1))*>)) is Relation-like NAT -defined finite countable set
(MultPlace ((S) -concatenation)) . X is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
E2 is Relation-like NAT -defined (S) * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support set
E1 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
<*E1*> is non empty trivial Relation-like NAT -defined (S) * -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of 1 -tuples_on ((S) *)
1 -tuples_on ((S) *) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S) *
E2 ^ <*E1*> is non empty Relation-like NAT -defined (S) * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support set
(MultPlace ((S) -concatenation)) . (E2 ^ <*E1*>) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(MultPlace ((S) -concatenation)) . <*E1*> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
SS2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of ((S) *) \ {{}}
N2 is set
(MultPlace ((S) -concatenation)) . E2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((S) -concatenation) . (((MultPlace ((S) -concatenation)) . E2),E1) is set
N2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (((S) *) *) \ {{}}
(MultPlace ((S) -concatenation)) . N2 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
SS2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of ((S) *) \ {{}}
((MultPlace ((S) -concatenation)) . N2) ^ SS2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
Y is set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
X is (S) (S) (S) (S) (S) (S) Element of (S)
<*X*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
(S) is non empty non trivial non finite Element of K10((S))
K10((S)) is non empty non trivial non finite set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
(S) is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty non trivial non finite set
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
(S) is non empty Relation-like NAT -defined bool ((S) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((S) *))))
bool ((S) *) is non empty non trivial non finite Element of K10(K10(((S) *)))
K10(K10(((S) *))) is non empty non trivial non finite set
K11(NAT,(bool ((S) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((S) *)))) is non empty non trivial non finite set
f is (S) Element of (S)
<*f*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
(S) . 0 is non empty functional V36() FinSequence-membered (S) -prefix (S) Element of bool ((S) *)
S2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of ((S) *) \ {{}}
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
X is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
S1 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
0 * S1 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
X + (0 * S1) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
X + S1 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
(S) is non empty Relation-like NAT -defined bool ((S) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((S) *))))
bool ((S) *) is non empty non trivial non finite Element of K10(K10(((S) *)))
K10(K10(((S) *))) is non empty non trivial non finite set
K11(NAT,(bool ((S) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((S) *)))) is non empty non trivial non finite set
SX is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of ((S) *) \ {{}}
(S) . X is non empty (S) -prefix (S) set
(S) . (X + S1) is non empty (S) -prefix (S) set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) is non empty non trivial non finite Element of K10((S))
(S) is non empty non trivial non finite set
K10((S)) is non empty non trivial non finite set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
(S) is set
the of S " (NAT \ {0}) is Element of K10(( the carrier of S \ { the OneF of S}))
(S) is Element of K10((S))
the ZeroF of S is Element of the carrier of S
{ the ZeroF of S, the OneF of S} is non empty finite countable set
the carrier of S \ { the ZeroF of S, the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
the carrier of S typed\ { the ZeroF of S, the OneF of S} is Element of K10( the carrier of S)
(S) is non empty set
the of S " NAT is Element of K10(( the carrier of S \ { the OneF of S}))
(S) \ (S) is Element of K10((S))
K10((S)) is non empty set
(S) typed\ (S) is Element of K10((S))
add is (S) (S) Element of (S)
f is (S) Element of (S)
S2 is (S) (S) (S) (S) Element of (S)
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) Element of ((S) *) \ {{}}
(S,X) is Relation-like NAT -defined (S) -valued Function-like finite abs (S,X) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S) is non empty functional V36() FinSequence-membered (S) -prefix (S) Element of K10(((S) *))
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
(S,X) is complex ext-real real integer Element of INT
(S) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
K11((((S) *) \ {{}}),(S)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) \ {{}}),(S))) is non empty non trivial non finite set
(S) -firstChar is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) -pr1 is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total associative Element of K10(K11(K11((S),(S)),(S)))
K11((S),(S)) is non empty non trivial Relation-like non finite set
K11(K11((S),(S)),(S)) is non empty non trivial Relation-like non finite set
K10(K11(K11((S),(S)),(S))) is non empty non trivial non finite set
K530((S),(S)) is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total Element of K10(K11(K11((S),(S)),(S)))
MultPlace ((S) -pr1) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) . X is (S) (S) (S) (S) Element of (S)
(S,((S) . X)) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of INT
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S . ((S) . X) is set
abs (S,X) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
rng X is non empty finite countable set
(rng X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of rng X
(S) is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
K11((((S) *) *),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) *),((S) *))) is non empty non trivial non finite set
(S) -multiCat is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
(S) -concatenation is non empty Relation-like K11(((S) *),((S) *)) -defined (S) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((S) *),((S) *)),((S) *)))
K11(((S) *),((S) *)) is non empty non trivial Relation-like non finite set
K11(K11(((S) *),((S) *)),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((S) *),((S) *)),((S) *))) is non empty non trivial non finite set
MultPlace ((S) -concatenation) is non empty Relation-like (((S) *) *) \ {{}} -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((S) *) *) \ {{}}),((S) *)))
(((S) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) *))
(((S) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((S) *) *))
K11(((((S) *) *) \ {{}}),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((S) *) *) \ {{}}),((S) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((S) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
(S) is non empty Relation-like NAT -defined bool ((S) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((S) *))))
bool ((S) *) is non empty non trivial non finite Element of K10(K10(((S) *)))
K10(K10(((S) *))) is non empty non trivial non finite set
K11(NAT,(bool ((S) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((S) *)))) is non empty non trivial non finite set
(S) is non empty functional V36() FinSequence-membered with_non-empty_elements (S) -prefix (S) Element of bool (((S) *) \ {{}})
K10((((S) *) \ {{}})) is non empty non trivial non finite set
bool (((S) *) \ {{}}) is non empty non trivial non finite Element of K10(K10((((S) *) \ {{}})))
K10(K10((((S) *) \ {{}}))) is non empty non trivial non finite set
<*((S) . X)*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
(S) . (S,X) is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
<*((S) . X)*> ^ ((S) . (S,X)) is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
rng ((S) . (S,X)) is finite countable Element of K10((S))
K10((S)) is non empty non trivial non finite set
E1 is Relation-like set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) Element of ((S) *) \ {{}}
(S,X) is Relation-like NAT -defined (S) -valued Function-like finite abs (S,((S) . X)) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
K11((((S) *) \ {{}}),(S)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) \ {{}}),(S))) is non empty non trivial non finite set
(S) -firstChar is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) -pr1 is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total associative Element of K10(K11(K11((S),(S)),(S)))
K11((S),(S)) is non empty non trivial Relation-like non finite set
K11(K11((S),(S)),(S)) is non empty non trivial Relation-like non finite set
K10(K11(K11((S),(S)),(S))) is non empty non trivial non finite set
K530((S),(S)) is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total Element of K10(K11(K11((S),(S)),(S)))
MultPlace ((S) -pr1) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) . X is (S) (S) (S) Element of (S)
(S,((S) . X)) is non empty complex ext-real non positive negative real integer Element of INT
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S . ((S) . X) is set
abs (S,((S) . X)) is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable Element of NAT
(S) is non empty functional V36() FinSequence-membered (S) -prefix (S) Element of K10(((S) *))
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
rng X is non empty finite countable set
(rng X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of rng X
(S) is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
K11((((S) *) *),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) *),((S) *))) is non empty non trivial non finite set
(S) -multiCat is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
(S) -concatenation is non empty Relation-like K11(((S) *),((S) *)) -defined (S) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((S) *),((S) *)),((S) *)))
K11(((S) *),((S) *)) is non empty non trivial Relation-like non finite set
K11(K11(((S) *),((S) *)),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((S) *),((S) *)),((S) *))) is non empty non trivial non finite set
MultPlace ((S) -concatenation) is non empty Relation-like (((S) *) *) \ {{}} -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((S) *) *) \ {{}}),((S) *)))
(((S) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) *))
(((S) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((S) *) *))
K11(((((S) *) *) \ {{}}),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((S) *) *) \ {{}}),((S) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((S) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
(S) is non empty Relation-like NAT -defined bool ((S) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((S) *))))
bool ((S) *) is non empty non trivial non finite Element of K10(K10(((S) *)))
K10(K10(((S) *))) is non empty non trivial non finite set
K11(NAT,(bool ((S) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((S) *)))) is non empty non trivial non finite set
(S) is non empty functional V36() FinSequence-membered with_non-empty_elements (S) -prefix (S) Element of bool (((S) *) \ {{}})
K10((((S) *) \ {{}})) is non empty non trivial non finite set
bool (((S) *) \ {{}}) is non empty non trivial non finite Element of K10(K10((((S) *) \ {{}})))
K10(K10((((S) *) \ {{}}))) is non empty non trivial non finite set
<*((S) . X)*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
(S) . (S,X) is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
<*((S) . X)*> ^ ((S) . (S,X)) is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
rng ((S) . (S,X)) is finite countable Element of K10((S))
K10((S)) is non empty non trivial non finite set
E1 is Relation-like set
S is non empty non degenerated non trivial non finite () ()
(S) is Relation-like Function-like set
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
bool (((S) *) \ {{}}) is non empty non trivial non finite Element of K10(K10((((S) *) \ {{}})))
K10((((S) *) \ {{}})) is non empty non trivial non finite set
K10(K10((((S) *) \ {{}}))) is non empty non trivial non finite set
K11(NAT,(bool (((S) *) \ {{}}))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool (((S) *) \ {{}})))) is non empty non trivial non finite set
(S) is non empty Relation-like NAT -defined bool ((S) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((S) *))))
bool ((S) *) is non empty non trivial non finite Element of K10(K10(((S) *)))
K10(K10(((S) *))) is non empty non trivial non finite set
K11(NAT,(bool ((S) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((S) *)))) is non empty non trivial non finite set
SS1 is set
rng (S) is non empty Element of K10((bool ((S) *)))
K10((bool ((S) *))) is non empty non trivial non finite set
dom (S) is non empty countable Element of K10(NAT)
SX is set
(S) . SX is set
add is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(S) . add is non empty functional V36() FinSequence-membered (S) -prefix (S) Element of bool ((S) *)
((S) . add) /\ {{}} is functional finite V36() FinSequence-membered countable Element of K10(((S) *))
((S) . add) typed/\ {{}} is functional V36() FinSequence-membered Element of K10(((S) . add))
K10(((S) . add)) is non empty set
((S) . add) /\ {{}} is finite countable set
((S) . add) /\typed {{}} is trivial functional finite V36() empty-membered with_common_domain countable Element of K10({{}})
K10({{}}) is non empty finite V36() countable set
f is set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
bool (((S) *) \ {{}}) is non empty non trivial non finite Element of K10(K10((((S) *) \ {{}})))
K10((((S) *) \ {{}})) is non empty non trivial non finite set
K10(K10((((S) *) \ {{}}))) is non empty non trivial non finite set
(S) is non empty Relation-like NAT -defined bool (((S) *) \ {{}}) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool (((S) *) \ {{}}))))
K11(NAT,(bool (((S) *) \ {{}}))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool (((S) *) \ {{}})))) is non empty non trivial non finite set
X is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(S) . X is non empty functional V36() FinSequence-membered with_non-empty_elements (S) -prefix (S) Element of bool (((S) *) \ {{}})
S is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
X is non empty non degenerated non trivial non finite () ()
(X) is non empty Relation-like NAT -defined bool (((X) *) \ {{}}) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool (((X) *) \ {{}}))))
(X) is non empty non trivial non finite set
the carrier of X is non empty non trivial non finite set
(X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X)
((X) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((X) *))
K10(((X) *)) is non empty non trivial non finite set
((X) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((X) *))
bool (((X) *) \ {{}}) is non empty non trivial non finite Element of K10(K10((((X) *) \ {{}})))
K10((((X) *) \ {{}})) is non empty non trivial non finite set
K10(K10((((X) *) \ {{}}))) is non empty non trivial non finite set
K11(NAT,(bool (((X) *) \ {{}}))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool (((X) *) \ {{}})))) is non empty non trivial non finite set
(X) . S is non empty (X) -prefix (X) set
(X) is non empty set
the OneF of X is Element of the carrier of X
{ the OneF of X} is non empty trivial finite 1 -element countable set
the carrier of X \ { the OneF of X} is non empty non trivial non finite Element of K10( the carrier of X)
K10( the carrier of X) is non empty non trivial non finite set
the carrier of X typed\ { the OneF of X} is Element of K10( the carrier of X)
the of X is non empty Relation-like the carrier of X \ { the OneF of X} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of X \ { the OneF of X}),INT))
K11(( the carrier of X \ { the OneF of X}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of X \ { the OneF of X}),INT)) is non empty non trivial non finite set
the of X " NAT is Element of K10(( the carrier of X \ { the OneF of X}))
K10(( the carrier of X \ { the OneF of X})) is non empty non trivial non finite set
(X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X)
(X) is non empty Relation-like ((X) *) \ {{}} -defined (X) -valued Function-like total quasi_total Element of K10(K11((((X) *) \ {{}}),(X)))
K11((((X) *) \ {{}}),(X)) is non empty non trivial Relation-like non finite set
K10(K11((((X) *) \ {{}}),(X))) is non empty non trivial non finite set
(X) -firstChar is non empty Relation-like ((X) *) \ {{}} -defined (X) -valued Function-like total quasi_total Element of K10(K11((((X) *) \ {{}}),(X)))
(X) -pr1 is non empty Relation-like K11((X),(X)) -defined (X) -valued Function-like total quasi_total associative Element of K10(K11(K11((X),(X)),(X)))
K11((X),(X)) is non empty non trivial Relation-like non finite set
K11(K11((X),(X)),(X)) is non empty non trivial Relation-like non finite set
K10(K11(K11((X),(X)),(X))) is non empty non trivial non finite set
K530((X),(X)) is non empty Relation-like K11((X),(X)) -defined (X) -valued Function-like total quasi_total Element of K10(K11(K11((X),(X)),(X)))
MultPlace ((X) -pr1) is non empty Relation-like ((X) *) \ {{}} -defined (X) -valued Function-like total quasi_total Element of K10(K11((((X) *) \ {{}}),(X)))
(X) is non empty Relation-like ((X) *) * -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((X) *) *),((X) *)))
((X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X) *
K11((((X) *) *),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11((((X) *) *),((X) *))) is non empty non trivial non finite set
(X) -multiCat is non empty Relation-like ((X) *) * -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((X) *) *),((X) *)))
(X) -concatenation is non empty Relation-like K11(((X) *),((X) *)) -defined (X) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((X) *),((X) *)),((X) *)))
K11(((X) *),((X) *)) is non empty non trivial Relation-like non finite set
K11(K11(((X) *),((X) *)),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((X) *),((X) *)),((X) *))) is non empty non trivial non finite set
MultPlace ((X) -concatenation) is non empty Relation-like (((X) *) *) \ {{}} -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((X) *) *) \ {{}}),((X) *)))
(((X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((X) *) *))
K10((((X) *) *)) is non empty non trivial non finite set
(((X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((X) *) *))
K11(((((X) *) *) \ {{}}),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((X) *) *) \ {{}}),((X) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((X) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
(X) is set
the of X " (NAT \ {0}) is Element of K10(( the carrier of X \ { the OneF of X}))
(X) -multiCat is non empty Relation-like ((X) *) * -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((X) *) *),((X) *)))
((X) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (X) *
K11((((X) *) *),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11((((X) *) *),((X) *))) is non empty non trivial non finite set
(X) -concatenation is non empty Relation-like K11(((X) *),((X) *)) -defined (X) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((X) *),((X) *)),((X) *)))
K11(((X) *),((X) *)) is non empty non trivial Relation-like non finite set
K11(K11(((X) *),((X) *)),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((X) *),((X) *)),((X) *))) is non empty non trivial non finite set
MultPlace ((X) -concatenation) is non empty Relation-like (((X) *) *) \ {{}} -defined (X) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((X) *) *) \ {{}}),((X) *)))
(((X) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((X) *) *))
K10((((X) *) *)) is non empty non trivial non finite set
(((X) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((X) *) *))
K11(((((X) *) *) \ {{}}),((X) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((X) *) *) \ {{}}),((X) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((X) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
(X) . 0 is non empty with_non-empty_elements (X) -prefix (X) set
E1 is set
(X) . 0 is non empty functional V36() FinSequence-membered with_non-empty_elements (X) -prefix (X) Element of bool (((X) *) \ {{}})
(X) is non empty non trivial non finite set
N1 is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support (X) ( 0 ,X) Element of ((X) *) \ {{}}
(X) . N1 is (X) (X) (X) (X) (X) (X) Element of (X)
(X,N1) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined (rng N1) * -valued (X) -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element abs (X,N1) -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of (X) *
rng N1 is non empty trivial finite 1 -element countable set
(rng N1) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of rng N1
(X) is non empty functional V36() FinSequence-membered (X) -prefix (X) Element of K10(((X) *))
(X) is Relation-like Function-like set
rng (X) is set
union (rng (X)) is set
(X,N1) is complex ext-real real integer Element of INT
(X,((X) . N1)) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of INT
the of X . ((X) . N1) is set
abs (X,N1) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((X) *) *))
E2 is (X) (X) (X) (X) Element of (X)
<*E2*> is non empty trivial Relation-like NAT -defined (X) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (X)
1 -tuples_on (X) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (X)
(X) . (X,N1) is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
<*E2*> ^ ((X) . (X,N1)) is non empty Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
<*E2*> ^ {} is non empty Relation-like NAT -defined Function-like finite 1 + {} -element FinSequence-like FinSubsequence-like countable finite-support set
1 + {} is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
<*E2*> null {} is Relation-like NAT -defined {} \/ (dom <*E2*>) -defined Seg (1 + {}) -defined {} \/ (rng <*E2*>) -valued Function-like total finite len <*E2*> -element FinSequence-like FinSubsequence-like countable finite-support set
dom <*E2*> is non empty trivial finite 1 -element countable set
{} \/ (dom <*E2*>) is non empty finite countable set
Seg (1 + {}) is non empty finite 1 + {} -element countable Element of K10(NAT)
rng <*E2*> is non empty trivial finite 1 -element countable set
{} \/ (rng <*E2*>) is non empty finite countable set
len <*E2*> is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable Element of NAT
<*E2*> \typed/ {} is Relation-like NAT -defined finite countable Element of K10((<*E2*> \/ {}))
<*E2*> \/ {} is non empty Relation-like NAT -defined finite countable set
K10((<*E2*> \/ {})) is non empty finite V36() countable set
{} ^ <*E2*> is non empty Relation-like NAT -defined Function-like finite {} + 1 -element {} + 1 -element FinSequence-like FinSubsequence-like countable finite-support set
{} + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
{} + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable Element of NAT
Y is Element of (X)
<*Y*> is non empty trivial Relation-like NAT -defined (X) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (X)
1 -tuples_on (X) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (X)
E1 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
(X) . E1 is non empty (X) -prefix (X) set
E1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
(X) . (E1 + 1) is non empty (X) -prefix (X) set
K10(((X) *)) is non empty non trivial non finite set
N1 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(X) . N1 is non empty functional V36() FinSequence-membered with_non-empty_elements (X) -prefix (X) Element of bool (((X) *) \ {{}})
Y is set
E2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(X) . E2 is non empty functional V36() FinSequence-membered with_non-empty_elements (X) -prefix (X) Element of bool (((X) *) \ {{}})
NN1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (X) (E1 + 1,X) Element of ((X) *) \ {{}}
(X) . NN1 is (X) (X) (X) (X) Element of (X)
(X,((X) . NN1)) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of INT
the of X . ((X) . NN1) is set
abs (X,((X) . NN1)) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
N1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
z2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (X) (N1 + 1,X) Element of ((X) *) \ {{}}
(X,z2) is Relation-like NAT -defined (X) . N1 -valued (rng z2) * -valued (X) -valued Function-like finite abs (X,z2) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (X) *
bool ((X) *) is non empty non trivial non finite Element of K10(K10(((X) *)))
K10(K10(((X) *))) is non empty non trivial non finite set
(X) is non empty Relation-like NAT -defined bool ((X) *) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool ((X) *))))
K11(NAT,(bool ((X) *))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool ((X) *)))) is non empty non trivial non finite set
(X) . N1 is non empty functional V36() FinSequence-membered with_non-empty_elements (X) -prefix (X) Element of bool ((X) *)
rng z2 is non empty finite countable set
(rng z2) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of rng z2
(X) is non empty functional V36() FinSequence-membered (X) -prefix (X) Element of K10(((X) *))
(X) is Relation-like Function-like set
rng (X) is set
union (rng (X)) is set
(X,z2) is complex ext-real real integer Element of INT
(X) . z2 is (X) (X) (X) (X) Element of (X)
(X,((X) . z2)) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of INT
the of X . ((X) . z2) is set
abs (X,z2) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((X) *) *))
a2 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
a2 + 0 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
N2 is non empty functional V36() FinSequence-membered Element of K10(((X) *))
(X,NN1) is Relation-like NAT -defined (rng NN1) * -valued (X) -valued Function-like finite abs (X,NN1) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (X) *
rng NN1 is non empty finite countable set
(rng NN1) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of rng NN1
(X,NN1) is complex ext-real real integer Element of INT
abs (X,NN1) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
ITT1 is non empty Relation-like NAT -defined N2 -valued Function-like finite a2 + 0 -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support FinSequence of N2
N2 * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((X) *) *))
o2 is Element of (X)
<*o2*> is non empty trivial Relation-like NAT -defined (X) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (X)
1 -tuples_on (X) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (X)
ITT2 is non empty Relation-like NAT -defined (X) * -valued Function-like finite a2 + 0 -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of ((X) *) *
((X) -multiCat) . ITT2 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
<*o2*> ^ (((X) -multiCat) . ITT2) is non empty Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
<*((X) . NN1)*> is non empty trivial Relation-like NAT -defined (X) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (X)
1 -tuples_on (X) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (X)
(X) . (X,NN1) is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (X) *
<*((X) . NN1)*> ^ ((X) . (X,NN1)) is non empty Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
ITT1 is Relation-like NAT -defined (X) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of (X)
(X) . 0 is non empty functional V36() FinSequence-membered with_non-empty_elements (X) -prefix (X) Element of bool (((X) *) \ {{}})
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
X is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
S1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) Element of ((S) *) \ {{}}
S1 null X is Relation-like NAT -defined X \/ (dom S1) -defined X \/ (rng S1) -valued Function-like finite len S1 -element FinSequence-like FinSubsequence-like countable finite-support set
dom S1 is non empty finite countable set
X \/ (dom S1) is non empty finite countable set
rng S1 is non empty finite countable set
X \/ (rng S1) is non empty finite countable set
len S1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable Element of NAT
S1 \typed/ X is finite countable Element of K10((S1 \/ X))
S1 \/ X is non empty finite countable set
K10((S1 \/ X)) is non empty finite V36() countable set
(S,S1) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
(S,S1) + X is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
0 * X is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
(S,S1) + (0 * X) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
SX is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of ((S) *) \ {{}}
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " NAT is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
(S) is non empty Relation-like NAT -defined bool (((S) *) \ {{}}) -valued Function-like total quasi_total Element of K10(K11(NAT,(bool (((S) *) \ {{}}))))
bool (((S) *) \ {{}}) is non empty non trivial non finite Element of K10(K10((((S) *) \ {{}})))
K10((((S) *) \ {{}})) is non empty non trivial non finite set
K10(K10((((S) *) \ {{}}))) is non empty non trivial non finite set
K11(NAT,(bool (((S) *) \ {{}}))) is non empty non trivial Relation-like non finite set
K10(K11(NAT,(bool (((S) *) \ {{}})))) is non empty non trivial non finite set
SS1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of ((S) *) \ {{}}
SX is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) Element of ((S) *) \ {{}}
(S,SX) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
(S,SX) + 0 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable set
SX null 0 is Relation-like NAT -defined 0 \/ (dom SX) -defined 0 \/ (rng SX) -valued Function-like finite len SX -element FinSequence-like FinSubsequence-like countable finite-support set
dom SX is non empty finite countable set
0 \/ (dom SX) is non empty finite countable set
rng SX is non empty finite countable set
0 \/ (rng SX) is non empty finite countable set
len SX is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable Element of NAT
SX \typed/ 0 is Relation-like NAT -defined finite countable Element of K10((SX \/ 0))
SX \/ 0 is non empty Relation-like NAT -defined finite countable set
K10((SX \/ 0)) is non empty finite V36() countable set
SX ^ 0 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
0 ^ SX is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) ((S,SX) + 0,S) Element of ((S) *) \ {{}}
(S) . (S,SX) is non empty (S) -prefix (S) set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty functional V36() FinSequence-membered with_non-empty_elements (S) -prefix (S) Element of bool (((S) *) \ {{}})
K10((((S) *) \ {{}})) is non empty non trivial non finite set
bool (((S) *) \ {{}}) is non empty non trivial non finite Element of K10(K10((((S) *) \ {{}})))
K10(K10((((S) *) \ {{}}))) is non empty non trivial non finite set
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
(S) is non empty set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " NAT is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
(S) \ ((S) *) is functional V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) \ {{}}))
(S) typed\ ((S) *) is functional V36() FinSequence-membered with_non-empty_elements Element of K10((S))
K10((S)) is non empty set
(S) \ ((S) *) is functional V36() FinSequence-membered with_non-empty_elements Element of K10((S))
SS1 is set
SX is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) Element of ((S) *) \ {{}}
SS1 is set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " NAT is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) Element of ((S) *) \ {{}}
(S,X) is Relation-like NAT -defined (rng X) * -valued (S) -valued Function-like finite abs (S,((S) . X)) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
K11((((S) *) \ {{}}),(S)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) \ {{}}),(S))) is non empty non trivial non finite set
(S) -firstChar is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) -pr1 is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total associative Element of K10(K11(K11((S),(S)),(S)))
K11((S),(S)) is non empty non trivial Relation-like non finite set
K11(K11((S),(S)),(S)) is non empty non trivial Relation-like non finite set
K10(K11(K11((S),(S)),(S))) is non empty non trivial non finite set
K530((S),(S)) is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total Element of K10(K11(K11((S),(S)),(S)))
MultPlace ((S) -pr1) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) . X is (S) (S) (S) Element of (S)
(S,((S) . X)) is non empty complex ext-real non positive negative real integer Element of INT
the of S . ((S) . X) is set
abs (S,((S) . X)) is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable Element of NAT
rng X is non empty finite countable set
(rng X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of rng X
(S) is non empty functional V36() FinSequence-membered (S) -prefix (S) Element of K10(((S) *))
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
(S) is non empty functional V36() FinSequence-membered with_non-empty_elements (S) -prefix (S) Element of bool (((S) *) \ {{}})
K10((((S) *) \ {{}})) is non empty non trivial non finite set
bool (((S) *) \ {{}}) is non empty non trivial non finite Element of K10(K10((((S) *) \ {{}})))
K10(K10((((S) *) \ {{}}))) is non empty non trivial non finite set
(S) \ ((S) *) is empty proper epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() with_non-empty_elements empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of K10((((S) *) \ {{}}))
(S) typed\ ((S) *) is functional V36() FinSequence-membered with_non-empty_elements Element of K10((S))
K10((S)) is non empty set
(S) \ ((S) *) is empty proper epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() with_non-empty_elements empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of K10((S))
K10(((S) *)) is non empty non trivial non finite set
add is non empty functional V36() FinSequence-membered Element of K10(((S) *))
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty Element of K10((S))
K10((S)) is non empty non trivial non finite set
(S) is non empty non trivial non finite set
(S) is set
the OneF of S is Element of the carrier of S
{(S)} is non empty trivial finite 1 -element countable set
(S) \ {(S)} is non empty non trivial non finite Element of K10((S))
K10((S)) is non empty non trivial non finite set
(S) typed\ {(S)} is Element of K10((S))
(S) is non empty set
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " NAT is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
(S) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
K11((((S) *) \ {{}}),(S)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) \ {{}}),(S))) is non empty non trivial non finite set
(S) -firstChar is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) -pr1 is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total associative Element of K10(K11(K11((S),(S)),(S)))
K11((S),(S)) is non empty non trivial Relation-like non finite set
K11(K11((S),(S)),(S)) is non empty non trivial Relation-like non finite set
K10(K11(K11((S),(S)),(S))) is non empty non trivial non finite set
K530((S),(S)) is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total Element of K10(K11(K11((S),(S)),(S)))
MultPlace ((S) -pr1) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
K11((((S) *) *),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) *),((S) *))) is non empty non trivial non finite set
(S) -multiCat is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
(S) -concatenation is non empty Relation-like K11(((S) *),((S) *)) -defined (S) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((S) *),((S) *)),((S) *)))
K11(((S) *),((S) *)) is non empty non trivial Relation-like non finite set
K11(K11(((S) *),((S) *)),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((S) *),((S) *)),((S) *))) is non empty non trivial non finite set
MultPlace ((S) -concatenation) is non empty Relation-like (((S) *) *) \ {{}} -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((S) *) *) \ {{}}),((S) *)))
(((S) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
(((S) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((S) *) *))
K11(((((S) *) *) \ {{}}),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((S) *) *) \ {{}}),((S) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((S) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
(S) is non empty functional V36() FinSequence-membered with_non-empty_elements (S) -prefix (S) Element of bool (((S) *) \ {{}})
K10((((S) *) \ {{}})) is non empty non trivial non finite set
bool (((S) *) \ {{}}) is non empty non trivial non finite Element of K10(K10((((S) *) \ {{}})))
K10(K10((((S) *) \ {{}}))) is non empty non trivial non finite set
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
(S) -multiCat is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
K11((((S) *) *),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) *),((S) *))) is non empty non trivial non finite set
(S) -concatenation is non empty Relation-like K11(((S) *),((S) *)) -defined (S) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((S) *),((S) *)),((S) *)))
K11(((S) *),((S) *)) is non empty non trivial Relation-like non finite set
K11(K11(((S) *),((S) *)),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((S) *),((S) *)),((S) *))) is non empty non trivial non finite set
MultPlace ((S) -concatenation) is non empty Relation-like (((S) *) *) \ {{}} -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((S) *) *) \ {{}}),((S) *)))
(((S) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
(((S) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((S) *) *))
K11(((((S) *) *) \ {{}}),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((S) *) *) \ {{}}),((S) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((S) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
SS2 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of ((S) *) \ {{}}
E1 is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) Element of ((S) *) \ {{}}
(S) . E1 is (S) (S) (S) Element of (S)
N1 is (S) (S) (S) Element of (S)
(S,N1) is non empty complex ext-real non positive negative real integer Element of INT
the of S . N1 is set
abs (S,N1) is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable Element of NAT
(abs (S,N1)) + 0 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable set
(((S) *) \ {{}}) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of ((S) *) \ {{}}
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10(((((S) *) \ {{}}) *))
K10(((((S) *) \ {{}}) *)) is non empty non trivial non finite set
(S,E1) is Relation-like NAT -defined (rng E1) * -valued (S) * -valued (S) -valued Function-like finite abs (S,((S) . E1)) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S,((S) . E1)) is non empty complex ext-real non positive negative real integer Element of INT
the of S . ((S) . E1) is set
abs (S,((S) . E1)) is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable Element of NAT
rng E1 is non empty finite countable set
(rng E1) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of rng E1
(S) is non empty functional V36() FinSequence-membered (S) -prefix (S) Element of K10(((S) *))
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((S) *) *))
(S) \ ((S) *) is empty proper epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() with_non-empty_elements empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of K10((((S) *) \ {{}}))
(S) typed\ ((S) *) is functional V36() FinSequence-membered with_non-empty_elements Element of K10((S))
K10((S)) is non empty set
(S) \ ((S) *) is empty proper epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() with_non-empty_elements empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of K10((S))
Y is non empty Relation-like non empty-yielding NAT -defined (S) -valued Function-like finite (abs (S,N1)) + 0 -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
N2 is Element of (S)
<*N2*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
((S) -multiCat) . Y is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
<*N2*> ^ (((S) -multiCat) . Y) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
<*N1*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
(S) . Y is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
<*N1*> ^ ((S) . Y) is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
S is non empty non degenerated non trivial non finite () ()
(S) is Element of K10((S))
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
K10((S)) is non empty non trivial non finite set
the ZeroF of S is Element of the carrier of S
the OneF of S is Element of the carrier of S
{ the ZeroF of S, the OneF of S} is non empty finite countable set
the carrier of S \ { the ZeroF of S, the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the ZeroF of S, the OneF of S} is Element of K10( the carrier of S)
X is set
S is non empty non degenerated non trivial non finite () ()
(S) is non empty Element of K10((S))
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
K10((S)) is non empty non trivial non finite set
(S) is non empty non trivial non finite set
(S) is set
the OneF of S is Element of the carrier of S
{(S)} is non empty trivial finite 1 -element countable set
(S) \ {(S)} is non empty non trivial non finite Element of K10((S))
K10((S)) is non empty non trivial non finite set
(S) typed\ {(S)} is Element of K10((S))
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
(S) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
K11((((S) *) \ {{}}),(S)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) \ {{}}),(S))) is non empty non trivial non finite set
(S) -firstChar is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) -pr1 is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total associative Element of K10(K11(K11((S),(S)),(S)))
K11((S),(S)) is non empty non trivial Relation-like non finite set
K11(K11((S),(S)),(S)) is non empty non trivial Relation-like non finite set
K10(K11(K11((S),(S)),(S))) is non empty non trivial non finite set
K530((S),(S)) is non empty Relation-like K11((S),(S)) -defined (S) -valued Function-like total quasi_total Element of K10(K11(K11((S),(S)),(S)))
MultPlace ((S) -pr1) is non empty Relation-like ((S) *) \ {{}} -defined (S) -valued Function-like total quasi_total Element of K10(K11((((S) *) \ {{}}),(S)))
(S) is Element of (S)
the ZeroF of S is Element of the carrier of S
(S) is non empty Element of K10((S))
{ the ZeroF of S, the OneF of S} is non empty finite countable set
the carrier of S \ { the ZeroF of S, the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the ZeroF of S, the OneF of S} is Element of K10( the carrier of S)
X is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support (S) Element of ((S) *) \ {{}}
(S) . X is (S) (S) (S) Element of (S)
(S) is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
((S) *) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S) *
K11((((S) *) *),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11((((S) *) *),((S) *))) is non empty non trivial non finite set
(S) -multiCat is non empty Relation-like ((S) *) * -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11((((S) *) *),((S) *)))
(S) -concatenation is non empty Relation-like K11(((S) *),((S) *)) -defined (S) * -valued Function-like total quasi_total associative Function-yielding V160() FinSequence-yielding Element of K10(K11(K11(((S) *),((S) *)),((S) *)))
K11(((S) *),((S) *)) is non empty non trivial Relation-like non finite set
K11(K11(((S) *),((S) *)),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(K11(((S) *),((S) *)),((S) *))) is non empty non trivial non finite set
MultPlace ((S) -concatenation) is non empty Relation-like (((S) *) *) \ {{}} -defined (S) * -valued Function-like total quasi_total Function-yielding V160() FinSequence-yielding Element of K10(K11(((((S) *) *) \ {{}}),((S) *)))
(((S) *) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10((((S) *) *))
K10((((S) *) *)) is non empty non trivial non finite set
(((S) *) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10((((S) *) *))
K11(((((S) *) *) \ {{}}),((S) *)) is non empty non trivial Relation-like non finite set
K10(K11(((((S) *) *) \ {{}}),((S) *))) is non empty non trivial non finite set
({} .--> {}) +* (MultPlace ((S) -concatenation)) is non empty Relation-like Function-like Function-yielding V160() set
(S,X) is Relation-like NAT -defined (rng X) * -valued (S) * -valued (S) -valued Function-like finite abs (S,((S) . X)) -element FinSequence-like FinSubsequence-like Function-yielding V160() countable FinSequence-yielding finite-support Element of (S) *
(S,((S) . X)) is non empty complex ext-real non positive negative real integer Element of INT
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S . ((S) . X) is set
abs (S,((S) . X)) is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative finite cardinal real integer countable Element of NAT
rng X is non empty finite countable set
(rng X) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of rng X
(S) is non empty set
the of S " NAT is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
(S) is non empty functional V36() FinSequence-membered (S) -prefix (S) Element of K10(((S) *))
(S) is Relation-like Function-like set
rng (S) is set
union (rng (S)) is set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered Element of K10((((S) *) *))
(S) is set
the of S " (INT \ NAT) is Element of K10(( the carrier of S \ { the OneF of S}))
K10((S)) is non empty set
{(S)} is non empty trivial finite 1 -element countable Element of K10((S))
K10((S)) is non empty set
(S) \ (S) is Element of K10((S))
K10((S)) is non empty set
(S) typed\ (S) is Element of K10((S))
E1 is non empty Element of K10((S))
(S) . (S,X) is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (S) *
N1 is Element of (S)
<*N1*> is non empty trivial Relation-like NAT -defined (S) -valued Function-like constant finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on (S)
1 -tuples_on (S) is non empty functional V36() FinSequence-membered with_non-empty_elements FinSequenceSet of (S)
E2 is Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
<*N1*> ^ E2 is non empty Relation-like NAT -defined (S) -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
K11((NAT \ {0}),INT) is non empty non trivial Relation-like non finite set
K10(K11((NAT \ {0}),INT)) is non empty non trivial non finite set
the non empty Relation-like NAT \ {0} -defined INT -valued Function-like total quasi_total Element of K10(K11((NAT \ {0}),INT)) is non empty Relation-like NAT \ {0} -defined INT -valued Function-like total quasi_total Element of K10(K11((NAT \ {0}),INT))
(NAT,0,0, the non empty Relation-like NAT \ {0} -defined INT -valued Function-like total quasi_total Element of K10(K11((NAT \ {0}),INT))) is () ()
X is () ()
S is non empty non degenerated non trivial non finite () ()
S null is set
(S) is Element of (S)
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) is non empty Element of K10((S))
K10((S)) is non empty non trivial non finite set
(S) is non empty non trivial non finite set
(S) is set
the OneF of S is Element of the carrier of S
{(S)} is non empty trivial finite 1 -element countable set
(S) \ {(S)} is non empty non trivial non finite Element of K10((S))
K10((S)) is non empty non trivial non finite set
(S) typed\ {(S)} is Element of K10((S))
the ZeroF of S is Element of the carrier of S
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
SX is ()
S is non empty non degenerated non trivial non finite () ()
S null is set
X is non empty non degenerated non trivial non finite () ()
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
(S) is non empty Element of K10((S))
K10((S)) is non empty non trivial non finite set
the ZeroF of S is Element of the carrier of S
the OneF of S is Element of the carrier of S
{ the ZeroF of S, the OneF of S} is non empty finite countable set
the carrier of S \ { the ZeroF of S, the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the ZeroF of S, the OneF of S} is Element of K10( the carrier of S)
X is non empty non degenerated non trivial non finite () (S) ()
(X) is non empty Element of K10((X))
(X) is non empty non trivial non finite set
the carrier of X is non empty non trivial non finite set
K10((X)) is non empty non trivial non finite set
the ZeroF of X is Element of the carrier of X
the OneF of X is Element of the carrier of X
{ the ZeroF of X, the OneF of X} is non empty finite countable set
the carrier of X \ { the ZeroF of X, the OneF of X} is non empty non trivial non finite Element of K10( the carrier of X)
K10( the carrier of X) is non empty non trivial non finite set
the carrier of X typed\ { the ZeroF of X, the OneF of X} is Element of K10( the carrier of X)
(S) \ (X) is Element of K10((S))
(S) typed\ (X) is Element of K10((S))
K10((S)) is non empty set
(S) \ (X) is Element of K10((S))
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of X is non empty Relation-like the carrier of X \ { the OneF of X} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of X \ { the OneF of X}),INT))
{ the OneF of X} is non empty trivial finite 1 -element countable set
the carrier of X \ { the OneF of X} is non empty non trivial non finite Element of K10( the carrier of X)
the carrier of X typed\ { the OneF of X} is Element of K10( the carrier of X)
K11(( the carrier of X \ { the OneF of X}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of X \ { the OneF of X}),INT)) is non empty non trivial non finite set
(S) is non empty Element of K10((S))
(S) is non empty non trivial non finite set
(S) is set
{(S)} is non empty trivial finite 1 -element countable set
(S) \ {(S)} is non empty non trivial non finite Element of K10((S))
K10((S)) is non empty non trivial non finite set
(S) typed\ {(S)} is Element of K10((S))
(S) is Element of (S)
(X) is Element of (X)
(X) is non empty Element of K10((X))
(X) is non empty non trivial non finite set
(X) is set
{(X)} is non empty trivial finite 1 -element countable set
(X) \ {(X)} is non empty non trivial non finite Element of K10((X))
K10((X)) is non empty non trivial non finite set
(X) typed\ {(X)} is Element of K10((X))
dom the of S is non empty Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
{ the OneF of S} is non empty trivial finite 1 -element countable Element of K10( the carrier of S)
(S) \ { the OneF of S} is non empty non trivial non finite Element of K10((S))
(S) typed\ { the OneF of S} is Element of K10((S))
dom the of X is non empty Element of K10(( the carrier of X \ { the OneF of X}))
K10(( the carrier of X \ { the OneF of X})) is non empty non trivial non finite set
{ the OneF of X} is non empty trivial finite 1 -element countable Element of K10( the carrier of X)
(X) \ { the OneF of X} is non empty non trivial non finite Element of K10((X))
(X) typed\ { the OneF of X} is Element of K10((X))
(S) \ {(S)} is non empty non trivial non finite Element of K10((S))
(S) typed\ {(S)} is Element of K10((S))
{(S)} is non empty trivial finite 1 -element countable Element of K10((S))
K10((S)) is non empty set
((S) \ {(S)}) \ {(S)} is non empty non trivial non finite Element of K10((S))
((S) \ {(S)}) typed\ {(S)} is Element of K10(((S) \ {(S)}))
K10(((S) \ {(S)})) is non empty non trivial non finite set
((S) \ {(S)}) \ {(S)} is non empty non trivial non finite Element of K10(((S) \ {(S)}))
(X) \ {(X)} is non empty non trivial non finite Element of K10((X))
(X) typed\ {(X)} is Element of K10((X))
((X) \ {(X)}) \ {(S)} is non empty non trivial non finite Element of K10((X))
((X) \ {(X)}) typed\ {(S)} is Element of K10(((X) \ {(X)}))
K10(((X) \ {(X)})) is non empty non trivial non finite set
((X) \ {(X)}) \ {(S)} is non empty non trivial non finite Element of K10(((X) \ {(X)}))
{(S)} \/ {(S)} is non empty finite countable set
(S) \ ({(S)} \/ {(S)}) is non empty non trivial non finite Element of K10((S))
(S) typed\ ({(S)} \/ {(S)}) is Element of K10((S))
{(S),(S)} is non empty finite countable set
(S) \ {(S),(S)} is non empty non trivial non finite Element of K10((S))
(S) typed\ {(S),(S)} is Element of K10((S))
{(X)} \/ {(S)} is non empty finite countable set
(X) \ ({(X)} \/ {(S)}) is non empty non trivial non finite Element of K10((X))
(X) typed\ ({(X)} \/ {(S)}) is Element of K10((X))
{(X)} is non empty trivial finite 1 -element countable Element of K10((X))
K10((X)) is non empty set
{(X)} \/ {(X)} is non empty finite countable set
(X) \ ({(X)} \/ {(X)}) is non empty non trivial non finite Element of K10((X))
(X) typed\ ({(X)} \/ {(X)}) is Element of K10((X))
{(X),(X)} is non empty finite countable set
(X) \ {(X),(X)} is non empty non trivial non finite Element of K10((X))
(X) typed\ {(X),(X)} is Element of K10((X))
X is non empty ()
the carrier of X is non empty set
the ZeroF of X is Element of the carrier of X
the OneF of X is Element of the carrier of X
the of X is Relation-like the carrier of X \ { the OneF of X} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of X \ { the OneF of X}),INT))
{ the OneF of X} is non empty trivial finite 1 -element countable set
the carrier of X \ { the OneF of X} is Element of K10( the carrier of X)
K10( the carrier of X) is non empty set
the carrier of X typed\ { the OneF of X} is Element of K10( the carrier of X)
K11(( the carrier of X \ { the OneF of X}),INT) is Relation-like set
K10(K11(( the carrier of X \ { the OneF of X}),INT)) is non empty set
S is Relation-like INT -valued Function-like set
dom S is set
{ the OneF of X} is non empty trivial finite 1 -element countable Element of K10( the carrier of X)
(dom S) \ { the OneF of X} is Element of K10((dom S))
K10((dom S)) is non empty set
(dom S) typed\ { the OneF of X} is Element of K10((dom S))
S | ((dom S) \ { the OneF of X}) is Relation-like (dom S) \ { the OneF of X} -defined INT -valued Function-like set
(S | ((dom S) \ { the OneF of X})) +* the of X is Relation-like INT -valued Function-like set
the carrier of X \/ (dom S) is non empty set
the carrier of X null (dom S) is set
the carrier of X \typed/ (dom S) is Element of K10(( the carrier of X \/ (dom S)))
K10(( the carrier of X \/ (dom S))) is non empty set
dom the of X is Element of K10(( the carrier of X \ { the OneF of X}))
K10(( the carrier of X \ { the OneF of X})) is non empty set
the carrier of X \ { the OneF of X} is Element of K10( the carrier of X)
the carrier of X typed\ { the OneF of X} is Element of K10( the carrier of X)
dom (S | ((dom S) \ { the OneF of X})) is Element of K10(((dom S) \ { the OneF of X}))
K10(((dom S) \ { the OneF of X})) is non empty set
(dom S) /\ ((dom S) \ { the OneF of X}) is Element of K10((dom S))
(dom S) typed/\ ((dom S) \ { the OneF of X}) is Element of K10((dom S))
(dom S) /\ ((dom S) \ { the OneF of X}) is set
(dom S) /\typed ((dom S) \ { the OneF of X}) is Element of K10(((dom S) \ { the OneF of X}))
((dom S) \ { the OneF of X}) null (dom S) is set
((dom S) \ { the OneF of X}) \typed/ (dom S) is Element of K10((((dom S) \ { the OneF of X}) \/ (dom S)))
((dom S) \ { the OneF of X}) \/ (dom S) is set
K10((((dom S) \ { the OneF of X}) \/ (dom S))) is non empty set
{ the OneF of X} null (dom S) is set
{ the OneF of X} \typed/ (dom S) is Element of K10(({ the OneF of X} \/ (dom S)))
{ the OneF of X} \/ (dom S) is non empty set
K10(({ the OneF of X} \/ (dom S))) is non empty set
(dom S) \ ({ the OneF of X} null (dom S)) is Element of K10((dom S))
(dom S) typed\ ({ the OneF of X} null (dom S)) is Element of K10((dom S))
dom ((S | ((dom S) \ { the OneF of X})) +* the of X) is set
((dom S) \ { the OneF of X}) \/ ( the carrier of X \ { the OneF of X}) is set
(dom S) \/ the carrier of X is non empty set
((dom S) \/ the carrier of X) \ { the OneF of X} is Element of K10(((dom S) \/ the carrier of X))
K10(((dom S) \/ the carrier of X)) is non empty set
((dom S) \/ the carrier of X) typed\ { the OneF of X} is Element of K10(((dom S) \/ the carrier of X))
E2 is Element of the carrier of X \/ (dom S)
{E2} is non empty trivial finite 1 -element countable Element of K10(( the carrier of X \/ (dom S)))
( the carrier of X \/ (dom S)) \ {E2} is Element of K10(( the carrier of X \/ (dom S)))
( the carrier of X \/ (dom S)) typed\ {E2} is Element of K10(( the carrier of X \/ (dom S)))
rng ((S | ((dom S) \ { the OneF of X})) +* the of X) is Element of K10(INT)
Funcs ((( the carrier of X \/ (dom S)) \ {E2}),INT) is non empty functional FUNCTION_DOMAIN of ( the carrier of X \/ (dom S)) \ {E2}, INT
K11((( the carrier of X \/ (dom S)) \ {E2}),INT) is Relation-like set
K10(K11((( the carrier of X \/ (dom S)) \ {E2}),INT)) is non empty set
N1 is Element of the carrier of X \/ (dom S)
N2 is Relation-like ( the carrier of X \/ (dom S)) \ {E2} -defined INT -valued Function-like total quasi_total Element of K10(K11((( the carrier of X \/ (dom S)) \ {E2}),INT))
(( the carrier of X \/ (dom S)),N1,E2,N2) is () ()
NN1 is non empty () ()
the of NN1 is Relation-like the carrier of NN1 \ { the OneF of NN1} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of NN1 \ { the OneF of NN1}),INT))
the carrier of NN1 is non empty set
the OneF of NN1 is Element of the carrier of NN1
{ the OneF of NN1} is non empty trivial finite 1 -element countable set
the carrier of NN1 \ { the OneF of NN1} is Element of K10( the carrier of NN1)
K10( the carrier of NN1) is non empty set
the carrier of NN1 typed\ { the OneF of NN1} is Element of K10( the carrier of NN1)
K11(( the carrier of NN1 \ { the OneF of NN1}),INT) is Relation-like set
K10(K11(( the carrier of NN1 \ { the OneF of NN1}),INT)) is non empty set
the ZeroF of NN1 is Element of the carrier of NN1
N1 is non empty () ()
the of N1 is Relation-like the carrier of N1 \ { the OneF of N1} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of N1 \ { the OneF of N1}),INT))
the carrier of N1 is non empty set
the OneF of N1 is Element of the carrier of N1
{ the OneF of N1} is non empty trivial finite 1 -element countable set
the carrier of N1 \ { the OneF of N1} is Element of K10( the carrier of N1)
K10( the carrier of N1) is non empty set
the carrier of N1 typed\ { the OneF of N1} is Element of K10( the carrier of N1)
K11(( the carrier of N1 \ { the OneF of N1}),INT) is Relation-like set
K10(K11(( the carrier of N1 \ { the OneF of N1}),INT)) is non empty set
the ZeroF of N1 is Element of the carrier of N1
E2 is non empty () ()
the of E2 is Relation-like the carrier of E2 \ { the OneF of E2} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of E2 \ { the OneF of E2}),INT))
the carrier of E2 is non empty set
the OneF of E2 is Element of the carrier of E2
{ the OneF of E2} is non empty trivial finite 1 -element countable set
the carrier of E2 \ { the OneF of E2} is Element of K10( the carrier of E2)
K10( the carrier of E2) is non empty set
the carrier of E2 typed\ { the OneF of E2} is Element of K10( the carrier of E2)
K11(( the carrier of E2 \ { the OneF of E2}),INT) is Relation-like set
K10(K11(( the carrier of E2 \ { the OneF of E2}),INT)) is non empty set
the ZeroF of E2 is Element of the carrier of E2
( the carrier of N1, the ZeroF of N1, the OneF of N1, the of N1) is () ()
( the carrier of E2, the ZeroF of E2, the OneF of E2, the of E2) is () ()
dom the of N1 is Element of K10(( the carrier of N1 \ { the OneF of N1}))
K10(( the carrier of N1 \ { the OneF of N1})) is non empty set
{ the OneF of N1} is non empty trivial finite 1 -element countable Element of K10( the carrier of N1)
the carrier of E2 \ { the OneF of N1} is Element of K10( the carrier of E2)
the carrier of E2 typed\ { the OneF of N1} is Element of K10( the carrier of E2)
the carrier of N1 \ { the OneF of N1} is Element of K10( the carrier of N1)
the carrier of N1 typed\ { the OneF of N1} is Element of K10( the carrier of N1)
{ the OneF of N1} null the carrier of N1 is set
the carrier of N1 /\ { the OneF of N1} is finite countable Element of K10( the carrier of N1)
the carrier of N1 typed/\ { the OneF of N1} is Element of K10( the carrier of N1)
the carrier of N1 /\ { the OneF of N1} is finite countable set
the carrier of N1 /\typed { the OneF of N1} is trivial finite countable Element of K10({ the OneF of N1})
K10({ the OneF of N1}) is non empty finite V36() countable set
{ the OneF of N1} \typed/ the carrier of N1 is Element of K10(({ the OneF of N1} \/ the carrier of N1))
{ the OneF of N1} \/ the carrier of N1 is non empty set
K10(({ the OneF of N1} \/ the carrier of N1)) is non empty set
( the carrier of N1 \ { the OneF of N1}) \/ ({ the OneF of N1} null the carrier of N1) is set
{ the OneF of E2} is non empty trivial finite 1 -element countable Element of K10( the carrier of E2)
the carrier of E2 \ { the OneF of E2} is Element of K10( the carrier of E2)
the carrier of E2 typed\ { the OneF of E2} is Element of K10( the carrier of E2)
{ the OneF of E2} null the carrier of E2 is set
the carrier of E2 /\ { the OneF of E2} is finite countable Element of K10( the carrier of E2)
the carrier of E2 typed/\ { the OneF of E2} is Element of K10( the carrier of E2)
the carrier of E2 /\ { the OneF of E2} is finite countable set
the carrier of E2 /\typed { the OneF of E2} is trivial finite countable Element of K10({ the OneF of E2})
K10({ the OneF of E2}) is non empty finite V36() countable set
{ the OneF of E2} \typed/ the carrier of E2 is Element of K10(({ the OneF of E2} \/ the carrier of E2))
{ the OneF of E2} \/ the carrier of E2 is non empty set
K10(({ the OneF of E2} \/ the carrier of E2)) is non empty set
( the carrier of E2 \ { the OneF of E2}) \/ ({ the OneF of E2} null the carrier of E2) is set
S is non empty ()
X is Relation-like INT -valued Function-like set
(X,S) is non empty () ()
the of S is Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the carrier of S is non empty set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is Element of K10( the carrier of S)
K10( the carrier of S) is non empty set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is Relation-like set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty set
the of (X,S) is Relation-like the carrier of (X,S) \ { the OneF of (X,S)} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of (X,S) \ { the OneF of (X,S)}),INT))
the carrier of (X,S) is non empty set
the OneF of (X,S) is Element of the carrier of (X,S)
{ the OneF of (X,S)} is non empty trivial finite 1 -element countable set
the carrier of (X,S) \ { the OneF of (X,S)} is Element of K10( the carrier of (X,S))
K10( the carrier of (X,S)) is non empty set
the carrier of (X,S) typed\ { the OneF of (X,S)} is Element of K10( the carrier of (X,S))
K11(( the carrier of (X,S) \ { the OneF of (X,S)}),INT) is Relation-like set
K10(K11(( the carrier of (X,S) \ { the OneF of (X,S)}),INT)) is non empty set
(S) is set
the ZeroF of S is Element of the carrier of S
((X,S)) is set
the ZeroF of (X,S) is Element of the carrier of (X,S)
(S) is set
((X,S)) is set
dom X is set
{ the OneF of S} is non empty trivial finite 1 -element countable Element of K10( the carrier of S)
(dom X) \ { the OneF of S} is Element of K10((dom X))
K10((dom X)) is non empty set
(dom X) typed\ { the OneF of S} is Element of K10((dom X))
X | ((dom X) \ { the OneF of S}) is Relation-like (dom X) \ { the OneF of S} -defined INT -valued Function-like set
(X | ((dom X) \ { the OneF of S})) +* the of S is Relation-like INT -valued Function-like set
S is non empty non degenerated non trivial ()
S1 is ()
(S) is Element of (S)
(S) is non empty set
the carrier of S is non empty non trivial set
(S) is non empty Element of K10((S))
K10((S)) is non empty set
(S) is set
(S) is set
the OneF of S is Element of the carrier of S
{(S)} is non empty trivial finite 1 -element countable set
(S) \ {(S)} is Element of K10((S))
K10((S)) is non empty set
(S) typed\ {(S)} is Element of K10((S))
the ZeroF of S is Element of the carrier of S
(S1) is set
the ZeroF of S1 is Element of the carrier of S1
the carrier of S1 is set
(S1) is set
the OneF of S1 is Element of the carrier of S1
0. S is zero Element of the carrier of S
0. S1 is zero Element of the carrier of S1
1. S is non zero Element of the carrier of S
1. S1 is Element of the carrier of S1
S is () ()
S1 is ()
(S) is non empty non trivial non finite set
the carrier of S is set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is Element of K10( the carrier of S)
K10( the carrier of S) is non empty set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is Relation-like set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty set
(S1) is set
the carrier of S1 is set
the OneF of S1 is Element of the carrier of S1
{ the OneF of S1} is non empty trivial finite 1 -element countable set
the carrier of S1 \ { the OneF of S1} is Element of K10( the carrier of S1)
K10( the carrier of S1) is non empty set
the carrier of S1 typed\ { the OneF of S1} is Element of K10( the carrier of S1)
the of S1 is Relation-like the carrier of S1 \ { the OneF of S1} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S1 \ { the OneF of S1}),INT))
K11(( the carrier of S1 \ { the OneF of S1}),INT) is Relation-like set
K10(K11(( the carrier of S1 \ { the OneF of S1}),INT)) is non empty set
the of S1 " {0} is Element of K10(( the carrier of S1 \ { the OneF of S1}))
K10(( the carrier of S1 \ { the OneF of S1})) is non empty set
(S) is set
(S) is set
(S) is set
{(S)} is non empty trivial finite 1 -element countable set
(S) \ {(S)} is Element of K10((S))
K10((S)) is non empty set
(S) typed\ {(S)} is Element of K10((S))
(S1) is set
(S1) is set
(S1) is set
{(S1)} is non empty trivial finite 1 -element countable set
(S1) \ {(S1)} is Element of K10((S1))
K10((S1)) is non empty set
(S1) typed\ {(S1)} is Element of K10((S1))
(S) is set
the ZeroF of S is Element of the carrier of S
(S1) is set
the ZeroF of S1 is Element of the carrier of S1
dom the of S is Element of K10(( the carrier of S \ { the OneF of S}))
dom the of S1 is Element of K10(( the carrier of S1 \ { the OneF of S1}))
K10( the of S1) is non empty set
E2 is Relation-like the carrier of S1 \ { the OneF of S1} -defined INT -valued Function-like Element of K10( the of S1)
E2 " {0} is set
K10((S1)) is non empty set
N2 is Element of K10((S1))
(S1) null N2 is set
(S1) \typed/ N2 is Element of K10(((S1) \/ N2))
(S1) \/ N2 is set
K10(((S1) \/ N2)) is non empty set
the of S1 . (S1) is set
the of S . (S) is set
the of S1 +* E2 is Relation-like the carrier of S1 \ { the OneF of S1} -defined INT -valued Function-like total set
( the of S1 +* E2) . (S) is set
X is set
S is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
X |` S is Relation-like empty-yielding NAT -defined X -valued {{}} -valued Function-like finite FinSubsequence-like countable finite-support set
S is non empty ()
(S) is non empty set
the carrier of S is non empty set
(S) is set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is Element of K10( the carrier of S)
K10( the carrier of S) is non empty set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is Relation-like set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty set
(S) is set
the ZeroF of S is Element of the carrier of S
{ the ZeroF of S, the OneF of S} is non empty finite countable set
the carrier of S \ { the ZeroF of S, the OneF of S} is Element of K10( the carrier of S)
the carrier of S typed\ { the ZeroF of S, the OneF of S} is Element of K10( the carrier of S)
the of S | (S) is Relation-like the carrier of S \ { the OneF of S} -defined (S) -defined the carrier of S \ { the OneF of S} -defined INT -valued Function-like Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
X is Relation-like INT -valued Function-like set
(X,S) is non empty () (S) ()
((X,S)) is set
the carrier of (X,S) is non empty set
the OneF of (X,S) is Element of the carrier of (X,S)
{ the OneF of (X,S)} is non empty trivial finite 1 -element countable set
the carrier of (X,S) \ { the OneF of (X,S)} is Element of K10( the carrier of (X,S))
K10( the carrier of (X,S)) is non empty set
the carrier of (X,S) typed\ { the OneF of (X,S)} is Element of K10( the carrier of (X,S))
the of (X,S) is Relation-like the carrier of (X,S) \ { the OneF of (X,S)} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of (X,S) \ { the OneF of (X,S)}),INT))
K11(( the carrier of (X,S) \ { the OneF of (X,S)}),INT) is Relation-like set
K10(K11(( the carrier of (X,S) \ { the OneF of (X,S)}),INT)) is non empty set
the of (X,S) " {0} is Element of K10(( the carrier of (X,S) \ { the OneF of (X,S)}))
K10(( the carrier of (X,S) \ { the OneF of (X,S)})) is non empty set
dom X is set
(dom X) \ (S) is Element of K10((dom X))
K10((dom X)) is non empty set
(dom X) typed\ (S) is Element of K10((dom X))
X | ((dom X) \ (S)) is Relation-like (dom X) \ (S) -defined INT -valued Function-like set
(X | ((dom X) \ (S))) " {0} is set
((X | ((dom X) \ (S))) " {0}) \/ (S) is set
the of (X,S) | (S) is Relation-like (S) -defined the carrier of (X,S) \ { the OneF of (X,S)} -defined INT -valued Function-like Element of K10(K11(( the carrier of (X,S) \ { the OneF of (X,S)}),INT))
{ the OneF of S} is non empty trivial finite 1 -element countable Element of K10( the carrier of S)
(dom X) \ { the OneF of S} is Element of K10((dom X))
(dom X) typed\ { the OneF of S} is Element of K10((dom X))
dom the of S is Element of K10(( the carrier of S \ { the OneF of S}))
((dom X) \ { the OneF of S}) \ (dom the of S) is Element of K10((dom X))
((dom X) \ { the OneF of S}) typed\ (dom the of S) is Element of K10(((dom X) \ { the OneF of S}))
K10(((dom X) \ { the OneF of S})) is non empty set
((dom X) \ { the OneF of S}) \ (dom the of S) is Element of K10(((dom X) \ { the OneF of S}))
X | (((dom X) \ { the OneF of S}) \ (dom the of S)) is Relation-like ((dom X) \ { the OneF of S}) \ (dom the of S) -defined INT -valued Function-like set
the carrier of S \ { the OneF of S} is Element of K10( the carrier of S)
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
{ the OneF of S} null the carrier of S is set
the carrier of S /\ { the OneF of S} is finite countable Element of K10( the carrier of S)
the carrier of S typed/\ { the OneF of S} is Element of K10( the carrier of S)
the carrier of S /\ { the OneF of S} is finite countable set
the carrier of S /\typed { the OneF of S} is trivial finite countable Element of K10({ the OneF of S})
K10({ the OneF of S}) is non empty finite V36() countable set
{ the OneF of S} \typed/ the carrier of S is Element of K10(({ the OneF of S} \/ the carrier of S))
{ the OneF of S} \/ the carrier of S is non empty set
K10(({ the OneF of S} \/ the carrier of S)) is non empty set
( the carrier of S \ { the OneF of S}) \/ ({ the OneF of S} null the carrier of S) is set
(dom the of S) \/ { the OneF of S} is non empty set
(dom X) \ the carrier of S is Element of K10((dom X))
(dom X) typed\ the carrier of S is Element of K10((dom X))
X | ((dom X) \ the carrier of S) is Relation-like (dom X) \ the carrier of S -defined INT -valued Function-like set
(X | ((dom X) \ the carrier of S)) \/ the of S is Relation-like INT -valued set
X | ((dom X) \ { the OneF of S}) is Relation-like (dom X) \ { the OneF of S} -defined INT -valued Function-like set
(X | ((dom X) \ { the OneF of S})) +* the of S is Relation-like INT -valued Function-like set
(S) /\ (dom X) is set
(S) typed/\ (dom X) is Element of K10((S))
K10((S)) is non empty set
(S) /\typed (dom X) is Element of K10((dom X))
(X | ((dom X) \ the carrier of S)) | (S) is Relation-like (S) -defined (dom X) \ the carrier of S -defined INT -valued Function-like set
( the of S | (S)) \/ ((X | ((dom X) \ the carrier of S)) | (S)) is Relation-like (S) -defined INT -valued set
(S) /\ ((dom X) \ the carrier of S) is Element of K10((dom X))
(S) typed/\ ((dom X) \ the carrier of S) is Element of K10((S))
(S) /\ ((dom X) \ the carrier of S) is set
(S) /\typed ((dom X) \ the carrier of S) is Element of K10(((dom X) \ the carrier of S))
K10(((dom X) \ the carrier of S)) is non empty set
X | ((S) /\ ((dom X) \ the carrier of S)) is Relation-like (S) /\ ((dom X) \ the carrier of S) -defined INT -valued Function-like set
( the of S | (S)) \/ (X | ((S) /\ ((dom X) \ the carrier of S))) is Relation-like INT -valued set
((S) /\ (dom X)) \ the carrier of S is Element of K10(((S) /\ (dom X)))
K10(((S) /\ (dom X))) is non empty set
((S) /\ (dom X)) typed\ the carrier of S is Element of K10(((S) /\ (dom X)))
X | (((S) /\ (dom X)) \ the carrier of S) is Relation-like ((S) /\ (dom X)) \ the carrier of S -defined INT -valued Function-like set
( the of S | (S)) \/ (X | (((S) /\ (dom X)) \ the carrier of S)) is Relation-like INT -valued set
NN1 is Element of K10( the carrier of S)
NN1 \ the carrier of S is empty proper epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of K10( the carrier of S)
NN1 typed\ the carrier of S is Element of K10(NN1)
K10(NN1) is non empty set
NN1 \ the carrier of S is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of K10(NN1)
X | (NN1 \ the carrier of S) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NN1 \ the carrier of S -defined NAT -defined INT -valued {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
( the of S | (S)) \/ (X | (NN1 \ the carrier of S)) is Relation-like INT -valued set
S is set
X is complex ext-real real integer set
S --> X is Relation-like S -defined {X} -valued Function-like constant total quasi_total Element of K10(K11(S,{X}))
{X} is non empty trivial finite 1 -element countable set
K11(S,{X}) is Relation-like set
K10(K11(S,{X})) is non empty set
S1 is complex ext-real real integer Element of INT
{S1} is non empty trivial finite 1 -element countable Element of K10(INT)
S is non empty non degenerated non trivial non finite () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
X is functional set
SymbolsOf X is set
X \/ {{}} is non empty functional set
{ (rng b₁) where b₁ is Relation-like Function-like Element of X \/ {{}} : b₁ in X } is set
union { (rng b₁) where b₁ is Relation-like Function-like Element of X \/ {{}} : b₁ in X } is set
{ (rng b₁) where b₁ is Relation-like Function-like Element of X : b₁ in X } is set
union { (rng b₁) where b₁ is Relation-like Function-like Element of X : b₁ in X } is set
(S) \/ (SymbolsOf X) is non empty non trivial non finite set
((S) \/ (SymbolsOf X)) -freeCountableSet is non empty non trivial non finite countable denumerable set
rng ((S) \/ (SymbolsOf X)) is set
K10((rng ((S) \/ (SymbolsOf X)))) is non empty set
bool (rng ((S) \/ (SymbolsOf X))) is non empty Element of K10(K10((rng ((S) \/ (SymbolsOf X)))))
K10(K10((rng ((S) \/ (SymbolsOf X))))) is non empty set
(bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X))) is non empty Element of K10(K10((rng ((S) \/ (SymbolsOf X)))))
(bool (rng ((S) \/ (SymbolsOf X)))) typed\ (rng ((S) \/ (SymbolsOf X))) is Element of K10((bool (rng ((S) \/ (SymbolsOf X)))))
K10((bool (rng ((S) \/ (SymbolsOf X))))) is non empty set
(bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X))) is non empty Element of K10((bool (rng ((S) \/ (SymbolsOf X)))))
the Element of (bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X))) is Element of (bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X)))
{ the Element of (bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X)))} is non empty trivial finite 1 -element countable Element of K10(((bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X)))))
K10(((bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X))))) is non empty set
K88(REAL,((bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X)))),NAT,{ the Element of (bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X)))}) is non empty non trivial Relation-like REAL -defined (bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X))) -valued non finite Element of K10(K11(REAL,((bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X))))))
K11(REAL,((bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X))))) is non empty non trivial Relation-like non finite set
K10(K11(REAL,((bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X)))))) is non empty non trivial non finite set
(((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0 is non empty non trivial Relation-like ((S) \/ (SymbolsOf X)) -freeCountableSet -defined NAT -valued INT -valued Function-like constant total quasi_total non finite Function-yielding V160() Cardinal-yielding Element of K10(K11((((S) \/ (SymbolsOf X)) -freeCountableSet),NAT))
K11((((S) \/ (SymbolsOf X)) -freeCountableSet),NAT) is non empty non trivial Relation-like non finite set
K10(K11((((S) \/ (SymbolsOf X)) -freeCountableSet),NAT)) is non empty non trivial non finite set
K11((((S) \/ (SymbolsOf X)) -freeCountableSet),{0}) is non empty non trivial Relation-like non finite set
(((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0),S) is non empty non degenerated non trivial non finite () () (S) ()
S is non empty non degenerated non trivial non finite () ()
X is functional set
(S,X) is non empty non degenerated non trivial non finite () (S) ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
SymbolsOf X is set
X \/ {{}} is non empty functional set
{ (rng b₁) where b₁ is Relation-like Function-like Element of X \/ {{}} : b₁ in X } is set
union { (rng b₁) where b₁ is Relation-like Function-like Element of X \/ {{}} : b₁ in X } is set
{ (rng b₁) where b₁ is Relation-like Function-like Element of X : b₁ in X } is set
union { (rng b₁) where b₁ is Relation-like Function-like Element of X : b₁ in X } is set
(S) \/ (SymbolsOf X) is non empty non trivial non finite set
((S) \/ (SymbolsOf X)) -freeCountableSet is non empty non trivial non finite countable denumerable set
rng ((S) \/ (SymbolsOf X)) is set
K10((rng ((S) \/ (SymbolsOf X)))) is non empty set
bool (rng ((S) \/ (SymbolsOf X))) is non empty Element of K10(K10((rng ((S) \/ (SymbolsOf X)))))
K10(K10((rng ((S) \/ (SymbolsOf X))))) is non empty set
(bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X))) is non empty Element of K10(K10((rng ((S) \/ (SymbolsOf X)))))
(bool (rng ((S) \/ (SymbolsOf X)))) typed\ (rng ((S) \/ (SymbolsOf X))) is Element of K10((bool (rng ((S) \/ (SymbolsOf X)))))
K10((bool (rng ((S) \/ (SymbolsOf X))))) is non empty set
(bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X))) is non empty Element of K10((bool (rng ((S) \/ (SymbolsOf X)))))
the Element of (bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X))) is Element of (bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X)))
{ the Element of (bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X)))} is non empty trivial finite 1 -element countable Element of K10(((bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X)))))
K10(((bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X))))) is non empty set
K88(REAL,((bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X)))),NAT,{ the Element of (bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X)))}) is non empty non trivial Relation-like REAL -defined (bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X))) -valued non finite Element of K10(K11(REAL,((bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X))))))
K11(REAL,((bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X))))) is non empty non trivial Relation-like non finite set
K10(K11(REAL,((bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X)))))) is non empty non trivial non finite set
(((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0 is non empty non trivial Relation-like ((S) \/ (SymbolsOf X)) -freeCountableSet -defined NAT -valued INT -valued Function-like constant total quasi_total non finite Function-yielding V160() Cardinal-yielding Element of K10(K11((((S) \/ (SymbolsOf X)) -freeCountableSet),NAT))
K11((((S) \/ (SymbolsOf X)) -freeCountableSet),NAT) is non empty non trivial Relation-like non finite set
K10(K11((((S) \/ (SymbolsOf X)) -freeCountableSet),NAT)) is non empty non trivial non finite set
K11((((S) \/ (SymbolsOf X)) -freeCountableSet),{0}) is non empty non trivial Relation-like non finite set
(((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0),S) is non empty non degenerated non trivial non finite () () (S) ()
((S,X)) is non empty non trivial non finite set
the carrier of (S,X) is non empty non trivial non finite set
((S,X)) is non empty non trivial non finite Element of K10(((S,X)))
K10(((S,X))) is non empty non trivial non finite set
the OneF of (S,X) is Element of the carrier of (S,X)
{ the OneF of (S,X)} is non empty trivial finite 1 -element countable set
the carrier of (S,X) \ { the OneF of (S,X)} is non empty non trivial non finite Element of K10( the carrier of (S,X))
K10( the carrier of (S,X)) is non empty non trivial non finite set
the carrier of (S,X) typed\ { the OneF of (S,X)} is Element of K10( the carrier of (S,X))
the of (S,X) is non empty Relation-like the carrier of (S,X) \ { the OneF of (S,X)} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of (S,X) \ { the OneF of (S,X)}),INT))
K11(( the carrier of (S,X) \ { the OneF of (S,X)}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of (S,X) \ { the OneF of (S,X)}),INT)) is non empty non trivial non finite set
the of (S,X) " {0} is Element of K10(( the carrier of (S,X) \ { the OneF of (S,X)}))
K10(( the carrier of (S,X) \ { the OneF of (S,X)})) is non empty non trivial non finite set
((S,X)) \ (SymbolsOf X) is Element of K10(((S,X)))
((S,X)) typed\ (SymbolsOf X) is Element of K10(((S,X)))
K10(((S,X))) is non empty non trivial non finite set
((S,X)) \ (SymbolsOf X) is Element of K10(((S,X)))
(S) is non empty non trivial non finite Element of K10((S))
K10((S)) is non empty non trivial non finite set
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is non empty non trivial non finite Element of K10( the carrier of S)
K10( the carrier of S) is non empty non trivial non finite set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
the of S is non empty Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
K11(( the carrier of S \ { the OneF of S}),INT) is non empty non trivial Relation-like non finite set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty non trivial non finite set
the of S " {0} is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty non trivial non finite set
dom ((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0) is non empty non trivial countable Element of K10((((S) \/ (SymbolsOf X)) -freeCountableSet))
K10((((S) \/ (SymbolsOf X)) -freeCountableSet)) is non empty non trivial non finite set
(((S) \/ (SymbolsOf X)) -freeCountableSet) /\ ((S) \/ (SymbolsOf X)) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
(((S) \/ (SymbolsOf X)) -freeCountableSet) typed/\ ((S) \/ (SymbolsOf X)) is countable Element of K10((((S) \/ (SymbolsOf X)) -freeCountableSet))
(((S) \/ (SymbolsOf X)) -freeCountableSet) /\typed ((S) \/ (SymbolsOf X)) is Element of K10(((S) \/ (SymbolsOf X)))
K10(((S) \/ (SymbolsOf X))) is non empty non trivial non finite set
(S) null (SymbolsOf X) is set
(S) \typed/ (SymbolsOf X) is Element of K10(((S) \/ (SymbolsOf X)))
(SymbolsOf X) null (S) is set
(SymbolsOf X) \typed/ (S) is Element of K10(((SymbolsOf X) \/ (S)))
(SymbolsOf X) \/ (S) is non empty non trivial non finite set
K10(((SymbolsOf X) \/ (S))) is non empty non trivial non finite set
(((S) \/ (SymbolsOf X)) -freeCountableSet) \ (S) is countable Element of K10((((S) \/ (SymbolsOf X)) -freeCountableSet))
(((S) \/ (SymbolsOf X)) -freeCountableSet) typed\ (S) is countable Element of K10((((S) \/ (SymbolsOf X)) -freeCountableSet))
(((S) \/ (SymbolsOf X)) -freeCountableSet) \ (SymbolsOf X) is countable Element of K10((((S) \/ (SymbolsOf X)) -freeCountableSet))
(((S) \/ (SymbolsOf X)) -freeCountableSet) typed\ (SymbolsOf X) is countable Element of K10((((S) \/ (SymbolsOf X)) -freeCountableSet))
E2 is Relation-like INT -valued Function-like set
dom E2 is set
(dom E2) \ (S) is Element of K10((dom E2))
K10((dom E2)) is non empty set
(dom E2) typed\ (S) is Element of K10((dom E2))
E2 | ((dom E2) \ (S)) is Relation-like (dom E2) \ (S) -defined INT -valued Function-like set
(E2 | ((dom E2) \ (S))) " {0} is set
((E2 | ((dom E2) \ (S))) " {0}) \/ (S) is non empty non trivial non finite set
E2 null {} is Relation-like {} \/ (dom E2) -defined {} \/ (rng E2) -valued Function-like set
{} \/ (dom E2) is set
rng E2 is set
{} \/ (rng E2) is set
E2 \typed/ {} is Relation-like Element of K10((E2 \/ {}))
E2 \/ {} is Relation-like set
K10((E2 \/ {})) is non empty set
(E2 null {}) | ({} \/ (dom E2)) is Relation-like {} \/ (dom E2) -defined {} \/ (dom E2) -defined {} \/ (rng E2) -valued Function-like set
(E2 null {}) null ({} \/ (dom E2)) is Relation-like ({} \/ (dom E2)) \/ (dom (E2 null {})) -defined ({} \/ (dom E2)) \/ (rng (E2 null {})) -valued Function-like set
dom (E2 null {}) is set
({} \/ (dom E2)) \/ (dom (E2 null {})) is set
rng (E2 null {}) is set
({} \/ (dom E2)) \/ (rng (E2 null {})) is set
(E2 null {}) \typed/ ({} \/ (dom E2)) is Element of K10(((E2 null {}) \/ ({} \/ (dom E2))))
(E2 null {}) \/ ({} \/ (dom E2)) is set
K10(((E2 null {}) \/ ({} \/ (dom E2)))) is non empty set
((E2 null {}) | ({} \/ (dom E2))) " {0} is set
(((E2 null {}) | ({} \/ (dom E2))) " {0}) \ (SymbolsOf X) is Element of K10((((E2 null {}) | ({} \/ (dom E2))) " {0}))
K10((((E2 null {}) | ({} \/ (dom E2))) " {0})) is non empty set
(((E2 null {}) | ({} \/ (dom E2))) " {0}) typed\ (SymbolsOf X) is Element of K10((((E2 null {}) | ({} \/ (dom E2))) " {0}))
(S) \ (SymbolsOf X) is Element of K10((S))
(S) typed\ (SymbolsOf X) is Element of K10((S))
K10((S)) is non empty non trivial non finite set
(S) \ (SymbolsOf X) is Element of K10((S))
((((E2 null {}) | ({} \/ (dom E2))) " {0}) \ (SymbolsOf X)) \/ ((S) \ (SymbolsOf X)) is set
(((S) \/ (SymbolsOf X)) -freeCountableSet) \/ ((S) \ (SymbolsOf X)) is non empty non trivial non finite set
X is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
{X} is non empty trivial finite V36() 1 -element countable Element of K10(NAT)
NAT \ {X} is non empty non trivial non finite Element of K10(REAL)
NAT typed\ {X} is countable Element of K10(NAT)
NAT \ {X} is non empty non trivial non finite countable denumerable Element of K10(NAT)
S is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative finite cardinal real integer countable Element of NAT
(NAT \ {X}) --> 0 is non empty non trivial Relation-like NAT \ {X} -defined NAT -valued INT -valued Function-like constant total quasi_total non finite Function-yielding V160() Cardinal-yielding Element of K10(K11((NAT \ {X}),NAT))
K11((NAT \ {X}),NAT) is non empty non trivial Relation-like non finite set
K10(K11((NAT \ {X}),NAT)) is non empty non trivial non finite set
K11((NAT \ {X}),{0}) is non empty non trivial Relation-like non finite set
SS1 is Element of NAT \ {X}
SS1 .--> (- 2) is trivial Relation-like NAT \ {X} -defined {SS1} -defined Function-like one-to-one constant finite countable finite-support set
{SS1} is non empty trivial finite 1 -element countable set
{SS1} --> (- 2) is non empty Relation-like non-empty {SS1} -defined INT -valued {(- 2)} -valued Function-like constant total quasi_total finite countable finite-support Element of K10(K11({SS1},{(- 2)}))
{(- 2)} is non empty trivial finite 1 -element countable set
K11({SS1},{(- 2)}) is non empty Relation-like finite countable set
K10(K11({SS1},{(- 2)})) is non empty finite V36() countable set
SX is Relation-like INT -valued Function-like set
add is Relation-like INT -valued Function-like set
SX +* add is Relation-like INT -valued Function-like set
{SS1} is non empty trivial finite 1 -element countable Element of K10((NAT \ {X}))
K10((NAT \ {X})) is non empty non trivial non finite set
dom add is set
dom SX is set
dom (SX +* add) is set
(NAT \ {X}) null {SS1} is set
(NAT \ {X}) \typed/ {SS1} is Element of K10(((NAT \ {X}) \/ {SS1}))
(NAT \ {X}) \/ {SS1} is non empty non trivial non finite set
K10(((NAT \ {X}) \/ {SS1})) is non empty non trivial non finite set
rng (SX +* add) is Element of K10(INT)
Funcs ((NAT \ {X}),INT) is non empty functional FUNCTION_DOMAIN of NAT \ {X}, INT
K11((NAT \ {X}),INT) is non empty non trivial Relation-like non finite set
K10(K11((NAT \ {X}),INT)) is non empty non trivial non finite set
S2 is non empty Relation-like NAT \ {X} -defined INT -valued Function-like total quasi_total Element of K10(K11((NAT \ {X}),INT))
(NAT,S,X,S2) is () ()
0. (NAT,S,X,S2) is zero Element of the carrier of (NAT,S,X,S2)
the carrier of (NAT,S,X,S2) is set
the ZeroF of (NAT,S,X,S2) is Element of the carrier of (NAT,S,X,S2)
1. (NAT,S,X,S2) is Element of the carrier of (NAT,S,X,S2)
the OneF of (NAT,S,X,S2) is Element of the carrier of (NAT,S,X,S2)
S2 . S is set
add . SS1 is set
((NAT,S,X,S2)) is set
S2 . ((NAT,S,X,S2)) is set
E1 is set
{S} is non empty trivial finite V36() 1 -element countable Element of K10(NAT)
(NAT \ {X}) \ {S} is non empty non trivial non finite Element of K10(REAL)
(NAT \ {X}) typed\ {S} is Element of K10((NAT \ {X}))
(NAT \ {X}) \ {S} is non empty non trivial non finite Element of K10((NAT \ {X}))
dom S2 is non empty Element of K10((NAT \ {X}))
S2 . E1 is set
SX . E1 is set
S2 " {0} is Element of K10((NAT \ {X}))
K10((S2 " {0})) is non empty set
E1 is Element of K10((S2 " {0}))
(S2 " {0}) \/ E1 is set
(S2 " {0}) null E1 is set
(S2 " {0}) \typed/ E1 is Element of K10(((S2 " {0}) \/ E1))
K10(((S2 " {0}) \/ E1)) is non empty set
((NAT,S,X,S2)) is set
{ the OneF of (NAT,S,X,S2)} is non empty trivial finite 1 -element countable set
the carrier of (NAT,S,X,S2) \ { the OneF of (NAT,S,X,S2)} is Element of K10( the carrier of (NAT,S,X,S2))
K10( the carrier of (NAT,S,X,S2)) is non empty set
the carrier of (NAT,S,X,S2) typed\ { the OneF of (NAT,S,X,S2)} is Element of K10( the carrier of (NAT,S,X,S2))
the of (NAT,S,X,S2) is Relation-like the carrier of (NAT,S,X,S2) \ { the OneF of (NAT,S,X,S2)} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of (NAT,S,X,S2) \ { the OneF of (NAT,S,X,S2)}),INT))
K11(( the carrier of (NAT,S,X,S2) \ { the OneF of (NAT,S,X,S2)}),INT) is Relation-like set
K10(K11(( the carrier of (NAT,S,X,S2) \ { the OneF of (NAT,S,X,S2)}),INT)) is non empty set
the of (NAT,S,X,S2) " {0} is Element of K10(( the carrier of (NAT,S,X,S2) \ { the OneF of (NAT,S,X,S2)}))
K10(( the carrier of (NAT,S,X,S2) \ { the OneF of (NAT,S,X,S2)})) is non empty set
N1 is non empty non degenerated non trivial non finite () ()
S is non empty non degenerated non trivial non finite countable () ()
(S) is non empty non trivial non finite set
the carrier of S is non empty non trivial non finite set
S is non empty non degenerated non trivial non finite countable () ()
(S) is non empty non trivial non finite countable denumerable set
the carrier of S is non empty non trivial non finite set
(S) * is non empty non trivial functional non finite V36() FinSequence-membered non empty-membered FinSequenceSet of (S)
((S) *) \ {{}} is non empty non trivial functional non finite V36() FinSequence-membered with_non-empty_elements Element of K10(((S) *))
K10(((S) *)) is non empty non trivial non finite set
((S) *) typed\ {{}} is functional V36() FinSequence-membered Element of K10(((S) *))
S1 is countable set
K10(S1) is non empty set
S1 \ {{}} is with_non-empty_elements countable Element of K10(S1)
S1 typed\ {{}} is countable Element of K10(S1)
SS1 is countable Element of K10(S1)
X is Relation-like INT -valued Function-like set
S is non empty ()
(X,S) is non empty () (S) ()
((X,S)) is non empty set
the carrier of (X,S) is non empty set
dom X is set
(S) is non empty set
the carrier of S is non empty set
(dom X) \/ (S) is non empty set
((X,S)) \+\ ((dom X) \/ (S)) is set
((X,S)) \ ((dom X) \/ (S)) is set
((X,S)) typed\ ((dom X) \/ (S)) is Element of K10(((X,S)))
K10(((X,S))) is non empty set
((X,S)) \ ((dom X) \/ (S)) is Element of K10(((X,S)))
((dom X) \/ (S)) \ ((X,S)) is set
((dom X) \/ (S)) typed\ ((X,S)) is Element of K10(((dom X) \/ (S)))
K10(((dom X) \/ (S))) is non empty set
((dom X) \/ (S)) \ ((X,S)) is Element of K10(((dom X) \/ (S)))
(((X,S)) \ ((dom X) \/ (S))) \/ (((dom X) \/ (S)) \ ((X,S))) is set
the of S is Relation-like the carrier of S \ { the OneF of S} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of S \ { the OneF of S}),INT))
the OneF of S is Element of the carrier of S
{ the OneF of S} is non empty trivial finite 1 -element countable set
the carrier of S \ { the OneF of S} is Element of K10( the carrier of S)
K10( the carrier of S) is non empty set
the carrier of S typed\ { the OneF of S} is Element of K10( the carrier of S)
K11(( the carrier of S \ { the OneF of S}),INT) is Relation-like set
K10(K11(( the carrier of S \ { the OneF of S}),INT)) is non empty set
the of (X,S) is Relation-like the carrier of (X,S) \ { the OneF of (X,S)} -defined INT -valued Function-like total quasi_total Element of K10(K11(( the carrier of (X,S) \ { the OneF of (X,S)}),INT))
the OneF of (X,S) is Element of the carrier of (X,S)
{ the OneF of (X,S)} is non empty trivial finite 1 -element countable set
the carrier of (X,S) \ { the OneF of (X,S)} is Element of K10( the carrier of (X,S))
K10( the carrier of (X,S)) is non empty set
the carrier of (X,S) typed\ { the OneF of (X,S)} is Element of K10( the carrier of (X,S))
K11(( the carrier of (X,S) \ { the OneF of (X,S)}),INT) is Relation-like set
K10(K11(( the carrier of (X,S) \ { the OneF of (X,S)}),INT)) is non empty set
(S) is set
the ZeroF of S is Element of the carrier of S
(S) is set
((X,S)) is set
the ZeroF of (X,S) is Element of the carrier of (X,S)
((X,S)) is set
K10((dom X)) is non empty set
{(S)} is non empty trivial finite 1 -element countable set
(dom X) \ {(S)} is Element of K10((dom X))
(dom X) typed\ {(S)} is Element of K10((dom X))
X | ((dom X) \ {(S)}) is Relation-like (dom X) \ {(S)} -defined INT -valued Function-like set
dom (X | ((dom X) \ {(S)})) is Element of K10(((dom X) \ {(S)}))
K10(((dom X) \ {(S)})) is non empty set
Y is Element of K10((dom X))
(dom X) /\ Y is Element of K10((dom X))
(dom X) typed/\ Y is Element of K10((dom X))
(dom X) /\ Y is set
(dom X) /\typed Y is Element of K10(Y)
K10(Y) is non empty set
Y null (dom X) is set
Y \typed/ (dom X) is Element of K10((Y \/ (dom X)))
Y \/ (dom X) is set
K10((Y \/ (dom X))) is non empty set
(X | ((dom X) \ {(S)})) +* the of S is Relation-like INT -valued Function-like set
dom the of (X,S) is Element of K10(( the carrier of (X,S) \ { the OneF of (X,S)}))
K10(( the carrier of (X,S) \ { the OneF of (X,S)})) is non empty set
X | Y is Relation-like Y -defined INT -valued Function-like set
dom (X | Y) is Element of K10(Y)
dom the of S is Element of K10(( the carrier of S \ { the OneF of S}))
K10(( the carrier of S \ { the OneF of S})) is non empty set
(dom (X | Y)) \/ (dom the of S) is set
{((X,S))} is non empty trivial finite 1 -element countable set
((X,S)) \ {((X,S))} is Element of K10(((X,S)))
((X,S)) typed\ {((X,S))} is Element of K10(((X,S)))
Y \/ (dom the of S) is set
(S) \ {(S)} is Element of K10((S))
K10((S)) is non empty set
(S) typed\ {(S)} is Element of K10((S))
Y \/ ((S) \ {(S)}) is set
NN1 is non empty Element of K10((S))
(S) null (dom X) is set
(S) \typed/ (dom X) is Element of K10(((S) \/ (dom X)))
(S) \/ (dom X) is non empty set
K10(((S) \/ (dom X))) is non empty set
NN2 is non empty Element of K10(((X,S)))
((X,S)) \ NN2 is Element of K10(((X,S)))
((X,S)) typed\ NN2 is Element of K10(((X,S)))
NN2 \/ (((X,S)) \ NN2) is non empty Element of K10(((X,S)))
(S) \ NN1 is Element of K10((S))
(S) typed\ NN1 is Element of K10((S))
NN1 \/ ((S) \ NN1) is non empty Element of K10((S))
NN2 \/ ((S) \ NN1) is non empty set
(NN2 \/ ((S) \ NN1)) \/ Y is non empty set
(NN1 \/ ((S) \ NN1)) \/ Y is non empty set
((S) \ NN1) \/ Y is set
NN1 \/ (((S) \ NN1) \/ Y) is non empty set
NN11 is non empty Element of K10(((S) \/ (dom X)))
((S) \/ (dom X)) \ NN11 is Element of K10(((S) \/ (dom X)))
((S) \/ (dom X)) typed\ NN11 is Element of K10(((S) \/ (dom X)))
NN11 \/ (((S) \/ (dom X)) \ NN11) is non empty Element of K10(((S) \/ (dom X)))
z2 is set
S is non empty non degenerated non trivial non finite countable () ()
X is functional set
(S,X) is non empty non degenerated non trivial non finite () (S) ()
(S) is non empty non trivial non finite countable denumerable set
the carrier of S is non empty non trivial non finite set
SymbolsOf X is set
X \/ {{}} is non empty functional set
{ (rng b₁) where b₁ is Relation-like Function-like Element of X \/ {{}} : b₁ in X } is set
union { (rng b₁) where b₁ is Relation-like Function-like Element of X \/ {{}} : b₁ in X } is set
{ (rng b₁) where b₁ is Relation-like Function-like Element of X : b₁ in X } is set
union { (rng b₁) where b₁ is Relation-like Function-like Element of X : b₁ in X } is set
(S) \/ (SymbolsOf X) is non empty non trivial non finite set
((S) \/ (SymbolsOf X)) -freeCountableSet is non empty non trivial non finite countable denumerable set
rng ((S) \/ (SymbolsOf X)) is set
K10((rng ((S) \/ (SymbolsOf X)))) is non empty set
bool (rng ((S) \/ (SymbolsOf X))) is non empty Element of K10(K10((rng ((S) \/ (SymbolsOf X)))))
K10(K10((rng ((S) \/ (SymbolsOf X))))) is non empty set
(bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X))) is non empty Element of K10(K10((rng ((S) \/ (SymbolsOf X)))))
(bool (rng ((S) \/ (SymbolsOf X)))) typed\ (rng ((S) \/ (SymbolsOf X))) is Element of K10((bool (rng ((S) \/ (SymbolsOf X)))))
K10((bool (rng ((S) \/ (SymbolsOf X))))) is non empty set
(bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X))) is non empty Element of K10((bool (rng ((S) \/ (SymbolsOf X)))))
the Element of (bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X))) is Element of (bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X)))
{ the Element of (bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X)))} is non empty trivial finite 1 -element countable Element of K10(((bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X)))))
K10(((bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X))))) is non empty set
K88(REAL,((bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X)))),NAT,{ the Element of (bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X)))}) is non empty non trivial Relation-like REAL -defined (bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X))) -valued non finite Element of K10(K11(REAL,((bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X))))))
K11(REAL,((bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X))))) is non empty non trivial Relation-like non finite set
K10(K11(REAL,((bool (rng ((S) \/ (SymbolsOf X)))) \ (rng ((S) \/ (SymbolsOf X)))))) is non empty non trivial non finite set
(((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0 is non empty non trivial Relation-like ((S) \/ (SymbolsOf X)) -freeCountableSet -defined NAT -valued INT -valued Function-like constant total quasi_total non finite Function-yielding V160() Cardinal-yielding Element of K10(K11((((S) \/ (SymbolsOf X)) -freeCountableSet),NAT))
K11((((S) \/ (SymbolsOf X)) -freeCountableSet),NAT) is non empty non trivial Relation-like non finite set
K10(K11((((S) \/ (SymbolsOf X)) -freeCountableSet),NAT)) is non empty non trivial non finite set
K11((((S) \/ (SymbolsOf X)) -freeCountableSet),{0}) is non empty non trivial Relation-like non finite set
(((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0),S) is non empty non degenerated non trivial non finite () () (S) ()
((((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0),S)) is non empty non trivial non finite set
the carrier of (((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0),S) is non empty non trivial non finite set
dom ((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0) is non empty non trivial countable Element of K10((((S) \/ (SymbolsOf X)) -freeCountableSet))
K10((((S) \/ (SymbolsOf X)) -freeCountableSet)) is non empty non trivial non finite set
(dom ((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0)) \/ (S) is non empty non trivial non finite set
((((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0),S)) \+\ ((dom ((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0)) \/ (S)) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional finite finite-yielding V36() cardinal {} -element real integer FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V160() empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
((((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0),S)) \ ((dom ((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0)) \/ (S)) is set
((((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0),S)) typed\ ((dom ((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0)) \/ (S)) is Element of K10(((((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0),S)))
K10(((((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0),S))) is non empty non trivial non finite set
((((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0),S)) \ ((dom ((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0)) \/ (S)) is Element of K10(((((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0),S)))
((dom ((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0)) \/ (S)) \ ((((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0),S)) is set
((dom ((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0)) \/ (S)) typed\ ((((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0),S)) is Element of K10(((dom ((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0)) \/ (S)))
K10(((dom ((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0)) \/ (S))) is non empty non trivial non finite set
((dom ((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0)) \/ (S)) \ ((((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0),S)) is Element of K10(((dom ((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0)) \/ (S)))
(((((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0),S)) \ ((dom ((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0)) \/ (S))) \/ (((dom ((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0)) \/ (S)) \ ((((((S) \/ (SymbolsOf X)) -freeCountableSet) --> 0),S))) is set
(((S) \/ (SymbolsOf X)) -freeCountableSet) \/ (S) is non empty non trivial non finite set
E1 is 1-sorted