REAL is set
NAT is non empty non trivial V8() V9() V10() non finite cardinal limit_cardinal Element of bool REAL
bool REAL is non empty cup-closed diff-closed preBoolean set
NAT is non empty non trivial V8() V9() V10() non finite cardinal limit_cardinal set
bool NAT is non empty non trivial cup-closed diff-closed preBoolean non finite set
bool NAT is non empty non trivial cup-closed diff-closed preBoolean non finite set
K236() is L6()
the carrier of K236() is set
{} is empty V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() set
the empty V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() set is empty V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() set
1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
2 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
3 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
Seg 1 is non empty trivial finite 1 -element Element of bool NAT
{ b1 where b1 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT : ( 1 <= b1 & b1 <= 1 ) } is set
{1} is non empty trivial finite V40() 1 -element set
Seg 2 is non empty finite 2 -element Element of bool NAT
{ b1 where b1 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT : ( 1 <= b1 & b1 <= 2 ) } is set
{1,2} is non empty finite V40() set
card {} is empty V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() set
0 is empty V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() Element of NAT
T is non empty trivial finite 1 -element RelStr
T is non empty trivial finite 1 -element RelStr
t is set
the InternalRel of T is Relation-like the carrier of T -defined the carrier of T -valued finite Element of bool [: the carrier of T, the carrier of T:]
the carrier of T is non empty trivial finite 1 -element set
[: the carrier of T, the carrier of T:] is non empty Relation-like finite set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean finite V40() set
field the InternalRel of T is finite set
t2 is non empty set
the Element of t2 is Element of t2
x is set
[ the Element of t2,x] is set
{ the Element of t2,x} is non empty finite set
{ the Element of t2} is non empty trivial finite 1 -element set
{{ the Element of t2,x},{ the Element of t2}} is non empty finite V40() set
the carrier of T \/ the carrier of T is non empty finite set
T is non empty RelStr
the carrier of T is non empty set
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
the InternalRel of T is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
[: the carrier of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
field the InternalRel of T is set
a is non empty Element of bool the carrier of T
the Element of a is Element of a
a /\ (field the InternalRel of T) is Element of bool the carrier of T
X is Element of the carrier of T
y is Element of the carrier of T
[X,y] is Element of [: the carrier of T, the carrier of T:]
{X,y} is non empty finite set
{X} is non empty trivial finite 1 -element set
{{X,y},{X}} is non empty finite V40() set
y is set
t1 is Element of the carrier of T
t2 is Element of the carrier of T
[t1,t2] is Element of [: the carrier of T, the carrier of T:]
{t1,t2} is non empty finite set
{t1} is non empty trivial finite 1 -element set
{{t1,t2},{t1}} is non empty finite V40() set
a is set
field the InternalRel of T is set
the carrier of T \/ the carrier of T is non empty set
t2 is non empty Element of bool the carrier of T
X is Element of the carrier of T
x is set
[X,x] is set
{X,x} is non empty finite set
{X} is non empty trivial finite 1 -element set
{{X,x},{X}} is non empty finite V40() set
y is Element of the carrier of T
T is reflexive transitive antisymmetric RelStr
t is non empty reflexive transitive antisymmetric with_suprema RelStr
the carrier of t is non empty set
the carrier of T is set
a is Element of the carrier of T
t2 is Element of the carrier of T
a "\/" t2 is Element of the carrier of T
T is non empty reflexive transitive antisymmetric with_suprema RelStr
the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr is non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr
T is () RelStr
the InternalRel of T is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
the carrier of T is set
[: the carrier of T, the carrier of T:] is Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () RelStr
the carrier of T is non empty set
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
t is non empty directed lower Element of bool the carrier of T
"\/" (t,T) is Element of the carrier of T
a is Element of the carrier of T
t2 is Element of the carrier of T
a "\/" t2 is Element of the carrier of T
t2 is Element of the carrier of T
T is ()
the of T is set
t is ()
the of t is set
T is ()
the of T is set
the of T is Relation-like the of T -defined the of T -valued Function-like V29( the of T) V33( the of T, the of T) Element of bool [: the of T, the of T:]
[: the of T, the of T:] is Relation-like set
bool [: the of T, the of T:] is non empty cup-closed diff-closed preBoolean set
t is Element of the of T
the of T . t is set
dom the of T is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
T is ()
the of T is set
t is ()
the of t is set
the of T is Relation-like the of T -defined the of T -valued Function-like V29( the of T) V33( the of T, the of T) Element of bool [: the of T, the of T:]
[: the of T, the of T:] is Relation-like set
bool [: the of T, the of T:] is non empty cup-closed diff-closed preBoolean set
( the of T, the of T) is () ()
the of t is Relation-like the of t -defined the of t -valued Function-like V29( the of t) V33( the of t, the of t) Element of bool [: the of t, the of t:]
[: the of t, the of t:] is Relation-like set
bool [: the of t, the of t:] is non empty cup-closed diff-closed preBoolean set
( the of t, the of t) is () ()
a is Element of the of T
t2 is Element of the of t
(T,a) is Element of the of T
the of T . a is set
(t,t2) is Element of the of t
the of t . t2 is set
T is set
t is set
{T,t} is non empty finite set
a is ()
the of a is set
the of a is Relation-like the of a -defined the of a -valued Function-like V29( the of a) V33( the of a, the of a) Element of bool [: the of a, the of a:]
[: the of a, the of a:] is Relation-like set
bool [: the of a, the of a:] is non empty cup-closed diff-closed preBoolean set
the of a . T is set
the of a . t is set
t2 is Element of the of a
(a,t2) is Element of the of a
the of a . t2 is set
(a,(a,t2)) is Element of the of a
the of a . (a,t2) is set
t2 is Element of the of a
(a,t2) is Element of the of a
the of a . t2 is set
T is ()
the of T is set
the of T is Relation-like the of T -defined the of T -valued Function-like V29( the of T) V33( the of T, the of T) Element of bool [: the of T, the of T:]
[: the of T, the of T:] is Relation-like set
bool [: the of T, the of T:] is non empty cup-closed diff-closed preBoolean set
( the of T, the of T) is () ()
t is ()
the of t is set
the of t is Relation-like the of t -defined the of t -valued Function-like V29( the of t) V33( the of t, the of t) Element of bool [: the of t, the of t:]
[: the of t, the of t:] is Relation-like set
bool [: the of t, the of t:] is non empty cup-closed diff-closed preBoolean set
( the of t, the of t) is () ()
a is Element of the of t
(t,a) is Element of the of t
the of t . a is set
(t,(t,a)) is Element of the of t
the of t . (t,a) is set
t2 is Element of the of T
(T,t2) is Element of the of T
the of T . t2 is set
(T,(T,t2)) is Element of the of T
the of T . (T,t2) is set
T is ()
the of T is set
the of T is Relation-like the of T -defined the of T -valued Function-like V29( the of T) V33( the of T, the of T) Element of bool [: the of T, the of T:]
[: the of T, the of T:] is Relation-like set
bool [: the of T, the of T:] is non empty cup-closed diff-closed preBoolean set
( the of T, the of T) is () ()
t is ()
the of t is set
the of t is Relation-like the of t -defined the of t -valued Function-like V29( the of t) V33( the of t, the of t) Element of bool [: the of t, the of t:]
[: the of t, the of t:] is Relation-like set
bool [: the of t, the of t:] is non empty cup-closed diff-closed preBoolean set
( the of t, the of t) is () ()
a is Element of the of t
(t,a) is Element of the of t
the of t . a is set
t2 is Element of the of T
(T,t2) is Element of the of T
the of T . t2 is set
{0,1} is non empty finite V40() Element of bool NAT
[:{0,1},{0,1}:] is non empty Relation-like finite set
bool [:{0,1},{0,1}:] is non empty cup-closed diff-closed preBoolean finite V40() set
t is finite Element of {0,1}
T is finite Element of {0,1}
(0,1) --> (t,T) is non empty Relation-like {0,1} -defined {0,1} -valued Function-like V29({0,1}) V33({0,1},{0,1}) finite Element of bool [:{0,1},{0,1}:]
{0,1} is non empty finite V40() set
[:{0,1},{0,1}:] is non empty Relation-like finite set
bool [:{0,1},{0,1}:] is non empty cup-closed diff-closed preBoolean finite V40() set
a is non empty Relation-like {0,1} -defined {0,1} -valued Function-like V29({0,1}) V33({0,1},{0,1}) finite Element of bool [:{0,1},{0,1}:]
({0,1},a) is () ()
a . t is finite Element of {0,1}
a . T is finite Element of {0,1}
T is () ()
the of T is set
T is non empty set
[:T,T:] is non empty Relation-like set
bool [:T,T:] is non empty cup-closed diff-closed preBoolean set
t is set
[:t,t:] is Relation-like set
bool [:t,t:] is non empty cup-closed diff-closed preBoolean set
Fin t is non empty cup-closed diff-closed preBoolean set
[:T,(Fin t):] is non empty Relation-like set
bool [:T,(Fin t):] is non empty cup-closed diff-closed preBoolean set
a is Relation-like T -defined T -valued Element of bool [:T,T:]
t2 is Relation-like t -defined t -valued Function-like V29(t) V33(t,t) Element of bool [:t,t:]
X is non empty Relation-like T -defined Fin t -valued Function-like V29(T) V33(T, Fin t) Element of bool [:T,(Fin t):]
(T,t,a,t2,X) is () ()
T is set
[:T,T:] is Relation-like set
bool [:T,T:] is non empty cup-closed diff-closed preBoolean set
t is non empty set
[:t,t:] is non empty Relation-like set
bool [:t,t:] is non empty cup-closed diff-closed preBoolean set
Fin t is non empty cup-closed diff-closed preBoolean set
[:T,(Fin t):] is Relation-like set
bool [:T,(Fin t):] is non empty cup-closed diff-closed preBoolean set
a is Relation-like T -defined T -valued Element of bool [:T,T:]
t2 is non empty Relation-like t -defined t -valued Function-like V29(t) V33(t,t) Element of bool [:t,t:]
X is Relation-like T -defined Fin t -valued Function-like V29(T) V33(T, Fin t) Element of bool [:T,(Fin t):]
(T,t,a,t2,X) is () ()
the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr is non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr
the () () () () is () () () ()
the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr is non empty trivial finite 1 -element set
the of the () () () () is non empty set
Fin the of the () () () () is non empty cup-closed diff-closed preBoolean set
[: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,(Fin the of the () () () ()):] is non empty Relation-like set
bool [: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,(Fin the of the () () () ()):] is non empty cup-closed diff-closed preBoolean set
the non empty Relation-like the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr -defined Fin the of the () () () () -valued Function-like V29( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ) V33( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr , Fin the of the () () () ()) finite Element of bool [: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,(Fin the of the () () () ()):] is non empty Relation-like the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr -defined Fin the of the () () () () -valued Function-like V29( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ) V33( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr , Fin the of the () () () ()) finite Element of bool [: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,(Fin the of the () () () ()):]
the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr is Relation-like the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr -defined the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr -valued finite co-well_founded Element of bool [: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr , the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr :]
[: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr , the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr :] is non empty Relation-like finite set
bool [: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr , the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr :] is non empty cup-closed diff-closed preBoolean finite V40() set
the of the () () () () is non empty Relation-like the of the () () () () -defined the of the () () () () -valued Function-like V29( the of the () () () ()) V33( the of the () () () (), the of the () () () ()) Element of bool [: the of the () () () (), the of the () () () ():]
[: the of the () () () (), the of the () () () ():] is non empty Relation-like set
bool [: the of the () () () (), the of the () () () ():] is non empty cup-closed diff-closed preBoolean set
( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr , the of the () () () (), the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr , the of the () () () (), the non empty Relation-like the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr -defined Fin the of the () () () () -valued Function-like V29( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ) V33( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr , Fin the of the () () () ()) finite Element of bool [: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,(Fin the of the () () () ()):]) is non empty () () ()
t2 is non empty () () ()
the carrier of t2 is non empty set
RelStr(# the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr , the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr #) is strict RelStr
the InternalRel of t2 is Relation-like the carrier of t2 -defined the carrier of t2 -valued Element of bool [: the carrier of t2, the carrier of t2:]
[: the carrier of t2, the carrier of t2:] is non empty Relation-like set
bool [: the carrier of t2, the carrier of t2:] is non empty cup-closed diff-closed preBoolean set
RelStr(# the carrier of t2, the InternalRel of t2 #) is strict RelStr
( the of the () () () (), the of the () () () ()) is () ()
the of t2 is non empty set
the of t2 is non empty Relation-like the of t2 -defined the of t2 -valued Function-like V29( the of t2) V33( the of t2, the of t2) Element of bool [: the of t2, the of t2:]
[: the of t2, the of t2:] is non empty Relation-like set
bool [: the of t2, the of t2:] is non empty cup-closed diff-closed preBoolean set
( the of t2, the of t2) is () ()
T is ()
the carrier of T is set
the of T is Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
the of T is set
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
the of T . t is set
bool the of T is non empty cup-closed diff-closed preBoolean set
dom the of T is Element of bool the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
{} the of T is empty V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() Element of bool the of T
T is ()
the carrier of T is set
t is ()
the carrier of t is set
the of T is set
the InternalRel of T is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
[: the carrier of T, the carrier of T:] is Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
the of T is Relation-like the of T -defined the of T -valued Function-like V29( the of T) V33( the of T, the of T) Element of bool [: the of T, the of T:]
[: the of T, the of T:] is Relation-like set
bool [: the of T, the of T:] is non empty cup-closed diff-closed preBoolean set
the of T is Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
( the carrier of T, the of T, the InternalRel of T, the of T, the of T) is () ()
the of t is set
the InternalRel of t is Relation-like the carrier of t -defined the carrier of t -valued Element of bool [: the carrier of t, the carrier of t:]
[: the carrier of t, the carrier of t:] is Relation-like set
bool [: the carrier of t, the carrier of t:] is non empty cup-closed diff-closed preBoolean set
the of t is Relation-like the of t -defined the of t -valued Function-like V29( the of t) V33( the of t, the of t) Element of bool [: the of t, the of t:]
[: the of t, the of t:] is Relation-like set
bool [: the of t, the of t:] is non empty cup-closed diff-closed preBoolean set
the of t is Relation-like the carrier of t -defined Fin the of t -valued Function-like V29( the carrier of t) V33( the carrier of t, Fin the of t) Element of bool [: the carrier of t,(Fin the of t):]
Fin the of t is non empty cup-closed diff-closed preBoolean set
[: the carrier of t,(Fin the of t):] is Relation-like set
bool [: the carrier of t,(Fin the of t):] is non empty cup-closed diff-closed preBoolean set
( the carrier of t, the of t, the InternalRel of t, the of t, the of t) is () ()
a is Element of the carrier of T
t2 is Element of the carrier of t
(T,a) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T . a is set
(t,t2) is Element of bool the of t
bool the of t is non empty cup-closed diff-closed preBoolean set
the of t . t2 is set
T is ()
the carrier of T is set
the of T is set
the InternalRel of T is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
[: the carrier of T, the carrier of T:] is Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
the of T is Relation-like the of T -defined the of T -valued Function-like V29( the of T) V33( the of T, the of T) Element of bool [: the of T, the of T:]
[: the of T, the of T:] is Relation-like set
bool [: the of T, the of T:] is non empty cup-closed diff-closed preBoolean set
the of T is Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
( the carrier of T, the of T, the InternalRel of T, the of T, the of T) is () ()
t is ()
the carrier of t is set
the of t is set
the InternalRel of t is Relation-like the carrier of t -defined the carrier of t -valued Element of bool [: the carrier of t, the carrier of t:]
[: the carrier of t, the carrier of t:] is Relation-like set
bool [: the carrier of t, the carrier of t:] is non empty cup-closed diff-closed preBoolean set
the of t is Relation-like the of t -defined the of t -valued Function-like V29( the of t) V33( the of t, the of t) Element of bool [: the of t, the of t:]
[: the of t, the of t:] is Relation-like set
bool [: the of t, the of t:] is non empty cup-closed diff-closed preBoolean set
the of t is Relation-like the carrier of t -defined Fin the of t -valued Function-like V29( the carrier of t) V33( the carrier of t, Fin the of t) Element of bool [: the carrier of t,(Fin the of t):]
Fin the of t is non empty cup-closed diff-closed preBoolean set
[: the carrier of t,(Fin the of t):] is Relation-like set
bool [: the carrier of t,(Fin the of t):] is non empty cup-closed diff-closed preBoolean set
( the carrier of t, the of t, the InternalRel of t, the of t, the of t) is () ()
a is Element of the carrier of t
(t,a) is Element of bool the of t
bool the of t is non empty cup-closed diff-closed preBoolean set
the of t . a is set
t2 is Element of the of t
(t,t2) is Element of the of t
the of t . t2 is set
X is Element of the of T
(T,X) is Element of the of T
the of T . X is set
x is Element of the carrier of T
(T,x) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T . x is set
T is non empty ()
the carrier of T is non empty set
the of T is set
the InternalRel of T is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
[: the carrier of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
the of T is Relation-like the of T -defined the of T -valued Function-like V29( the of T) V33( the of T, the of T) Element of bool [: the of T, the of T:]
[: the of T, the of T:] is Relation-like set
bool [: the of T, the of T:] is non empty cup-closed diff-closed preBoolean set
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
( the carrier of T, the of T, the InternalRel of T, the of T, the of T) is non empty () ()
t is non empty ()
the carrier of t is non empty set
the of t is set
the InternalRel of t is Relation-like the carrier of t -defined the carrier of t -valued Element of bool [: the carrier of t, the carrier of t:]
[: the carrier of t, the carrier of t:] is non empty Relation-like set
bool [: the carrier of t, the carrier of t:] is non empty cup-closed diff-closed preBoolean set
the of t is Relation-like the of t -defined the of t -valued Function-like V29( the of t) V33( the of t, the of t) Element of bool [: the of t, the of t:]
[: the of t, the of t:] is Relation-like set
bool [: the of t, the of t:] is non empty cup-closed diff-closed preBoolean set
the of t is non empty Relation-like the carrier of t -defined Fin the of t -valued Function-like V29( the carrier of t) V33( the carrier of t, Fin the of t) Element of bool [: the carrier of t,(Fin the of t):]
Fin the of t is non empty cup-closed diff-closed preBoolean set
[: the carrier of t,(Fin the of t):] is non empty Relation-like set
bool [: the carrier of t,(Fin the of t):] is non empty cup-closed diff-closed preBoolean set
( the carrier of t, the of t, the InternalRel of t, the of t, the of t) is non empty () ()
BoolePoset the of T is non empty strict reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() up-complete /\-complete RelStr
(BoolePoset the of T) ~ is non empty strict reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() up-complete /\-complete RelStr
the carrier of (BoolePoset the of T) is non empty set
the InternalRel of (BoolePoset the of T) is Relation-like the carrier of (BoolePoset the of T) -defined the carrier of (BoolePoset the of T) -valued Element of bool [: the carrier of (BoolePoset the of T), the carrier of (BoolePoset the of T):]
[: the carrier of (BoolePoset the of T), the carrier of (BoolePoset the of T):] is non empty Relation-like set
bool [: the carrier of (BoolePoset the of T), the carrier of (BoolePoset the of T):] is non empty cup-closed diff-closed preBoolean set
the InternalRel of (BoolePoset the of T) ~ is Relation-like the carrier of (BoolePoset the of T) -defined the carrier of (BoolePoset the of T) -valued Element of bool [: the carrier of (BoolePoset the of T), the carrier of (BoolePoset the of T):]
RelStr(# the carrier of (BoolePoset the of T),( the InternalRel of (BoolePoset the of T) ~) #) is strict RelStr
the carrier of ((BoolePoset the of T) ~) is non empty set
[: the carrier of T, the carrier of ((BoolePoset the of T) ~):] is non empty Relation-like set
bool [: the carrier of T, the carrier of ((BoolePoset the of T) ~):] is non empty cup-closed diff-closed preBoolean set
BoolePoset the of t is non empty strict reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() up-complete /\-complete RelStr
(BoolePoset the of t) ~ is non empty strict reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() up-complete /\-complete RelStr
the carrier of (BoolePoset the of t) is non empty set
the InternalRel of (BoolePoset the of t) is Relation-like the carrier of (BoolePoset the of t) -defined the carrier of (BoolePoset the of t) -valued Element of bool [: the carrier of (BoolePoset the of t), the carrier of (BoolePoset the of t):]
[: the carrier of (BoolePoset the of t), the carrier of (BoolePoset the of t):] is non empty Relation-like set
bool [: the carrier of (BoolePoset the of t), the carrier of (BoolePoset the of t):] is non empty cup-closed diff-closed preBoolean set
the InternalRel of (BoolePoset the of t) ~ is Relation-like the carrier of (BoolePoset the of t) -defined the carrier of (BoolePoset the of t) -valued Element of bool [: the carrier of (BoolePoset the of t), the carrier of (BoolePoset the of t):]
RelStr(# the carrier of (BoolePoset the of t),( the InternalRel of (BoolePoset the of t) ~) #) is strict RelStr
the carrier of ((BoolePoset the of t) ~) is non empty set
[: the carrier of t, the carrier of ((BoolePoset the of t) ~):] is non empty Relation-like set
bool [: the carrier of t, the carrier of ((BoolePoset the of t) ~):] is non empty cup-closed diff-closed preBoolean set
a is non empty Relation-like the carrier of T -defined the carrier of ((BoolePoset the of T) ~) -valued Function-like V29( the carrier of T) V33( the carrier of T, the carrier of ((BoolePoset the of T) ~)) join-preserving Element of bool [: the carrier of T, the carrier of ((BoolePoset the of T) ~):]
RelStr(# the carrier of T, the InternalRel of T #) is strict RelStr
RelStr(# the carrier of t, the InternalRel of t #) is strict RelStr
t2 is non empty Relation-like the carrier of t -defined the carrier of ((BoolePoset the of t) ~) -valued Function-like V29( the carrier of t) V33( the carrier of t, the carrier of ((BoolePoset the of t) ~)) Element of bool [: the carrier of t, the carrier of ((BoolePoset the of t) ~):]
X is Element of the carrier of t
x is Element of the carrier of t
{X,x} is non empty finite Element of bool the carrier of t
bool the carrier of t is non empty cup-closed diff-closed preBoolean set
t2 .: {X,x} is finite Element of bool the carrier of ((BoolePoset the of t) ~)
bool the carrier of ((BoolePoset the of t) ~) is non empty cup-closed diff-closed preBoolean set
"\/" ((t2 .: {X,x}),((BoolePoset the of t) ~)) is Element of the carrier of ((BoolePoset the of t) ~)
"\/" ({X,x},t) is Element of the carrier of t
t2 . ("\/" ({X,x},t)) is Element of the carrier of ((BoolePoset the of t) ~)
y is Element of the carrier of T
t1 is Element of the carrier of T
{y,t1} is non empty finite Element of bool the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
a .: {y,t1} is finite Element of bool the carrier of ((BoolePoset the of T) ~)
bool the carrier of ((BoolePoset the of T) ~) is non empty cup-closed diff-closed preBoolean set
"\/" ((a .: {y,t1}),((BoolePoset the of T) ~)) is Element of the carrier of ((BoolePoset the of T) ~)
"\/" ({y,t1},T) is Element of the carrier of T
a . ("\/" ({y,t1},T)) is Element of the carrier of ((BoolePoset the of T) ~)
T is non empty reflexive transitive antisymmetric with_suprema ()
the carrier of T is non empty set
the of T is set
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
dom the of T is non empty Element of bool the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
BoolePoset the of T is non empty strict reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() up-complete /\-complete RelStr
InclPoset (bool the of T) is non empty strict reflexive transitive antisymmetric RelStr
RelIncl (bool the of T) is Relation-like bool the of T -defined bool the of T -valued V29( bool the of T) V33( bool the of T, bool the of T) reflexive antisymmetric transitive Element of bool [:(bool the of T),(bool the of T):]
[:(bool the of T),(bool the of T):] is non empty Relation-like set
bool [:(bool the of T),(bool the of T):] is non empty cup-closed diff-closed preBoolean set
RelStr(# (bool the of T),(RelIncl (bool the of T)) #) is strict RelStr
rng the of T is non empty Element of bool (Fin the of T)
bool (Fin the of T) is non empty cup-closed diff-closed preBoolean set
(BoolePoset the of T) ~ is non empty strict reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() up-complete /\-complete RelStr
the carrier of (BoolePoset the of T) is non empty set
the InternalRel of (BoolePoset the of T) is Relation-like the carrier of (BoolePoset the of T) -defined the carrier of (BoolePoset the of T) -valued Element of bool [: the carrier of (BoolePoset the of T), the carrier of (BoolePoset the of T):]
[: the carrier of (BoolePoset the of T), the carrier of (BoolePoset the of T):] is non empty Relation-like set
bool [: the carrier of (BoolePoset the of T), the carrier of (BoolePoset the of T):] is non empty cup-closed diff-closed preBoolean set
the InternalRel of (BoolePoset the of T) ~ is Relation-like the carrier of (BoolePoset the of T) -defined the carrier of (BoolePoset the of T) -valued Element of bool [: the carrier of (BoolePoset the of T), the carrier of (BoolePoset the of T):]
RelStr(# the carrier of (BoolePoset the of T),( the InternalRel of (BoolePoset the of T) ~) #) is strict RelStr
the carrier of ((BoolePoset the of T) ~) is non empty set
[: the carrier of T, the carrier of ((BoolePoset the of T) ~):] is non empty Relation-like set
bool [: the carrier of T, the carrier of ((BoolePoset the of T) ~):] is non empty cup-closed diff-closed preBoolean set
t2 is Element of the carrier of T
X is Element of the carrier of T
t2 "\/" X is Element of the carrier of T
(T,(t2 "\/" X)) is Element of bool the of T
the of T . (t2 "\/" X) is set
(T,t2) is Element of bool the of T
the of T . t2 is set
(T,X) is Element of bool the of T
the of T . X is set
(T,t2) /\ (T,X) is Element of bool the of T
a is non empty Relation-like the carrier of T -defined the carrier of ((BoolePoset the of T) ~) -valued Function-like V29( the carrier of T) V33( the carrier of T, the carrier of ((BoolePoset the of T) ~)) join-preserving Element of bool [: the carrier of T, the carrier of ((BoolePoset the of T) ~):]
a . t2 is Element of the carrier of ((BoolePoset the of T) ~)
a . X is Element of the carrier of ((BoolePoset the of T) ~)
(a . t2) "\/" (a . X) is Element of the carrier of ((BoolePoset the of T) ~)
~ (a . t2) is Element of the carrier of (BoolePoset the of T)
~ (a . X) is Element of the carrier of (BoolePoset the of T)
(~ (a . t2)) "/\" (~ (a . X)) is Element of the carrier of (BoolePoset the of T)
t is non empty Relation-like the carrier of T -defined the carrier of ((BoolePoset the of T) ~) -valued Function-like V29( the carrier of T) V33( the carrier of T, the carrier of ((BoolePoset the of T) ~)) Element of bool [: the carrier of T, the carrier of ((BoolePoset the of T) ~):]
a is Element of the carrier of T
t2 is Element of the carrier of T
a "\/" t2 is Element of the carrier of T
t . (a "\/" t2) is Element of the carrier of ((BoolePoset the of T) ~)
(T,(a "\/" t2)) is Element of bool the of T
the of T . (a "\/" t2) is set
(T,a) is Element of bool the of T
the of T . a is set
(T,t2) is Element of bool the of T
the of T . t2 is set
(T,a) /\ (T,t2) is Element of bool the of T
t . a is Element of the carrier of ((BoolePoset the of T) ~)
~ (t . a) is Element of the carrier of (BoolePoset the of T)
t . t2 is Element of the carrier of ((BoolePoset the of T) ~)
~ (t . t2) is Element of the carrier of (BoolePoset the of T)
(~ (t . a)) "/\" (~ (t . t2)) is Element of the carrier of (BoolePoset the of T)
(t . a) "\/" (t . t2) is Element of the carrier of ((BoolePoset the of T) ~)
T is non empty reflexive transitive antisymmetric with_suprema ()
the carrier of T is non empty set
the of T is set
bool the of T is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
a is Element of the carrier of T
(T,a) is Element of bool the of T
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . a is set
(T,t) is Element of bool the of T
the of T . t is set
t "\/" a is Element of the carrier of T
(T,t) /\ (T,a) is Element of bool the of T
T is ()
the of T is set
the carrier of T is set
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
t is Element of the of T
a is set
t2 is set
t2 is Element of bool the carrier of T
X is set
x is Element of the carrier of T
(T,x) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T is Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . x is set
dom the of T is Element of bool the carrier of T
a is Element of bool the carrier of T
t2 is Element of bool the carrier of T
T is non empty ()
the of T is set
bool the of T is non empty cup-closed diff-closed preBoolean set
the carrier of T is non empty set
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
t is Element of bool the of T
a is set
t2 is set
t2 is Element of bool the carrier of T
X is Element of the carrier of T
x is Element of the of T
(T,x) is Element of bool the carrier of T
y is Element of the carrier of T
a is Element of bool the carrier of T
t2 is Element of bool the carrier of T
X is set
x is Element of the of T
(T,x) is Element of bool the carrier of T
x is Element of the of T
(T,x) is Element of bool the carrier of T
T is ()
the carrier of T is set
the of T is set
the InternalRel of T is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
[: the carrier of T, the carrier of T:] is Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
the of T is Relation-like the of T -defined the of T -valued Function-like V29( the of T) V33( the of T, the of T) Element of bool [: the of T, the of T:]
[: the of T, the of T:] is Relation-like set
bool [: the of T, the of T:] is non empty cup-closed diff-closed preBoolean set
the of T is Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
( the carrier of T, the of T, the InternalRel of T, the of T, the of T) is () ()
t is ()
the carrier of t is set
the of t is set
the InternalRel of t is Relation-like the carrier of t -defined the carrier of t -valued Element of bool [: the carrier of t, the carrier of t:]
[: the carrier of t, the carrier of t:] is Relation-like set
bool [: the carrier of t, the carrier of t:] is non empty cup-closed diff-closed preBoolean set
the of t is Relation-like the of t -defined the of t -valued Function-like V29( the of t) V33( the of t, the of t) Element of bool [: the of t, the of t:]
[: the of t, the of t:] is Relation-like set
bool [: the of t, the of t:] is non empty cup-closed diff-closed preBoolean set
the of t is Relation-like the carrier of t -defined Fin the of t -valued Function-like V29( the carrier of t) V33( the carrier of t, Fin the of t) Element of bool [: the carrier of t,(Fin the of t):]
Fin the of t is non empty cup-closed diff-closed preBoolean set
[: the carrier of t,(Fin the of t):] is Relation-like set
bool [: the carrier of t,(Fin the of t):] is non empty cup-closed diff-closed preBoolean set
( the carrier of t, the of t, the InternalRel of t, the of t, the of t) is () ()
a is Element of the of T
(T,a) is Element of bool the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
t2 is Element of the of t
(t,t2) is Element of bool the carrier of t
bool the carrier of t is non empty cup-closed diff-closed preBoolean set
X is set
x is Element of the carrier of T
(T,x) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T . x is set
y is Element of the carrier of t
(t,y) is Element of bool the of t
bool the of t is non empty cup-closed diff-closed preBoolean set
the of t . y is set
x is Element of the carrier of t
(t,x) is Element of bool the of t
the of t . x is set
y is Element of the carrier of T
(T,y) is Element of bool the of T
the of T . y is set
T is non empty ()
the of T is set
the carrier of T is non empty set
t is Element of the of T
(T,t) is Element of bool the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
{ b1 where b1 is Element of the carrier of T : t in (T,b1) } is set
t2 is set
X is Element of the carrier of T
(T,X) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . X is set
t2 is Element of bool the carrier of T
X is set
x is set
y is Element of the carrier of T
(T,y) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . y is set
T is ()
the carrier of T is set
the of T is set
t is Element of the carrier of T
(T,t) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T is Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . t is set
a is Element of the of T
(T,a) is Element of bool the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
t2 is Element of the carrier of T
(T,t2) is Element of bool the of T
the of T . t2 is set
T is non empty ()
the carrier of T is non empty set
the of T is set
bool the of T is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
(T,t) is Element of bool the of T
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . t is set
a is Element of bool the of T
(T,a) is Element of bool the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
t2 is Element of the of T
(T,t2) is Element of bool the carrier of T
t2 is set
X is Element of the of T
(T,X) is Element of bool the carrier of T
T is () ()
the carrier of T is set
the of T is non empty set
t is Element of the carrier of T
(T,t) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T is Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . t is set
{ b1 where b1 is Element of the of T : t in (T,b1) } is set
t2 is set
X is Element of the of T
(T,X) is Element of bool the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
t2 is set
X is Element of the of T
(T,X) is Element of bool the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
T is non empty ()
the of T is set
{} the of T is empty V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
(T,({} the of T)) is Element of bool the carrier of T
the carrier of T is non empty set
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
t is set
a is Element of the carrier of T
t2 is Element of the of T
(T,t2) is Element of bool the carrier of T
T is ()
the carrier of T is set
the of T is set
the InternalRel of T is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
[: the carrier of T, the carrier of T:] is Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
the of T is Relation-like the of T -defined the of T -valued Function-like V29( the of T) V33( the of T, the of T) Element of bool [: the of T, the of T:]
[: the of T, the of T:] is Relation-like set
bool [: the of T, the of T:] is non empty cup-closed diff-closed preBoolean set
the of T is Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
( the carrier of T, the of T, the InternalRel of T, the of T, the of T) is () ()
t is ()
the carrier of t is set
the of t is set
the InternalRel of t is Relation-like the carrier of t -defined the carrier of t -valued Element of bool [: the carrier of t, the carrier of t:]
[: the carrier of t, the carrier of t:] is Relation-like set
bool [: the carrier of t, the carrier of t:] is non empty cup-closed diff-closed preBoolean set
the of t is Relation-like the of t -defined the of t -valued Function-like V29( the of t) V33( the of t, the of t) Element of bool [: the of t, the of t:]
[: the of t, the of t:] is Relation-like set
bool [: the of t, the of t:] is non empty cup-closed diff-closed preBoolean set
the of t is Relation-like the carrier of t -defined Fin the of t -valued Function-like V29( the carrier of t) V33( the carrier of t, Fin the of t) Element of bool [: the carrier of t,(Fin the of t):]
Fin the of t is non empty cup-closed diff-closed preBoolean set
[: the carrier of t,(Fin the of t):] is Relation-like set
bool [: the carrier of t,(Fin the of t):] is non empty cup-closed diff-closed preBoolean set
( the carrier of t, the of t, the InternalRel of t, the of t, the of t) is () ()
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
bool the carrier of t is non empty cup-closed diff-closed preBoolean set
a is Element of the of t
(t,a) is Element of bool the carrier of t
(t,a) is Element of the of t
the of t . a is set
(t,(t,a)) is Element of bool the carrier of t
(t,a) \/ (t,(t,a)) is Element of bool the carrier of t
t2 is Element of the of T
(T,t2) is Element of bool the carrier of T
(T,t2) is Element of the of T
the of T . t2 is set
(T,(T,t2)) is Element of bool the carrier of T
(T,t2) \/ (T,(T,t2)) is Element of bool the carrier of T
{0} is non empty trivial finite V40() 1 -element Element of bool NAT
{0,1} is non empty finite V40() Element of bool NAT
Fin {0,1} is non empty cup-closed diff-closed preBoolean set
the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr is non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr
[:{0,1},{0,1}:] is non empty Relation-like finite set
bool [:{0,1},{0,1}:] is non empty cup-closed diff-closed preBoolean finite V40() set
a is finite Element of {0,1}
t is finite Element of {0,1}
(0,1) --> (a,t) is non empty Relation-like {0,1} -defined {0,1} -valued Function-like V29({0,1}) V33({0,1},{0,1}) finite Element of bool [:{0,1},{0,1}:]
{0,1} is non empty finite V40() set
[:{0,1},{0,1}:] is non empty Relation-like finite set
bool [:{0,1},{0,1}:] is non empty cup-closed diff-closed preBoolean finite V40() set
the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr is non empty trivial finite 1 -element set
T is finite Element of Fin {0,1}
the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr --> T is non empty Relation-like the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr -defined Fin {0,1} -valued Function-like V29( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ) V33( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr , Fin {0,1}) finite Element of bool [: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,(Fin {0,1}):]
[: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,(Fin {0,1}):] is non empty Relation-like set
bool [: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,(Fin {0,1}):] is non empty cup-closed diff-closed preBoolean set
the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr is Relation-like the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr -defined the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr -valued finite co-well_founded Element of bool [: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr , the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr :]
[: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr , the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr :] is non empty Relation-like finite set
bool [: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr , the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr :] is non empty cup-closed diff-closed preBoolean finite V40() set
X is non empty Relation-like {0,1} -defined {0,1} -valued Function-like V29({0,1}) V33({0,1},{0,1}) finite Element of bool [:{0,1},{0,1}:]
( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,{0,1}, the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,X,( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr --> T)) is non empty () () ()
the carrier of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,{0,1}, the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,X,( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr --> T)) is non empty set
the InternalRel of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,{0,1}, the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,X,( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr --> T)) is Relation-like the carrier of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,{0,1}, the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,X,( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr --> T)) -defined the carrier of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,{0,1}, the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,X,( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr --> T)) -valued Element of bool [: the carrier of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,{0,1}, the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,X,( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr --> T)), the carrier of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,{0,1}, the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,X,( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr --> T)):]
[: the carrier of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,{0,1}, the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,X,( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr --> T)), the carrier of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,{0,1}, the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,X,( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr --> T)):] is non empty Relation-like set
bool [: the carrier of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,{0,1}, the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,X,( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr --> T)), the carrier of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,{0,1}, the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,X,( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr --> T)):] is non empty cup-closed diff-closed preBoolean set
RelStr(# the carrier of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,{0,1}, the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,X,( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr --> T)), the InternalRel of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,{0,1}, the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr ,X,( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr --> T)) #) is strict RelStr
RelStr(# the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr , the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () RelStr #) is strict RelStr
t1 is non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ()
X . a is finite Element of {0,1}
X . t is finite Element of {0,1}
the carrier of t1 is non empty trivial finite 1 -element set
the of t1 is set
t2 is Element of the carrier of t1
(t1,t2) is Element of bool the of t1
bool the of t1 is non empty cup-closed diff-closed preBoolean set
the of t1 is non empty Relation-like the carrier of t1 -defined Fin the of t1 -valued Function-like V29( the carrier of t1) V33( the carrier of t1, Fin the of t1) finite Element of bool [: the carrier of t1,(Fin the of t1):]
Fin the of t1 is non empty cup-closed diff-closed preBoolean set
[: the carrier of t1,(Fin the of t1):] is non empty Relation-like set
bool [: the carrier of t1,(Fin the of t1):] is non empty cup-closed diff-closed preBoolean set
the of t1 . t2 is set
v2 is Element of the of t1
(t1,v2) is Element of the of t1
the of t1 is Relation-like the of t1 -defined the of t1 -valued Function-like V29( the of t1) V33( the of t1, the of t1) Element of bool [: the of t1, the of t1:]
[: the of t1, the of t1:] is Relation-like set
bool [: the of t1, the of t1:] is non empty cup-closed diff-closed preBoolean set
the of t1 . v2 is set
the Element of the carrier of t1 is Element of the carrier of t1
a3 is Element of the carrier of t1
(t1,a3) is Element of bool the of t1
the of t1 . a3 is set
v2 is Element of the carrier of t1
(t1,v2) is Element of bool the of t1
the of t1 . v2 is set
v2 "\/" a3 is Element of the carrier of t1
(t1,(v2 "\/" a3)) is Element of bool the of t1
the of t1 . (v2 "\/" a3) is set
(t1,v2) /\ (t1,a3) is Element of bool the of t1
bool the carrier of t1 is non empty cup-closed diff-closed preBoolean finite V40() set
v2 is Element of the of t1
(t1,v2) is trivial finite Element of bool the carrier of t1
(t1,v2) is Element of the of t1
the of t1 . v2 is set
(t1,(t1,v2)) is trivial finite Element of bool the carrier of t1
(t1,v2) \/ (t1,(t1,v2)) is trivial finite Element of bool the carrier of t1
(t1, the Element of the carrier of t1) is Element of bool the of t1
the of t1 . the Element of the carrier of t1 is set
T is () ()
the of T is set
t is Element of the of T
(T,t) is Element of bool the carrier of T
the carrier of T is set
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,t) is Element of the of T
the of T is Relation-like the of T -defined the of T -valued Function-like V29( the of T) V33( the of T, the of T) Element of bool [: the of T, the of T:]
[: the of T, the of T:] is Relation-like set
bool [: the of T, the of T:] is non empty cup-closed diff-closed preBoolean set
the of T . t is set
(T,(T,t)) is Element of bool the carrier of T
a is set
t2 is Element of the carrier of T
(T,t2) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T is Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . t2 is set
X is Element of the carrier of T
(T,X) is Element of bool the of T
the of T . X is set
T is non empty reflexive transitive antisymmetric with_suprema () ()
the of T is set
t is Element of the of T
(T,t) is Element of bool the carrier of T
the carrier of T is non empty set
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
a is Element of the carrier of T
t2 is Element of the carrier of T
(T,a) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . a is set
(T,t2) is Element of bool the of T
the of T . t2 is set
a is Element of the carrier of T
t2 is Element of the carrier of T
a "\/" t2 is Element of the carrier of T
(T,t2) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . t2 is set
(T,a) is Element of bool the of T
the of T . a is set
(T,a) /\ (T,t2) is Element of bool the of T
(T,(a "\/" t2)) is Element of bool the of T
the of T . (a "\/" t2) is set
T is non empty reflexive transitive antisymmetric with_suprema () ()
the of T is set
bool the of T is non empty cup-closed diff-closed preBoolean set
t is Element of bool the of T
(T,t) is Element of bool the carrier of T
the carrier of T is non empty set
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
a is Element of the carrier of T
t2 is Element of the carrier of T
X is Element of the of T
(T,X) is directed lower Element of bool the carrier of T
(T,a) is Element of bool the of T
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . a is set
(T,t2) is Element of bool the of T
the of T . t2 is set
a is Element of the carrier of T
t2 is Element of the carrier of T
a "\/" t2 is Element of the carrier of T
X is Element of the of T
(T,X) is directed lower Element of bool the carrier of T
(T,t2) is Element of bool the of T
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . t2 is set
(T,a) is Element of bool the of T
the of T . a is set
(T,a) /\ (T,t2) is Element of bool the of T
(T,(a "\/" t2)) is Element of bool the of T
the of T . (a "\/" t2) is set
T is ()
the carrier of T is set
the of T is set
T is ()
the carrier of T is set
the of T is set
bool the of T is non empty cup-closed diff-closed preBoolean set
T is non empty reflexive transitive antisymmetric with_suprema () ()
the of T is set
the carrier of T is non empty set
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
t is Element of the of T
(T,t) is directed lower Element of bool the carrier of T
a is Element of the carrier of T
downarrow a is non empty directed lower Element of bool the carrier of T
{a} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {a} is non empty lower Element of bool the carrier of T
(T,t) /\ (downarrow a) is Element of bool the carrier of T
t2 is Element of the carrier of T
T is non empty reflexive transitive ()
the carrier of T is non empty set
the of T is set
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
a is Element of the of T
(T,a) is Element of bool the carrier of T
t is Element of the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow t)),T) is Element of the carrier of T
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () ()
the carrier of T is non empty set
the of T is set
t is Element of the carrier of T
a is Element of the of T
(T,t,a) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,a) is directed lower Element of bool the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow t)),T) is Element of the carrier of T
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () ()
the carrier of T is non empty set
the of T is set
t is Element of the carrier of T
a is Element of the of T
(T,t,a) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,a) is directed lower Element of bool the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow t)),T) is Element of the carrier of T
(T,(T,t,a)) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . (T,t,a) is set
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () ()
the carrier of T is non empty set
the of T is set
t is Element of the carrier of T
a is Element of the of T
(T,t,a) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,a) is directed lower Element of bool the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow t)),T) is Element of the carrier of T
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () ()
the carrier of T is non empty set
the of T is set
t is Element of the carrier of T
a is Element of the of T
(T,t,a) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,a) is directed lower Element of bool the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow t)),T) is Element of the carrier of T
t2 is Element of the carrier of T
(T,t2) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . t2 is set
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () ()
the carrier of T is non empty set
the of T is set
t is Element of the carrier of T
(T,t) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . t is set
a is Element of the of T
(T,t,a) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,a) is directed lower Element of bool the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow t)),T) is Element of the carrier of T
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () ()
the carrier of T is non empty set
the of T is set
t is Element of the carrier of T
a is Element of the of T
(T,t,a) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,a) is directed lower Element of bool the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow t)),T) is Element of the carrier of T
t2 is Element of the of T
(T,t,t2) is Element of the carrier of T
(T,t2) is directed lower Element of bool the carrier of T
(T,t2) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,t2) /\ (downarrow t)),T) is Element of the carrier of T
(T,(T,t,t2),a) is Element of the carrier of T
downarrow (T,t,t2) is non empty directed lower Element of bool the carrier of T
{(T,t,t2)} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {(T,t,t2)} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow (T,t,t2)) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow (T,t,t2))),T) is Element of the carrier of T
(T,(T,t,a),t2) is Element of the carrier of T
downarrow (T,t,a) is non empty directed lower Element of bool the carrier of T
{(T,t,a)} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {(T,t,a)} is non empty lower Element of bool the carrier of T
(T,t2) /\ (downarrow (T,t,a)) is Element of bool the carrier of T
"\/" (((T,t2) /\ (downarrow (T,t,a))),T) is Element of the carrier of T
X is Element of the carrier of T
(T,X) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . X is set
x is Element of the carrier of T
(T,x) is Element of bool the of T
the of T . x is set
(T,(T,(T,t,t2),a)) is Element of bool the of T
the of T . (T,(T,t,t2),a) is set
x is Element of the carrier of T
T is non empty reflexive transitive antisymmetric with_suprema () ()
the of T is set
bool the of T is non empty cup-closed diff-closed preBoolean set
the carrier of T is non empty set
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
t is Element of bool the of T
(T,t) is directed lower Element of bool the carrier of T
a is Element of the carrier of T
downarrow a is non empty directed lower Element of bool the carrier of T
{a} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {a} is non empty lower Element of bool the carrier of T
(T,t) /\ (downarrow a) is Element of bool the carrier of T
t2 is Element of the carrier of T
(T,t2) is Element of bool the of T
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . t2 is set
T is non empty reflexive transitive ()
the carrier of T is non empty set
the of T is set
bool the of T is non empty cup-closed diff-closed preBoolean set
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
a is Element of bool the of T
(T,a) is Element of bool the carrier of T
t is Element of the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow t)),T) is Element of the carrier of T
T is non empty reflexive transitive antisymmetric ()
the carrier of T is non empty set
the of T is set
{} the of T is empty V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
(T,t,({} the of T)) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,({} the of T)) is Element of bool the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,({} the of T)) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,({} the of T)) /\ (downarrow t)),T) is Element of the carrier of T
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
len a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len a) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
t is Element of the carrier of T
dom a is finite Element of bool NAT
t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
a . t2 is set
rng a is finite Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
x is set
X is Element of the of T
y is Element of the carrier of T
X is Element of the of T
(T,y,X) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,X) is Element of bool the carrier of T
downarrow y is non empty directed lower Element of bool the carrier of T
{y} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {y} is non empty lower Element of bool the carrier of T
(T,X) /\ (downarrow y) is Element of bool the carrier of T
"\/" (((T,X) /\ (downarrow y)),T) is Element of the carrier of T
t2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
t2 . 1 is set
dom t2 is finite Element of bool NAT
X is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
t2 . X is set
X + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
0 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
a . X is set
t2 . (X + 1) is set
x is Element of the of T
y is Element of the carrier of T
(T,y,x) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,x) is Element of bool the carrier of T
downarrow y is non empty directed lower Element of bool the carrier of T
{y} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {y} is non empty lower Element of bool the carrier of T
(T,x) /\ (downarrow y) is Element of bool the carrier of T
"\/" (((T,x) /\ (downarrow y)),T) is Element of the carrier of T
t2 . 0 is set
rng t2 is finite set
X is set
x is set
t2 . x is set
X is Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len X is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
X . 1 is set
x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
a . x is set
X . x is set
x + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
X . (x + 1) is set
y is Element of the of T
t1 is Element of the carrier of T
(T,t1,y) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,y) is Element of bool the carrier of T
downarrow t1 is non empty directed lower Element of bool the carrier of T
{t1} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t1} is non empty lower Element of bool the carrier of T
(T,y) /\ (downarrow t1) is Element of bool the carrier of T
"\/" (((T,y) /\ (downarrow t1)),T) is Element of the carrier of T
t2 is Element of the of T
v2 is Element of the carrier of T
(T,v2,t2) is Element of the carrier of T
(T,t2) is Element of bool the carrier of T
downarrow v2 is non empty directed lower Element of bool the carrier of T
{v2} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {v2} is non empty lower Element of bool the carrier of T
(T,t2) /\ (downarrow v2) is Element of bool the carrier of T
"\/" (((T,t2) /\ (downarrow v2)),T) is Element of the carrier of T
t2 is Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
t2 . 1 is set
X is Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len X is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
X . 1 is set
dom t2 is finite Element of bool NAT
x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
t2 . x is set
X . x is set
x + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
t2 . (x + 1) is set
X . (x + 1) is set
0 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
a . x is set
t2 . (x + 1) is set
t1 is Element of the carrier of T
y is Element of the of T
(T,t1,y) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,y) is Element of bool the carrier of T
downarrow t1 is non empty directed lower Element of bool the carrier of T
{t1} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t1} is non empty lower Element of bool the carrier of T
(T,y) /\ (downarrow t1) is Element of bool the carrier of T
"\/" (((T,y) /\ (downarrow t1)),T) is Element of the carrier of T
X . (x + 1) is set
t2 . (x + 1) is set
X . (x + 1) is set
t2 . (x + 1) is set
X . (x + 1) is set
t2 . 0 is set
X . 0 is set
dom X is finite Element of bool NAT
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
(T,t,a) is Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len (T,t,a) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
len a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len a) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
<*> the of T is empty proper V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined the of T -valued Function-like functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() FinSequence of the of T
[:NAT, the of T:] is non empty non trivial Relation-like non finite set
t is Element of the carrier of T
(T,t,(<*> the of T)) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
<*t*> is non empty trivial Relation-like NAT -defined the carrier of T -valued Function-like finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of T
[1,t] is set
{1,t} is non empty finite set
{{1,t},{1}} is non empty finite V40() set
{[1,t]} is non empty trivial Relation-like finite 1 -element set
(T,t,(<*> the of T)) . 1 is set
len (T,t,(<*> the of T)) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
0 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Element of the of T
<*a*> is non empty trivial Relation-like NAT -defined the of T -valued Function-like finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the of T
[1,a] is set
{1,a} is non empty finite set
{{1,a},{1}} is non empty finite V40() set
{[1,a]} is non empty trivial Relation-like finite 1 -element set
(T,t,<*a*>) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(T,t,a) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,a) is Element of bool the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow t)),T) is Element of the carrier of T
<*t,(T,t,a)*> is non empty non trivial Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like set
<*t*> is non empty trivial Relation-like NAT -defined Function-like finite 1 -element FinSequence-like FinSubsequence-like set
[1,t] is set
{1,t} is non empty finite set
{{1,t},{1}} is non empty finite V40() set
{[1,t]} is non empty trivial Relation-like finite 1 -element set
<*(T,t,a)*> is non empty trivial Relation-like NAT -defined Function-like finite 1 -element FinSequence-like FinSubsequence-like set
[1,(T,t,a)] is set
{1,(T,t,a)} is non empty finite set
{{1,(T,t,a)},{1}} is non empty finite V40() set
{[1,(T,t,a)]} is non empty trivial Relation-like finite 1 -element set
<*t*> ^ <*(T,t,a)*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like set
1 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
<*a*> . 1 is set
(T,t,<*a*>) . 1 is set
len <*a*> is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
len (T,t,<*a*>) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
1 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
dom <*a*> is non empty trivial finite 1 -element Element of bool NAT
(len <*a*>) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,<*a*>) . ((len <*a*>) + 1) is set
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
(T,t,a) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len a) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,a) . ((len a) + 1) is set
len (T,t,a) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
dom (T,t,a) is non empty finite Element of bool NAT
T is non empty reflexive transitive () ()
the carrier of T is non empty set
t is Element of the carrier of T
the of T is non empty set
<*> the of T is empty proper V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined the of T -valued Function-like functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() FinSequence of the of T
[:NAT, the of T:] is non empty non trivial Relation-like non finite set
(T,t,(<*> the of T)) is Element of the carrier of T
(T,t,(<*> the of T)) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len (<*> the of T) is empty V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() Element of NAT
(len (<*> the of T)) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,(<*> the of T)) . ((len (<*> the of T)) + 1) is set
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Element of the of T
<*a*> is non empty trivial Relation-like NAT -defined the of T -valued Function-like finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the of T
[1,a] is set
{1,a} is non empty finite set
{{1,a},{1}} is non empty finite V40() set
{[1,a]} is non empty trivial Relation-like finite 1 -element set
(T,t,<*a*>) is Element of the carrier of T
(T,t,<*a*>) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len <*a*> is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(len <*a*>) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,<*a*>) . ((len <*a*>) + 1) is set
(T,t,a) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,a) is Element of bool the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow t)),T) is Element of the carrier of T
<*t,(T,t,a)*> is non empty non trivial Relation-like NAT -defined Function-like finite 2 -element FinSequence-like FinSubsequence-like set
<*t*> is non empty trivial Relation-like NAT -defined Function-like finite 1 -element FinSequence-like FinSubsequence-like set
[1,t] is set
{1,t} is non empty finite set
{{1,t},{1}} is non empty finite V40() set
{[1,t]} is non empty trivial Relation-like finite 1 -element set
<*(T,t,a)*> is non empty trivial Relation-like NAT -defined Function-like finite 1 -element FinSequence-like FinSubsequence-like set
[1,(T,t,a)] is set
{1,(T,t,a)} is non empty finite set
{{1,(T,t,a)},{1}} is non empty finite V40() set
{[1,(T,t,a)]} is non empty trivial Relation-like finite 1 -element set
<*t*> ^ <*(T,t,a)*> is non empty Relation-like NAT -defined Function-like finite 1 + 1 -element FinSequence-like FinSubsequence-like set
1 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
T is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len T is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
t is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
T $^ t is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
(T $^ t) . a is set
T . a is set
t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
t2 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
X is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
Seg t2 is finite t2 -element Element of bool NAT
{ b1 where b1 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT : ( 1 <= b1 & b1 <= t2 ) } is set
T | (Seg t2) is Relation-like Seg t2 -defined NAT -defined finite FinSubsequence-like set
X ^ t is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
T . (len T) is set
<*(T . (len T))*> is non empty trivial Relation-like NAT -defined Function-like finite 1 -element FinSequence-like FinSubsequence-like set
[1,(T . (len T))] is set
{1,(T . (len T))} is non empty finite set
{{1,(T . (len T))},{1}} is non empty finite V40() set
{[1,(T . (len T))]} is non empty trivial Relation-like finite 1 -element set
X ^ <*(T . (len T))*> is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len X is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
dom X is finite Element of bool NAT
X . a is set
T is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len T is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
t is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len t is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
T $^ t is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
(len T) + a is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T $^ t) . ((len T) + a) is set
a + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
t . (a + 1) is set
t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
t2 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
X is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
Seg t2 is finite t2 -element Element of bool NAT
{ b1 where b1 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT : ( 1 <= b1 & b1 <= t2 ) } is set
T | (Seg t2) is Relation-like Seg t2 -defined NAT -defined finite FinSubsequence-like set
X ^ t is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom t is finite Element of bool NAT
len X is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len X) + (a + 1) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
a ^ t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
(T,t,(a ^ t2)) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(T,t,a) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(T,t,a) is Element of the carrier of T
len a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len a) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,a) . ((len a) + 1) is set
(T,(T,t,a),t2) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(T,t,a) $^ (T,(T,t,a),t2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
X is Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
x is Element of the carrier of T
<*x*> is non empty trivial Relation-like NAT -defined the carrier of T -valued Function-like finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of T
[1,x] is set
{1,x} is non empty finite set
{{1,x},{1}} is non empty finite V40() set
{[1,x]} is non empty trivial Relation-like finite 1 -element set
X ^ <*x*> is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len (T,t,a) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
X ^ (T,(T,t,a),t2) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len <*x*> is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
len X is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len X) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
((T,t,a) $^ (T,(T,t,a),t2)) . 1 is set
0 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
dom X is finite Element of bool NAT
X . 1 is set
(T,t,a) . 1 is set
len (a ^ t2) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
len t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len a) + (len t2) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
len (T,(T,t,a),t2) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(len t2) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
dom (a ^ t2) is finite Element of bool NAT
v2 is Element of the of T
(a ^ t2) . t2 is set
a3 is Element of the carrier of T
((T,t,a) $^ (T,(T,t,a),t2)) . t2 is set
t2 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
dom X is finite Element of bool NAT
((T,t,a) $^ (T,(T,t,a),t2)) . (t2 + 1) is set
X . (t2 + 1) is set
X . t2 is set
(T,t,a) . (t2 + 1) is set
(T,t,a) . t2 is set
dom a is finite Element of bool NAT
a . t2 is set
(T,a3,v2) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,v2) is Element of bool the carrier of T
downarrow a3 is non empty directed lower Element of bool the carrier of T
{a3} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {a3} is non empty lower Element of bool the carrier of T
(T,v2) /\ (downarrow a3) is Element of bool the carrier of T
"\/" (((T,v2) /\ (downarrow a3)),T) is Element of the carrier of T
dom (T,(T,t,a),t2) is non empty finite Element of bool NAT
t2 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
((T,t,a) $^ (T,(T,t,a),t2)) . (t2 + 1) is set
(T,(T,t,a),t2) . 1 is set
dom X is finite Element of bool NAT
X . t2 is set
(T,t,a) . t2 is set
dom a is finite Element of bool NAT
a . t2 is set
(T,a3,v2) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,v2) is Element of bool the carrier of T
downarrow a3 is non empty directed lower Element of bool the carrier of T
{a3} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {a3} is non empty lower Element of bool the carrier of T
(T,v2) /\ (downarrow a3) is Element of bool the carrier of T
"\/" (((T,v2) /\ (downarrow a3)),T) is Element of the carrier of T
c12 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
((len a) + 1) + c12 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
1 + c12 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(1 + c12) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
c12 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(c12 + 1) + (len a) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
((c12 + 1) + (len a)) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(c12 + 1) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
((c12 + 1) + 1) + (len a) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(1 + c12) + 0 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
dom (T,(T,t,a),t2) is non empty finite Element of bool NAT
(T,(T,t,a),t2) . (c12 + 1) is set
t2 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
((T,t,a) $^ (T,(T,t,a),t2)) . (t2 + 1) is set
(T,(T,t,a),t2) . ((c12 + 1) + 1) is set
dom t2 is finite Element of bool NAT
t2 . (c12 + 1) is set
(T,a3,v2) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,v2) is Element of bool the carrier of T
downarrow a3 is non empty directed lower Element of bool the carrier of T
{a3} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {a3} is non empty lower Element of bool the carrier of T
(T,v2) /\ (downarrow a3) is Element of bool the carrier of T
"\/" (((T,v2) /\ (downarrow a3)),T) is Element of the carrier of T
len ((T,t,a) $^ (T,(T,t,a),t2)) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len X) + ((len t2) + 1) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
((len a) + (len t2)) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(len (a ^ t2)) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
dom a is finite Element of bool NAT
t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
a ^ t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
(T,t,(a ^ t2)) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(T,t,a) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
x is Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
y is Element of the carrier of T
<*y*> is non empty trivial Relation-like NAT -defined the carrier of T -valued Function-like finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of T
[1,y] is set
{1,y} is non empty finite set
{{1,y},{1}} is non empty finite V40() set
{[1,y]} is non empty trivial Relation-like finite 1 -element set
x ^ <*y*> is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
t1 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
(T,t,(a ^ t2)) . t1 is set
(T,t,a) . t1 is set
len (T,t,a) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
len a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len a) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
len <*y*> is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
len x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len x) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
dom x is finite Element of bool NAT
(T,t,a) is Element of the carrier of T
(T,t,a) . ((len a) + 1) is set
(T,(T,t,a),t2) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(T,t,a) $^ (T,(T,t,a),t2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
x ^ (T,(T,t,a),t2) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
x . t1 is set
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
a ^ t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
(T,t,(a ^ t2)) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len a) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,(a ^ t2)) . ((len a) + 1) is set
(T,t,a) is Element of the carrier of T
(T,t,a) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(T,t,a) . ((len a) + 1) is set
(T,(T,t,a),t2) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len (T,(T,t,a),t2) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
len t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len t2) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,a) $^ (T,(T,t,a),t2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (T,t,a) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
((len a) + 1) + 0 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,(a ^ t2)) . (((len a) + 1) + 0) is set
0 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,(T,t,a),t2) . (0 + 1) is set
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
(T,t,a) is Element of the carrier of T
(T,t,a) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len a) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,a) . ((len a) + 1) is set
t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
(T,(T,t,a),t2) is Element of the carrier of T
(T,(T,t,a),t2) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len t2) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,(T,t,a),t2) . ((len t2) + 1) is set
a ^ t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
(T,t,(a ^ t2)) is Element of the carrier of T
(T,t,(a ^ t2)) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len (a ^ t2) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len (a ^ t2)) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,(a ^ t2)) . ((len (a ^ t2)) + 1) is set
x is Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
y is Element of the carrier of T
<*y*> is non empty trivial Relation-like NAT -defined the carrier of T -valued Function-like finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of T
[1,y] is set
{1,y} is non empty finite set
{{1,y},{1}} is non empty finite V40() set
{[1,y]} is non empty trivial Relation-like finite 1 -element set
x ^ <*y*> is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len (T,t,a) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
len <*y*> is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
len x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len x) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
len (T,(T,t,a),t2) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
dom (T,(T,t,a),t2) is non empty finite Element of bool NAT
(T,t,a) $^ (T,(T,t,a),t2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
x ^ (T,(T,t,a),t2) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(len x) + ((len t2) + 1) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,(a ^ t2)) . ((len x) + ((len t2) + 1)) is set
(len a) + (len t2) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
((len a) + (len t2)) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,(a ^ t2)) . (((len a) + (len t2)) + 1) is set
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
<*> the of T is empty proper V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined the of T -valued Function-like functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() FinSequence of the of T
[:NAT, the of T:] is non empty non trivial Relation-like non finite set
t is Element of the carrier of T
a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
dom (<*> the of T) is empty proper V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() Element of bool NAT
(<*> the of T) . a is finite set
(T,t,(<*> the of T)) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(T,t,(<*> the of T)) . a is set
t2 is Element of the of T
X is Element of the carrier of T
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Element of the of T
<*a*> is non empty trivial Relation-like NAT -defined the of T -valued Function-like finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the of T
[1,a] is set
{1,a} is non empty finite set
{{1,a},{1}} is non empty finite V40() set
{[1,a]} is non empty trivial Relation-like finite 1 -element set
<*a*> . 1 is set
X is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
dom <*a*> is non empty trivial finite 1 -element Element of bool NAT
<*a*> . X is set
(T,t,<*a*>) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(T,t,<*a*>) . X is set
x is Element of the of T
y is Element of the carrier of T
dom <*a*> is non empty trivial finite 1 -element Element of bool NAT
(T,t,<*a*>) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len <*a*> is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,<*a*>) . 1 is set
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
a ^ t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
(T,t,a) is Element of the carrier of T
(T,t,a) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len a) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,a) . ((len a) + 1) is set
(T,t,(a ^ t2)) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(T,(T,t,a),t2) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(T,t,a) $^ (T,(T,t,a),t2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (T,(T,t,a),t2) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
len t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len t2) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
dom (a ^ t2) is finite Element of bool NAT
dom a is finite Element of bool NAT
x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
y is Element of the of T
a . x is set
t1 is Element of the carrier of T
(T,t,a) . x is set
(a ^ t2) . x is set
(T,t,(a ^ t2)) . x is set
x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
dom t2 is finite Element of bool NAT
t2 . x is set
(T,(T,t,a),t2) . x is set
y is Element of the of T
t1 is Element of the carrier of T
(len a) + x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(a ^ t2) . ((len a) + x) is set
t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
1 + t2 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
len (T,t,a) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(len (T,t,a)) + t2 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,(a ^ t2)) . ((len a) + x) is set
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
len a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len a) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,a) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
dom a is finite Element of bool NAT
t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
X is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
(T,t,a) . t2 is set
(T,t,a) . X is set
x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
t2 + x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
y is Element of the carrier of T
t1 is Element of the carrier of T
len (T,t,a) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
t2 + t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(T,t,a) . (t2 + t2) is set
t2 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
t2 + (t2 + 1) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,a) . (t2 + (t2 + 1)) is set
(t2 + t2) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
a . (t2 + t2) is set
rng a is finite Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
dom (T,t,a) is non empty finite Element of bool NAT
rng (T,t,a) is non empty finite Element of bool the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,t,a) . ((t2 + t2) + 1) is set
a3 is Element of the carrier of T
v2 is Element of the of T
(T,a3,v2) is Element of the carrier of T
(T,v2) is directed lower Element of bool the carrier of T
downarrow a3 is non empty directed lower Element of bool the carrier of T
{a3} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {a3} is non empty lower Element of bool the carrier of T
(T,v2) /\ (downarrow a3) is Element of bool the carrier of T
"\/" (((T,v2) /\ (downarrow a3)),T) is Element of the carrier of T
c12 is Element of the carrier of T
t2 + 0 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(T,t,a) . (t2 + 0) is set
t2 is Element of the carrier of T
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
(T,t,a) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
rng (T,t,a) is non empty finite Element of bool the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,t,a) is Element of the carrier of T
len a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len a) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,a) . ((len a) + 1) is set
len (T,t,a) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
t2 is Element of the carrier of T
dom (T,t,a) is non empty finite Element of bool NAT
X is set
(T,t,a) . X is set
x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(T,t,a) . 1 is set
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
(T,t,a) is Element of the carrier of T
(T,t,a) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len a) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,a) . ((len a) + 1) is set
len (T,t,a) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
dom (T,t,a) is non empty finite Element of bool NAT
rng (T,t,a) is non empty finite Element of bool the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
rng a is finite Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
(T,t,a) is Element of the carrier of T
(T,t,a) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len a) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,a) . ((len a) + 1) is set
(T,(T,t,a)) is Element of bool the of T
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . (T,t,a) is set
t2 is set
dom a is finite Element of bool NAT
X is set
a . X is set
y is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
y + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
len (T,t,a) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
dom (T,t,a) is non empty finite Element of bool NAT
(T,t,a) . (y + 1) is set
rng (T,t,a) is non empty finite Element of bool the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,t,a) . y is set
t1 is Element of the carrier of T
x is Element of the of T
(T,t1,x) is Element of the carrier of T
(T,x) is directed lower Element of bool the carrier of T
downarrow t1 is non empty directed lower Element of bool the carrier of T
{t1} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t1} is non empty lower Element of bool the carrier of T
(T,x) /\ (downarrow t1) is Element of bool the carrier of T
"\/" (((T,x) /\ (downarrow t1)),T) is Element of the carrier of T
(T,(T,t1,x)) is Element of bool the of T
the of T . (T,t1,x) is set
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () ()
the carrier of T is non empty set
the of T is non empty set
bool the of T is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
rng a is finite Element of bool the of T
(T,t,a) is Element of the carrier of T
(T,t,a) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len a) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,a) . ((len a) + 1) is set
(T,(T,t,a)) is Element of bool the of T
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . (T,t,a) is set
t2 is Element of bool the of T
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
rng t2 is finite Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
rng a is finite Element of bool the of T
(T,t,t2) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
rng (T,t,t2) is non empty finite Element of bool the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,t,a) is Element of the carrier of T
(T,t,a) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len a) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,a) . ((len a) + 1) is set
len (T,t,t2) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,(T,t,a)) is Element of bool the of T
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . (T,t,a) is set
X is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() set
(T,t,t2) . X is set
X + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,t2) . (X + 1) is set
0 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
len t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len t2) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
dom (T,t,t2) is non empty finite Element of bool NAT
x is Element of the carrier of T
dom t2 is finite Element of bool NAT
t2 . X is set
y is Element of the of T
(T,x,y) is Element of the carrier of T
(T,y) is directed lower Element of bool the carrier of T
downarrow x is non empty directed lower Element of bool the carrier of T
{x} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {x} is non empty lower Element of bool the carrier of T
(T,y) /\ (downarrow x) is Element of bool the carrier of T
"\/" (((T,y) /\ (downarrow x)),T) is Element of the carrier of T
t1 is Element of the carrier of T
(T,t,t2) . 1 is set
X is Element of the carrier of T
X is Element of the carrier of T
dom (T,t,t2) is non empty finite Element of bool NAT
x is set
(T,t,t2) . x is set
Seg (len (T,t,t2)) is non empty finite len (T,t,t2) -element Element of bool NAT
{ b1 where b1 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT : ( 1 <= b1 & b1 <= len (T,t,t2) ) } is set
y is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
t1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
a ^ t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
t2 ^ a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
rng (a ^ t2) is finite Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
rng a is finite Element of bool the of T
rng t2 is finite Element of bool the of T
(rng a) \/ (rng t2) is finite Element of bool the of T
(T,t,(a ^ t2)) is Element of the carrier of T
(T,t,(a ^ t2)) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len (a ^ t2) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len (a ^ t2)) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,(a ^ t2)) . ((len (a ^ t2)) + 1) is set
(T,(T,t,(a ^ t2))) is Element of bool the of T
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . (T,t,(a ^ t2)) is set
X is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
dom (t2 ^ a) is finite Element of bool NAT
(t2 ^ a) . X is set
(T,t,(t2 ^ a)) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(T,t,(t2 ^ a)) . X is set
x is Element of the of T
y is Element of the carrier of T
rng (t2 ^ a) is finite Element of bool the of T
len (T,t,(t2 ^ a)) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
len (t2 ^ a) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len (t2 ^ a)) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
dom (T,t,(t2 ^ a)) is non empty finite Element of bool NAT
rng (T,t,(t2 ^ a)) is non empty finite Element of bool the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
a ^ t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
(T,t,(a ^ t2)) is Element of the carrier of T
(T,t,(a ^ t2)) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len (a ^ t2) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len (a ^ t2)) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,(a ^ t2)) . ((len (a ^ t2)) + 1) is set
t2 ^ a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
(T,t,(t2 ^ a)) is Element of the carrier of T
(T,t,(t2 ^ a)) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len (t2 ^ a) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len (t2 ^ a)) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,(t2 ^ a)) . ((len (t2 ^ a)) + 1) is set
len a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
len t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len a) + (len t2) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
rng (a ^ t2) is finite Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
rng a is finite Element of bool the of T
rng t2 is finite Element of bool the of T
(rng a) \/ (rng t2) is finite Element of bool the of T
rng (t2 ^ a) is finite Element of bool the of T
len (T,t,(t2 ^ a)) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
dom (T,t,(t2 ^ a)) is non empty finite Element of bool NAT
rng (T,t,(t2 ^ a)) is non empty finite Element of bool the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
len (T,t,(a ^ t2)) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
dom (T,t,(a ^ t2)) is non empty finite Element of bool NAT
rng (T,t,(a ^ t2)) is non empty finite Element of bool the carrier of T
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () ()
the carrier of T is non empty set
the of T is set
bool the of T is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
a is Element of bool the of T
(T,t,a) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,a) is directed lower Element of bool the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow t)),T) is Element of the carrier of T
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () ()
the carrier of T is non empty set
the of T is set
bool the of T is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
a is Element of bool the of T
(T,t,a) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,a) is directed lower Element of bool the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow t)),T) is Element of the carrier of T
(T,(T,t,a)) is Element of bool the of T
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . (T,t,a) is set
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () ()
the carrier of T is non empty set
the of T is set
bool the of T is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
a is Element of bool the of T
(T,t,a) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,a) is directed lower Element of bool the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow t)),T) is Element of the carrier of T
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () ()
the carrier of T is non empty set
the of T is set
bool the of T is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
a is Element of bool the of T
(T,t,a) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,a) is directed lower Element of bool the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow t)),T) is Element of the carrier of T
t2 is Element of the carrier of T
(T,t2) is Element of bool the of T
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . t2 is set
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () ()
the carrier of T is non empty set
the of T is set
bool the of T is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
(T,t) is Element of bool the of T
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . t is set
a is Element of bool the of T
(T,t,a) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,a) is directed lower Element of bool the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow t)),T) is Element of the carrier of T
T is ()
the carrier of T is set
the of T is set
bool the of T is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
a is Element of bool the of T
t2 is Element of bool the of T
X is Element of the carrier of T
(T,X) is Element of bool the of T
the of T is Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . X is set
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () ()
the carrier of T is non empty set
the of T is non empty set
bool the of T is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
a is Element of the of T
{a} is non empty trivial finite 1 -element Element of bool the of T
X is Element of bool the of T
t2 is Element of bool the of T
t2 \/ {a} is non empty Element of bool the of T
(T,t,t2) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,t2) is directed lower Element of bool the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,t2) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,t2) /\ (downarrow t)),T) is Element of the carrier of T
(T,(T,t,t2),a) is Element of the carrier of T
(T,a) is directed lower Element of bool the carrier of T
downarrow (T,t,t2) is non empty directed lower Element of bool the carrier of T
{(T,t,t2)} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {(T,t,t2)} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow (T,t,t2)) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow (T,t,t2))),T) is Element of the carrier of T
(T,t,X) is Element of the carrier of T
(T,X) is directed lower Element of bool the carrier of T
(T,X) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,X) /\ (downarrow t)),T) is Element of the carrier of T
x is set
y is Element of the carrier of T
(T,y) is Element of bool the of T
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . y is set
(T,(T,t,t2)) is Element of bool the of T
the of T . (T,t,t2) is set
x is set
y is Element of the carrier of T
(T,y) is Element of bool the of T
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . y is set
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () ()
the carrier of T is non empty set
the of T is non empty set
bool the of T is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
rng a is finite Element of bool the of T
(T,t,a) is Element of the carrier of T
(T,t,a) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len a) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,a) . ((len a) + 1) is set
t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
t2 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
x is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
len x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
X is Element of the carrier of T
y is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
t1 is Element of the of T
<*t1*> is non empty trivial Relation-like NAT -defined the of T -valued Function-like finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the of T
[1,t1] is set
{1,t1} is non empty finite set
{{1,t1},{1}} is non empty finite V40() set
{[1,t1]} is non empty trivial Relation-like finite 1 -element set
y ^ <*t1*> is non empty Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
rng y is finite Element of bool the of T
v2 is Element of the of T
<*v2*> is non empty trivial Relation-like NAT -defined the of T -valued Function-like finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the of T
[1,v2] is set
{1,v2} is non empty finite set
{{1,v2},{1}} is non empty finite V40() set
{[1,v2]} is non empty trivial Relation-like finite 1 -element set
len <*v2*> is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
len y is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len y) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,X,y) is Element of the carrier of T
(T,X,y) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(T,X,y) . ((len y) + 1) is set
t2 is Element of bool the of T
(T,X,t2) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,t2) is directed lower Element of bool the carrier of T
downarrow X is non empty directed lower Element of bool the carrier of T
{X} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {X} is non empty lower Element of bool the carrier of T
(T,t2) /\ (downarrow X) is Element of bool the carrier of T
"\/" (((T,t2) /\ (downarrow X)),T) is Element of the carrier of T
a3 is Element of bool the of T
rng x is finite Element of bool the of T
rng <*v2*> is non empty trivial finite 1 -element Element of bool the of T
t2 \/ (rng <*v2*>) is non empty Element of bool the of T
{v2} is non empty trivial finite 1 -element Element of bool the of T
t2 \/ {v2} is non empty Element of bool the of T
(T,X,x) is Element of the carrier of T
(T,X,x) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(len x) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,X,x) . ((len x) + 1) is set
(T,(T,X,y),<*v2*>) is Element of the carrier of T
(T,(T,X,y),<*v2*>) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(len <*v2*>) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,(T,X,y),<*v2*>) . ((len <*v2*>) + 1) is set
(T,(T,X,t2),v2) is Element of the carrier of T
(T,v2) is directed lower Element of bool the carrier of T
downarrow (T,X,t2) is non empty directed lower Element of bool the carrier of T
{(T,X,t2)} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {(T,X,t2)} is non empty lower Element of bool the carrier of T
(T,v2) /\ (downarrow (T,X,t2)) is Element of bool the carrier of T
"\/" (((T,v2) /\ (downarrow (T,X,t2))),T) is Element of the carrier of T
(T,X,a3) is Element of the carrier of T
(T,a3) is directed lower Element of bool the carrier of T
(T,a3) /\ (downarrow X) is Element of bool the carrier of T
"\/" (((T,a3) /\ (downarrow X)),T) is Element of the carrier of T
x is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
len x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
X is Element of the carrier of T
y is Element of bool the of T
rng x is finite Element of bool the of T
(T,X,x) is Element of the carrier of T
(T,X,x) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(len x) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,X,x) . ((len x) + 1) is set
(T,X,y) is Element of the carrier of T
(T,y) is directed lower Element of bool the carrier of T
downarrow X is non empty directed lower Element of bool the carrier of T
{X} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {X} is non empty lower Element of bool the carrier of T
(T,y) /\ (downarrow X) is Element of bool the carrier of T
"\/" (((T,y) /\ (downarrow X)),T) is Element of the carrier of T
t2 is Element of the carrier of T
X is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
len X is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
rng X is finite Element of bool the of T
(T,t2,X) is Element of the carrier of T
(T,t2,X) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(len X) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t2,X) . ((len X) + 1) is set
<*> the of T is empty proper V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined the of T -valued Function-like functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() FinSequence of the of T
[:NAT, the of T:] is non empty non trivial Relation-like non finite set
{} the of T is empty proper V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() Element of bool the of T
x is Element of bool the of T
(T,t2,x) is Element of the carrier of T
(T,x) is directed lower Element of bool the carrier of T
downarrow t2 is non empty directed lower Element of bool the carrier of T
{t2} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t2} is non empty lower Element of bool the carrier of T
(T,x) /\ (downarrow t2) is Element of bool the carrier of T
"\/" (((T,x) /\ (downarrow t2)),T) is Element of the carrier of T
t2 is Element of bool the of T
(T,t,t2) is Element of the carrier of T
(T,t2) is directed lower Element of bool the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,t2) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,t2) /\ (downarrow t)),T) is Element of the carrier of T
T is non empty () ()
the of T is non empty set
the carrier of T is non empty set
[: the of T, the carrier of T:] is non empty Relation-like set
bool [: the of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
t is non empty Relation-like the of T -defined the carrier of T -valued Function-like V29( the of T) V33( the of T, the carrier of T) Element of bool [: the of T, the carrier of T:]
a is Element of the of T
t . a is Element of the carrier of T
(T,a) is Element of bool the carrier of T
(T,a) is Element of the of T
the of T is non empty Relation-like the of T -defined the of T -valued Function-like V29( the of T) V33( the of T, the of T) Element of bool [: the of T, the of T:]
[: the of T, the of T:] is non empty Relation-like set
bool [: the of T, the of T:] is non empty cup-closed diff-closed preBoolean set
the of T . a is set
(T,(T,a)) is Element of bool the carrier of T
(T,a) \/ (T,(T,a)) is Element of bool the carrier of T
"\/" (((T,a) \/ (T,(T,a))),T) is Element of the carrier of T
t is non empty Relation-like the of T -defined the carrier of T -valued Function-like V29( the of T) V33( the of T, the carrier of T) Element of bool [: the of T, the carrier of T:]
a is non empty Relation-like the of T -defined the carrier of T -valued Function-like V29( the of T) V33( the of T, the carrier of T) Element of bool [: the of T, the carrier of T:]
t2 is Element of the of T
t . t2 is Element of the carrier of T
X is Element of the of T
(T,X) is Element of bool the carrier of T
(T,X) is Element of the of T
the of T is non empty Relation-like the of T -defined the of T -valued Function-like V29( the of T) V33( the of T, the of T) Element of bool [: the of T, the of T:]
[: the of T, the of T:] is non empty Relation-like set
bool [: the of T, the of T:] is non empty cup-closed diff-closed preBoolean set
the of T . X is set
(T,(T,X)) is Element of bool the carrier of T
(T,X) \/ (T,(T,X)) is Element of bool the carrier of T
"\/" (((T,X) \/ (T,(T,X))),T) is Element of the carrier of T
a . t2 is Element of the carrier of T
the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () is non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ()
the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () is non empty set
the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () is non empty trivial finite 1 -element set
[: the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ():] is non empty Relation-like set
bool [: the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ():] is non empty cup-closed diff-closed preBoolean set
the non empty Relation-like the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () -defined the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () -valued Function-like V29( the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ()) V33( the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ()) Element of bool [: the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ():] is non empty Relation-like the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () -defined the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () -valued Function-like V29( the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ()) V33( the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ()) Element of bool [: the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ():]
the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () is Relation-like the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () -defined the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () -valued finite co-well_founded Element of bool [: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ():]
[: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ():] is non empty Relation-like finite set
bool [: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ():] is non empty cup-closed diff-closed preBoolean finite V40() set
the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () is non empty Relation-like the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () -defined the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () -valued Function-like V29( the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ()) V33( the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ()) Element of bool [: the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ():]
[: the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ():] is non empty Relation-like set
bool [: the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ():] is non empty cup-closed diff-closed preBoolean set
the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () is non empty Relation-like the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () -defined Fin the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () -valued Function-like V29( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ()) V33( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), Fin the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ()) finite Element of bool [: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (),(Fin the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ()):]
Fin the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () is non empty cup-closed diff-closed preBoolean set
[: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (),(Fin the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ()):] is non empty Relation-like set
bool [: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (),(Fin the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ()):] is non empty cup-closed diff-closed preBoolean set
( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), the non empty Relation-like the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () -defined the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () -valued Function-like V29( the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ()) V33( the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ()) Element of bool [: the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () ():]) is () ()
a is () ()
RelStr(# the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () (), the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () #) is strict RelStr
the carrier of a is set
the InternalRel of a is Relation-like the carrier of a -defined the carrier of a -valued Element of bool [: the carrier of a, the carrier of a:]
[: the carrier of a, the carrier of a:] is Relation-like set
bool [: the carrier of a, the carrier of a:] is non empty cup-closed diff-closed preBoolean set
RelStr(# the carrier of a, the InternalRel of a #) is strict RelStr
T is non empty () ()
the of T is non empty set
the carrier of T is non empty set
the of T is non empty Relation-like the of T -defined the carrier of T -valued Function-like V29( the of T) V33( the of T, the carrier of T) Element of bool [: the of T, the carrier of T:]
[: the of T, the carrier of T:] is non empty Relation-like set
bool [: the of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
t is Element of the of T
the of T . t is Element of the carrier of T
T is non empty () ()
the of T is non empty set
the carrier of T is non empty set
the of T is non empty Relation-like the of T -defined the of T -valued Function-like V29( the of T) V33( the of T, the of T) Element of bool [: the of T, the of T:]
[: the of T, the of T:] is non empty Relation-like set
bool [: the of T, the of T:] is non empty cup-closed diff-closed preBoolean set
the of T is non empty Relation-like the of T -defined the carrier of T -valued Function-like V29( the of T) V33( the of T, the carrier of T) Element of bool [: the of T, the carrier of T:]
[: the of T, the carrier of T:] is non empty Relation-like set
bool [: the of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
the of T * the of T is non empty Relation-like the of T -defined the carrier of T -valued Function-like V29( the of T) V33( the of T, the carrier of T) Element of bool [: the of T, the carrier of T:]
t is Element of the of T
(T,t) is Element of the of T
the of T . t is set
(T,(T,t)) is Element of the carrier of T
the of T . (T,t) is Element of the carrier of T
(T,t) is Element of the carrier of T
the of T . t is Element of the carrier of T
t is Element of the of T
the carrier of T is non empty set
the of T is non empty Relation-like the of T -defined the of T -valued Function-like V29( the of T) V33( the of T, the of T) Element of bool [: the of T, the of T:]
[: the of T, the of T:] is non empty Relation-like set
bool [: the of T, the of T:] is non empty cup-closed diff-closed preBoolean set
the of T is non empty Relation-like the of T -defined the carrier of T -valued Function-like V29( the of T) V33( the of T, the carrier of T) Element of bool [: the of T, the carrier of T:]
[: the of T, the carrier of T:] is non empty Relation-like set
bool [: the of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
the of T * the of T is non empty Relation-like the of T -defined the carrier of T -valued Function-like V29( the of T) V33( the of T, the carrier of T) Element of bool [: the of T, the carrier of T:]
( the of T * the of T) . t is Element of the carrier of T
a is Element of the of T
(T,a) is Element of the of T
the of T . a is set
(T,(T,a)) is Element of the carrier of T
the of T . (T,a) is Element of the carrier of T
(T,a) is Element of the carrier of T
the of T . a is Element of the carrier of T
the of T . t is Element of the carrier of T
T is non empty () ()
the carrier of T is non empty set
the of T is non empty set
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
dom a is finite Element of bool NAT
(T,t,a) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
a . t2 is set
(T,t,a) . t2 is set
X is Element of the of T
x is Element of the carrier of T
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
<*> the of T is empty proper V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined the of T -valued Function-like functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() FinSequence of the of T
[:NAT, the of T:] is non empty non trivial Relation-like non finite set
t is Element of the carrier of T
a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
dom (<*> the of T) is empty proper V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() Element of bool NAT
(<*> the of T) . a is finite set
(T,t,(<*> the of T)) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(T,t,(<*> the of T)) . a is set
t2 is Element of the of T
X is Element of the carrier of T
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Element of the of T
<*a*> is non empty trivial Relation-like NAT -defined the of T -valued Function-like finite 1 -element FinSequence-like FinSubsequence-like FinSequence of the of T
[1,a] is set
{1,a} is non empty finite set
{{1,a},{1}} is non empty finite V40() set
{[1,a]} is non empty trivial Relation-like finite 1 -element set
<*a*> . 1 is set
X is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
dom <*a*> is non empty trivial finite 1 -element Element of bool NAT
<*a*> . X is set
(T,t,<*a*>) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(T,t,<*a*>) . X is set
x is Element of the of T
y is Element of the carrier of T
dom <*a*> is non empty trivial finite 1 -element Element of bool NAT
(T,t,<*a*>) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len <*a*> is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,<*a*>) . 1 is set
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
a ^ t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
(T,t,a) is Element of the carrier of T
(T,t,a) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len a) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,a) . ((len a) + 1) is set
(T,t,(a ^ t2)) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(T,(T,t,a),t2) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(T,t,a) $^ (T,(T,t,a),t2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (T,(T,t,a),t2) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
len t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len t2) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
dom (a ^ t2) is finite Element of bool NAT
dom a is finite Element of bool NAT
x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
y is Element of the of T
a . x is set
t1 is Element of the carrier of T
(T,t,a) . x is set
(a ^ t2) . x is set
(T,t,(a ^ t2)) . x is set
x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
dom t2 is finite Element of bool NAT
t2 . x is set
(T,(T,t,a),t2) . x is set
y is Element of the of T
t1 is Element of the carrier of T
(len a) + x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(a ^ t2) . ((len a) + x) is set
t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
1 + t2 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
len (T,t,a) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(len (T,t,a)) + t2 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,(a ^ t2)) . ((len a) + x) is set
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
(T,t,a) is Element of the carrier of T
(T,t,a) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len a) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,a) . ((len a) + 1) is set
t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
a ^ t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
dom a is finite Element of bool NAT
dom t2 is finite Element of bool NAT
(T,(T,t,a),t2) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(T,t,(a ^ t2)) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(T,t,a) $^ (T,(T,t,a),t2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
dom (a ^ t2) is finite Element of bool NAT
(a ^ t2) . x is set
(T,t,(a ^ t2)) . x is set
y is Element of the of T
t1 is Element of the carrier of T
len (a ^ t2) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
a . x is set
(T,t,a) . x is set
1 + (len a) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
((len a) + 1) + t2 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
len (T,(T,t,a),t2) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
len t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len t2) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(len a) + (len t2) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
len (T,t,a) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
t2 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(len a) + (t2 + 1) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
1 + t2 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,(T,t,a),t2) . (1 + t2) is set
(len (T,t,a)) + t2 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
t2 . (1 + t2) is set
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
bool the of T is non empty cup-closed diff-closed preBoolean set
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
bool the of T is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
a is Element of bool the of T
t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
rng t2 is finite Element of bool the of T
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
{} the of T is empty proper V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
[:NAT, the of T:] is non empty non trivial Relation-like non finite set
<*> the of T is empty proper V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined the of T -valued Function-like functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() FinSequence of the of T
a is empty proper V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding NAT -defined the of T -valued Function-like functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() FinSequence of the of T
rng a is empty proper V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() Element of bool the of T
t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
dom a is empty proper V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() Element of bool NAT
a . t2 is finite set
(T,t,a) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(T,t,a) . t2 is set
X is Element of the of T
x is Element of the carrier of T
T is finite set
T is finite set
bool T is non empty cup-closed diff-closed preBoolean finite V40() set
t is set
a is non empty set
t2 is set
t2 is non empty finite set
X is Element of t2
x is Element of t2
X is Element of t2
x is Element of t2
y is Element of t2
X is set
the Element of t2 is Element of t2
y is Element of t2
the Element of X is Element of X
{ b1 where b1 is Element of t2 : ( b1 in X & b1 c< a1 ) } is set
card { b1 where b1 is Element of t2 : ( b1 in X & b1 c< a1 ) } is V8() V9() V10() cardinal set
t1 is Relation-like Function-like set
dom t1 is set
t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
v2 is Element of t2
t1 . v2 is set
{ b1 where b1 is Element of t2 : ( b1 in X & b1 c< v2 ) } is set
c12 is set
a is Element of t2
c12 is finite set
card c12 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
s is non empty set
the Element of s is Element of s
k is Element of t2
{ b1 where b1 is Element of t2 : ( b1 in X & b1 c< k ) } is set
b is set
u is Element of t2
b is finite set
card b is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
u is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
s22 is Element of t2
s22 is set
a is Element of t2
t1 . k is set
y is Element of t2
{ b1 where b1 is Element of t2 : ( b1 in X & b1 c< y ) } is set
v2 is set
a3 is Element of t2
t1 . y is set
v2 is finite set
card v2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
a3 is Element of t2
t1 . a3 is set
a3 is Element of t2
t1 . a3 is set
c12 is Element of t2
{ b1 where b1 is Element of t2 : ( b1 in X & b1 c< a3 ) } is set
card { b1 where b1 is Element of t2 : ( b1 in X & b1 c< a3 ) } is V8() V9() V10() cardinal set
X is Element of t2
X is Element of t2
x is finite set
y is set
T is non empty reflexive transitive () ()
the carrier of T is non empty set
the of T is non empty set
bool the of T is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
a is Element of bool the of T
(T,t,a) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,a) is Element of bool the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow t)),T) is Element of the carrier of T
t2 is finite set
x is Element of bool the of T
(T,t,x) is Element of the carrier of T
(T,x) is Element of bool the carrier of T
(T,x) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,x) /\ (downarrow t)),T) is Element of the carrier of T
X is Element of bool the of T
(T,t,X) is Element of the carrier of T
(T,X) is Element of bool the carrier of T
(T,X) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,X) /\ (downarrow t)),T) is Element of the carrier of T
x is Element of bool the of T
(T,t,x) is Element of the carrier of T
(T,x) is Element of bool the carrier of T
(T,x) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,x) /\ (downarrow t)),T) is Element of the carrier of T
x is Element of bool the of T
(T,t,x) is Element of the carrier of T
(T,x) is Element of bool the carrier of T
(T,x) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,x) /\ (downarrow t)),T) is Element of the carrier of T
y is Element of bool the of T
(T,t,y) is Element of the carrier of T
(T,y) is Element of bool the carrier of T
(T,y) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,y) /\ (downarrow t)),T) is Element of the carrier of T
the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () () is non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()
the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () () is non empty trivial finite 1 -element set
the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () () is non empty set
the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () () is Relation-like the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () () -defined the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () () -valued finite co-well_founded Element of bool [: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ():]
[: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ():] is non empty Relation-like finite set
bool [: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ():] is non empty cup-closed diff-closed preBoolean finite V40() set
the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () () is non empty Relation-like the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () () -defined the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () () -valued Function-like V29( the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()) V33( the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()) Element of bool [: the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ():]
[: the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ():] is non empty Relation-like set
bool [: the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ():] is non empty cup-closed diff-closed preBoolean set
the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () () is non empty Relation-like the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () () -defined Fin the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () () -valued Function-like V29( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()) V33( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), Fin the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()) finite Element of bool [: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),(Fin the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()):]
Fin the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () () is non empty cup-closed diff-closed preBoolean set
[: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),(Fin the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()):] is non empty Relation-like set
bool [: the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),(Fin the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()):] is non empty cup-closed diff-closed preBoolean set
( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()) is non empty Relation-like the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () () -defined the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () () -valued Function-like V29( the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()) V33( the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()) Element of bool [: the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ():]
[: the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ():] is non empty Relation-like set
bool [: the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ():] is non empty cup-closed diff-closed preBoolean set
( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ())) is () ()
RelStr(# the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () () #) is strict RelStr
the carrier of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ())) is set
the InternalRel of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ())) is Relation-like the carrier of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ())) -defined the carrier of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ())) -valued Element of bool [: the carrier of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ())), the carrier of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ())):]
[: the carrier of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ())), the carrier of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ())):] is Relation-like set
bool [: the carrier of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ())), the carrier of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ())):] is non empty cup-closed diff-closed preBoolean set
RelStr(# the carrier of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ())), the InternalRel of ( the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the InternalRel of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ())) #) is strict RelStr
a is non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () ()
( the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (), the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()) is () ()
the of a is non empty set
the of a is non empty Relation-like the of a -defined the of a -valued Function-like V29( the of a) V33( the of a, the of a) Element of bool [: the of a, the of a:]
[: the of a, the of a:] is non empty Relation-like set
bool [: the of a, the of a:] is non empty cup-closed diff-closed preBoolean set
( the of a, the of a) is () ()
t2 is Element of the of a
(a,t2) is Element of the of a
the of a . t2 is set
(a,(a,t2)) is Element of the carrier of a
the carrier of a is non empty trivial finite 1 -element set
the of a is non empty Relation-like the of a -defined the carrier of a -valued Function-like V29( the of a) V33( the of a, the carrier of a) Element of bool [: the of a, the carrier of a:]
[: the of a, the carrier of a:] is non empty Relation-like set
bool [: the of a, the carrier of a:] is non empty cup-closed diff-closed preBoolean set
the of a . (a,t2) is Element of the carrier of a
bool the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () () is non empty cup-closed diff-closed preBoolean finite V40() set
X is Element of the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()
( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),X) is Element of the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()
the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () () . X is set
( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),X)) is trivial finite directed lower Element of bool the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()
( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),X)) is Element of the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()
the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () () . ( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),X) is set
( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),X))) is trivial finite directed lower Element of bool the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()
( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),X)) \/ ( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),X))) is trivial finite Element of bool the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()
"\/" ((( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),X)) \/ ( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),X)))), the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()) is Element of the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()
( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),X) is trivial finite directed lower Element of bool the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()
( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),X)) \/ ( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),X) is trivial finite Element of bool the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()
"\/" ((( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),X)) \/ ( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),X)), the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()) is Element of the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()
(a,t2) is Element of the carrier of a
the of a . t2 is Element of the carrier of a
the InternalRel of a is Relation-like the carrier of a -defined the carrier of a -valued finite co-well_founded Element of bool [: the carrier of a, the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty Relation-like finite set
bool [: the carrier of a, the carrier of a:] is non empty cup-closed diff-closed preBoolean finite V40() set
RelStr(# the carrier of a, the InternalRel of a #) is strict RelStr
bool the carrier of a is non empty cup-closed diff-closed preBoolean finite V40() set
t2 is Element of the of a
(a,t2) is trivial finite Element of bool the carrier of a
(a,t2) is Element of the of a
the of a . t2 is set
(a,(a,t2)) is trivial finite Element of bool the carrier of a
(a,t2) \/ (a,(a,t2)) is trivial finite Element of bool the carrier of a
(a,t2) is Element of the carrier of a
the of a . t2 is Element of the carrier of a
"\/" (((a,t2) \/ (a,(a,t2))),a) is Element of the carrier of a
X is Element of the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()
( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),X) is Element of the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()
the of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () () . X is set
( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),X)) is trivial finite directed lower Element of bool the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()
( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),X) is trivial finite directed lower Element of bool the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()
( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),X) \/ ( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),X)) is trivial finite Element of bool the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()
"\/" ((( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),X) \/ ( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),( the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () (),X))), the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()) is Element of the carrier of the non empty trivial finite 1 -element reflexive transitive antisymmetric with_suprema with_infima complete lower-bounded upper-bounded V139() connected up-complete /\-complete () () () () () () () () () ()
t2 is Element of the carrier of a
X is Element of the carrier of a
bool the of a is non empty cup-closed diff-closed preBoolean set
t2 "\/" X is Element of the carrier of a
x is Element of the of a
(a,t2,x) is Element of the carrier of a
bool the carrier of a is non empty cup-closed diff-closed preBoolean finite V40() set
(a,x) is trivial finite Element of bool the carrier of a
downarrow t2 is non empty trivial finite 1 -element directed lower Element of bool the carrier of a
{t2} is non empty trivial finite 1 -element Element of bool the carrier of a
downarrow {t2} is non empty trivial finite 1 -element lower Element of bool the carrier of a
(a,x) /\ (downarrow t2) is trivial finite Element of bool the carrier of a
"\/" (((a,x) /\ (downarrow t2)),a) is Element of the carrier of a
{} the of a is empty proper V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() Element of bool the of a
y is empty proper V8() V9() V10() V12() V13() V14() V15() ext-real non positive non negative Relation-like non-empty empty-yielding functional finite finite-yielding V40() cardinal {} -element FinSequence-like FinSequence-membered co-well_founded weakly-normalizing strongly-normalizing with_UN_property with_NF_property subcommutative confluent with_Church-Rosser_property locally-confluent complete irreflexive V173() Element of bool the of a
(a,(t2 "\/" X),y) is Element of the carrier of a
(a,y) is trivial finite Element of bool the carrier of a
downarrow (t2 "\/" X) is non empty trivial finite 1 -element directed lower Element of bool the carrier of a
{(t2 "\/" X)} is non empty trivial finite 1 -element Element of bool the carrier of a
downarrow {(t2 "\/" X)} is non empty trivial finite 1 -element lower Element of bool the carrier of a
(a,y) /\ (downarrow (t2 "\/" X)) is trivial finite Element of bool the carrier of a
"\/" (((a,y) /\ (downarrow (t2 "\/" X))),a) is Element of the carrier of a
t2 "\/" X is Element of the carrier of a
(a,(t2 "\/" X),y) is Element of the carrier of a
downarrow (t2 "\/" X) is non empty trivial finite 1 -element directed lower Element of bool the carrier of a
{(t2 "\/" X)} is non empty trivial finite 1 -element Element of bool the carrier of a
downarrow {(t2 "\/" X)} is non empty trivial finite 1 -element lower Element of bool the carrier of a
(a,y) /\ (downarrow (t2 "\/" X)) is trivial finite Element of bool the carrier of a
"\/" (((a,y) /\ (downarrow (t2 "\/" X))),a) is Element of the carrier of a
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () ()
the carrier of T is non empty set
the of T is non empty set
bool the of T is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
a is Element of bool the of T
t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
rng t2 is finite Element of bool the of T
len t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
X is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
x is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
len x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
rng x is finite Element of bool the of T
x is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
len x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
rng x is finite Element of bool the of T
y is set
dom x is finite set
t1 is set
x . y is set
x . t1 is set
dom x is finite Element of bool NAT
v2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
a3 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
c12 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
x . a3 is set
x . c12 is set
a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
1 + a is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
s is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
Seg s is finite s -element Element of bool NAT
{ b1 where b1 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT : ( 1 <= b1 & b1 <= s ) } is set
x | (Seg s) is Relation-like NAT -defined Seg s -defined NAT -defined the of T -valued Function-like finite FinSubsequence-like Element of bool [:NAT, the of T:]
[:NAT, the of T:] is non empty non trivial Relation-like non finite set
bool [:NAT, the of T:] is non empty non trivial cup-closed diff-closed preBoolean non finite set
k is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
len k is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
dom k is finite Element of bool NAT
k is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
k ^ k is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
o is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
len o is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len k) + (len o) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
dom o is finite Element of bool NAT
o | (Seg 1) is Relation-like NAT -defined Seg 1 -defined NAT -defined the of T -valued Function-like finite FinSubsequence-like Element of bool [:NAT, the of T:]
b is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
u is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
b ^ u is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len b is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
b . 1 is set
<*(b . 1)*> is non empty trivial Relation-like NAT -defined Function-like finite 1 -element FinSequence-like FinSubsequence-like set
[1,(b . 1)] is set
{1,(b . 1)} is non empty finite set
{{1,(b . 1)},{1}} is non empty finite V40() set
{[1,(b . 1)]} is non empty trivial Relation-like finite 1 -element set
rng b is finite Element of bool the of T
{(b . 1)} is non empty trivial finite 1 -element set
rng o is finite Element of bool the of T
s22 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
rng s22 is finite Element of bool the of T
(rng b) \/ (rng s22) is finite Element of bool the of T
a is Element of the of T
o . 1 is set
k . a3 is set
rng k is finite Element of bool the of T
(rng k) \/ (rng b) is finite Element of bool the of T
k ^ s22 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
rng (k ^ s22) is finite Element of bool the of T
((rng k) \/ (rng b)) \/ (rng s22) is finite Element of bool the of T
(T,t,k) is Element of the carrier of T
(T,t,k) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(len k) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,k) . ((len k) + 1) is set
(T,(T,t,k)) is Element of bool the of T
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . (T,t,k) is set
(T,(T,t,k),a) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,a) is directed lower Element of bool the carrier of T
downarrow (T,t,k) is non empty directed lower Element of bool the carrier of T
{(T,t,k)} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {(T,t,k)} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow (T,t,k)) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow (T,t,k))),T) is Element of the carrier of T
(T,(T,t,k),b) is Element of the carrier of T
(T,(T,t,k),b) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(len b) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,(T,t,k),b) . ((len b) + 1) is set
len s22 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len b) + (len s22) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(rng k) \/ (rng o) is finite Element of bool the of T
len (k ^ s22) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len k) + (len s22) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
0 + (len s22) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
T is non empty reflexive transitive () ()
the carrier of T is non empty set
[: the carrier of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
the of T is non empty set
t is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
a is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
t2 is Element of the carrier of T
X is Element of the carrier of T
[t2,X] is Element of [: the carrier of T, the carrier of T:]
{t2,X} is non empty finite set
{t2} is non empty trivial finite 1 -element set
{{t2,X},{t2}} is non empty finite V40() set
(T,X) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . X is set
t1 is Element of the of T
y is Element of the carrier of T
(T,y) is Element of bool the of T
the of T . y is set
(T,y,t1) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,t1) is Element of bool the carrier of T
downarrow y is non empty directed lower Element of bool the carrier of T
{y} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {y} is non empty lower Element of bool the carrier of T
(T,t1) /\ (downarrow y) is Element of bool the carrier of T
"\/" (((T,t1) /\ (downarrow y)),T) is Element of the carrier of T
x is Element of the carrier of T
[x,y] is Element of [: the carrier of T, the carrier of T:]
{x,y} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,y},{x}} is non empty finite V40() set
t is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
a is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
t2 is Element of the carrier of T
X is Element of the carrier of T
[t2,X] is set
{t2,X} is non empty finite set
{t2} is non empty trivial finite 1 -element set
{{t2,X},{t2}} is non empty finite V40() set
[t2,X] is Element of [: the carrier of T, the carrier of T:]
(T,X) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . X is set
x is Element of the of T
(T,X,x) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,x) is Element of bool the carrier of T
downarrow X is non empty directed lower Element of bool the carrier of T
{X} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {X} is non empty lower Element of bool the carrier of T
(T,x) /\ (downarrow X) is Element of bool the carrier of T
"\/" (((T,x) /\ (downarrow X)),T) is Element of the carrier of T
x is Element of the of T
(T,X,x) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,x) is Element of bool the carrier of T
downarrow X is non empty directed lower Element of bool the carrier of T
{X} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {X} is non empty lower Element of bool the carrier of T
(T,x) /\ (downarrow X) is Element of bool the carrier of T
"\/" (((T,x) /\ (downarrow X)),T) is Element of the carrier of T
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () ()
the carrier of T is non empty set
(T) is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
[: the carrier of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
the InternalRel of T is Relation-like the carrier of T -defined the carrier of T -valued co-well_founded Element of bool [: the carrier of T, the carrier of T:]
t is Element of the carrier of T
a is Element of the carrier of T
[t,a] is set
{t,a} is non empty finite set
{t} is non empty trivial finite 1 -element set
{{t,a},{t}} is non empty finite V40() set
[t,a] is Element of [: the carrier of T, the carrier of T:]
the of T is non empty set
X is Element of the carrier of T
(T,X) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . X is set
t2 is Element of the carrier of T
x is Element of the of T
(T,X,x) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,x) is directed lower Element of bool the carrier of T
downarrow X is non empty directed lower Element of bool the carrier of T
{X} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {X} is non empty lower Element of bool the carrier of T
(T,x) /\ (downarrow X) is Element of bool the carrier of T
"\/" (((T,x) /\ (downarrow X)),T) is Element of the carrier of T
F1() is non empty set
[:F1(),F1():] is non empty Relation-like set
bool [:F1(),F1():] is non empty cup-closed diff-closed preBoolean set
F2() is Relation-like F1() -defined F1() -valued Element of bool [:F1(),F1():]
T is Element of F1()
t is Element of F1()
a is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like RedSequence of F2()
a . 1 is set
len a is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
a . (len a) is set
t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
1 + t2 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
a . (1 + t2) is set
t2 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
1 + (t2 + 1) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
dom a is non empty finite Element of bool NAT
a . (t2 + 1) is set
a . (1 + (t2 + 1)) is set
[(a . (t2 + 1)),(a . (1 + (t2 + 1)))] is set
{(a . (t2 + 1)),(a . (1 + (t2 + 1)))} is non empty finite set
{(a . (t2 + 1))} is non empty trivial finite 1 -element set
{{(a . (t2 + 1)),(a . (1 + (t2 + 1)))},{(a . (t2 + 1))}} is non empty finite V40() set
1 + 0 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
a . (1 + 0) is set
0 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
1 + t2 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () ()
the carrier of T is non empty set
(T) is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
[: the carrier of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
a is Element of the carrier of T
X is Element of the carrier of T
x is Element of the carrier of T
y is Element of the carrier of T
the InternalRel of T is Relation-like the carrier of T -defined the carrier of T -valued co-well_founded Element of bool [: the carrier of T, the carrier of T:]
X is Element of the carrier of T
x is Element of the carrier of T
[X,x] is Element of [: the carrier of T, the carrier of T:]
{X,x} is non empty finite set
{X} is non empty trivial finite 1 -element set
{{X,x},{X}} is non empty finite V40() set
X is Element of the carrier of T
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () ()
(T) is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
the carrier of T is non empty set
[: the carrier of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
a is set
field (T) is set
[a,a] is set
{a,a} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,a},{a}} is non empty finite V40() set
the of T is non empty set
t2 is Element of the carrier of T
(T,t2) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . t2 is set
X is Element of the of T
(T,t2,X) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,X) is directed lower Element of bool the carrier of T
downarrow t2 is non empty directed lower Element of bool the carrier of T
{t2} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t2} is non empty lower Element of bool the carrier of T
(T,X) /\ (downarrow t2) is Element of bool the carrier of T
"\/" (((T,X) /\ (downarrow t2)),T) is Element of the carrier of T
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () ()
(T) is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
the carrier of T is non empty set
[: the carrier of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
the InternalRel of T is Relation-like the carrier of T -defined the carrier of T -valued co-well_founded Element of bool [: the carrier of T, the carrier of T:]
field (T) is set
field the InternalRel of T is set
t2 is set
X is set
x is set
[X,x] is set
{X,x} is non empty finite set
{X} is non empty trivial finite 1 -element set
{{X,x},{X}} is non empty finite V40() set
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () ()
the carrier of T is non empty set
the of T is non empty set
bool the of T is non empty cup-closed diff-closed preBoolean set
(T) is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
[: the carrier of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
a is finite Element of bool the of T
(T,t,a) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,a) is directed lower Element of bool the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow t)),T) is Element of the carrier of T
t2 is Relation-like NAT -defined the of T -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like FinSequence of the of T
rng t2 is finite Element of bool the of T
len t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(T,t,t2) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
X is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
X + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,t2) . (X + 1) is set
(T,t,t2) . X is set
[((T,t,t2) . (X + 1)),((T,t,t2) . X)] is set
{((T,t,t2) . (X + 1)),((T,t,t2) . X)} is non empty finite set
{((T,t,t2) . (X + 1))} is non empty trivial finite 1 -element set
{{((T,t,t2) . (X + 1)),((T,t,t2) . X)},{((T,t,t2) . (X + 1))}} is non empty finite V40() set
len (T,t,t2) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(len t2) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
dom (T,t,t2) is non empty finite Element of bool NAT
rng (T,t,t2) is non empty finite Element of bool the carrier of T
dom t2 is finite Element of bool NAT
t2 . X is set
x is Element of the carrier of T
y is Element of the of T
(T,x,y) is Element of the carrier of T
(T,y) is directed lower Element of bool the carrier of T
downarrow x is non empty directed lower Element of bool the carrier of T
{x} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {x} is non empty lower Element of bool the carrier of T
(T,y) /\ (downarrow x) is Element of bool the carrier of T
"\/" (((T,y) /\ (downarrow x)),T) is Element of the carrier of T
(T,x) is Element of bool the of T
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . x is set
t1 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
1 + t1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
Seg t2 is finite t2 -element Element of bool NAT
{ b1 where b1 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT : ( 1 <= b1 & b1 <= t2 ) } is set
t2 | (Seg t2) is Relation-like NAT -defined Seg t2 -defined NAT -defined the of T -valued Function-like finite FinSubsequence-like Element of bool [:NAT, the of T:]
[:NAT, the of T:] is non empty non trivial Relation-like non finite set
bool [:NAT, the of T:] is non empty non trivial cup-closed diff-closed preBoolean non finite set
v2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
a3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
v2 ^ a3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len v2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
c12 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
len c12 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len v2) + (len c12) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
c12 | (Seg 1) is Relation-like NAT -defined Seg 1 -defined NAT -defined the of T -valued Function-like finite FinSubsequence-like Element of bool [:NAT, the of T:]
a is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
len a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
a . 1 is set
<*(a . 1)*> is non empty trivial Relation-like NAT -defined Function-like finite 1 -element FinSequence-like FinSubsequence-like set
[1,(a . 1)] is set
{1,(a . 1)} is non empty finite set
{{1,(a . 1)},{1}} is non empty finite V40() set
{[1,(a . 1)]} is non empty trivial Relation-like finite 1 -element set
rng a is finite Element of bool the of T
{(a . 1)} is non empty trivial finite 1 -element set
dom c12 is finite Element of bool NAT
k is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
a ^ k is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng c12 is finite Element of bool the of T
k is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
rng k is finite Element of bool the of T
(rng a) \/ (rng k) is finite Element of bool the of T
s is Element of the of T
c12 . 1 is set
(T,t,v2) is Element of the carrier of T
(T,t,v2) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(len v2) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,v2) . ((len v2) + 1) is set
(T,(T,t,v2),y) is Element of the carrier of T
downarrow (T,t,v2) is non empty directed lower Element of bool the carrier of T
{(T,t,v2)} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {(T,t,v2)} is non empty lower Element of bool the carrier of T
(T,y) /\ (downarrow (T,t,v2)) is Element of bool the carrier of T
"\/" (((T,y) /\ (downarrow (T,t,v2))),T) is Element of the carrier of T
(T,(T,t,v2),a) is Element of the carrier of T
(T,(T,t,v2),a) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(len a) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,(T,t,v2),a) . ((len a) + 1) is set
v2 ^ k is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
rng (v2 ^ k) is finite Element of bool the of T
o is Element of bool the of T
rng v2 is finite Element of bool the of T
(rng v2) \/ (rng k) is finite Element of bool the of T
(rng v2) \/ (rng c12) is finite Element of bool the of T
(T,t,t2) is Element of the carrier of T
(T,t,t2) . ((len t2) + 1) is set
(T,(T,t,v2),c12) is Element of the carrier of T
(T,(T,t,v2),c12) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
(len c12) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,(T,t,v2),c12) . ((len c12) + 1) is set
(T,(T,t,v2),k) is Element of the carrier of T
(T,(T,t,v2),k) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len k is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len k) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,(T,t,v2),k) . ((len k) + 1) is set
(T,t,(v2 ^ k)) is Element of the carrier of T
(T,t,(v2 ^ k)) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len (v2 ^ k) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len (v2 ^ k)) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,t,(v2 ^ k)) . ((len (v2 ^ k)) + 1) is set
(T,t,o) is Element of the carrier of T
(T,o) is directed lower Element of bool the carrier of T
(T,o) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,o) /\ (downarrow t)),T) is Element of the carrier of T
dom v2 is finite Element of bool NAT
b is set
v2 . b is set
u is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
t2 . u is set
dom k is finite Element of bool NAT
b is set
k . b is set
u is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
1 + u is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
0 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
X + u is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
X + 0 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
c12 . (1 + u) is set
t2 + (1 + u) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
t2 . (t2 + (1 + u)) is set
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () ()
the carrier of T is non empty set
the of T is non empty set
bool the of T is non empty cup-closed diff-closed preBoolean set
(T) is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
[: the carrier of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
a is finite Element of bool the of T
(T,t,a) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,a) is directed lower Element of bool the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow t)),T) is Element of the carrier of T
t2 is Relation-like NAT -defined the of T -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like FinSequence of the of T
rng t2 is finite Element of bool the of T
(T,t,t2) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
Rev (T,t,t2) is Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len (Rev (T,t,t2)) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
len (T,t,t2) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
dom (Rev (T,t,t2)) is finite Element of bool NAT
X is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
X + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(Rev (T,t,t2)) . X is set
(Rev (T,t,t2)) . (X + 1) is set
[((Rev (T,t,t2)) . X),((Rev (T,t,t2)) . (X + 1))] is set
{((Rev (T,t,t2)) . X),((Rev (T,t,t2)) . (X + 1))} is non empty finite set
{((Rev (T,t,t2)) . X)} is non empty trivial finite 1 -element set
{{((Rev (T,t,t2)) . X),((Rev (T,t,t2)) . (X + 1))},{((Rev (T,t,t2)) . X)}} is non empty finite V40() set
len t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len t2) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
((len t2) + 1) - X is V15() ext-real V173() set
(((len t2) + 1) - X) + 1 is V15() ext-real V173() set
(T,t,t2) . ((((len t2) + 1) - X) + 1) is set
x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
(X + 1) + x is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
((len t2) + 1) - (X + 1) is V15() ext-real V173() set
(((len t2) + 1) - (X + 1)) + 1 is V15() ext-real V173() set
(T,t,t2) . ((((len t2) + 1) - (X + 1)) + 1) is set
X + x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
x + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () ()
the carrier of T is non empty set
the of T is non empty set
bool the of T is non empty cup-closed diff-closed preBoolean set
(T) is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
[: the carrier of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
a is Element of the carrier of T
t2 is finite Element of bool the of T
(T,a,t2) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,t2) is directed lower Element of bool the carrier of T
downarrow a is non empty directed lower Element of bool the carrier of T
{a} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {a} is non empty lower Element of bool the carrier of T
(T,t2) /\ (downarrow a) is Element of bool the carrier of T
"\/" (((T,t2) /\ (downarrow a)),T) is Element of the carrier of T
X is Element of bool the of T
(T,a,X) is Element of the carrier of T
(T,X) is directed lower Element of bool the carrier of T
(T,X) /\ (downarrow a) is Element of bool the carrier of T
"\/" (((T,X) /\ (downarrow a)),T) is Element of the carrier of T
x is Relation-like NAT -defined the of T -valued Function-like one-to-one finite FinSequence-like FinSubsequence-like FinSequence of the of T
rng x is finite Element of bool the of T
(T,a,x) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
Rev (T,a,x) is Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
y is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like RedSequence of (T)
y . 1 is set
len y is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
y . (len y) is set
len (T,a,x) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,a,x) . (len (T,a,x)) is set
(T,a,x) is Element of the carrier of T
len x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len x) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,a,x) . ((len x) + 1) is set
y . (len (T,a,x)) is set
(T,a,x) . 1 is set
T is non empty set
[:T,T:] is non empty Relation-like set
bool [:T,T:] is non empty cup-closed diff-closed preBoolean set
t is Relation-like T -defined T -valued Element of bool [:T,T:]
a is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like RedSequence of t
a . 1 is set
t2 is set
rng a is non empty finite set
dom a is non empty finite Element of bool NAT
X is set
a . X is set
x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
1 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
y is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
(1 + 1) + y is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
y + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(y + 1) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
len a is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
a . (y + 1) is set
[(a . (y + 1)),t2] is set
{(a . (y + 1)),t2} is non empty finite set
{(a . (y + 1))} is non empty trivial finite 1 -element set
{{(a . (y + 1)),t2},{(a . (y + 1))}} is non empty finite V40() set
T is non empty set
[:T,T:] is non empty Relation-like set
bool [:T,T:] is non empty cup-closed diff-closed preBoolean set
t is Relation-like T -defined T -valued Element of bool [:T,T:]
a is Element of T
t2 is set
X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like RedSequence of t
X . 1 is set
len X is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
X . (len X) is set
0 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
dom X is non empty finite Element of bool NAT
rng X is non empty finite set
T is non empty set
[:T,T:] is non empty Relation-like set
bool [:T,T:] is non empty cup-closed diff-closed preBoolean set
t is Relation-like T -defined T -valued Element of bool [:T,T:]
a is Element of T
nf (a,t) is set
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () ()
the carrier of T is non empty set
(T) is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
[: the carrier of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
the of T is non empty set
bool the of T is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
a is Element of the carrier of T
X is non empty Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like RedSequence of (T)
X . 1 is set
len X is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
X . (len X) is set
Rev X is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (Rev X) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len X) - 1 is V15() ext-real V173() set
((len X) - 1) + 1 is V15() ext-real V173() set
0 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
x is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
1 + x is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
t1 is set
y is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
Seg y is finite y -element Element of bool NAT
{ b1 where b1 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT : ( 1 <= b1 & b1 <= y ) } is set
t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
t2 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
dom X is non empty finite Element of bool NAT
X . t2 is set
X . (t2 + 1) is set
[(X . t2),(X . (t2 + 1))] is set
{(X . t2),(X . (t2 + 1))} is non empty finite set
{(X . t2)} is non empty trivial finite 1 -element set
{{(X . t2),(X . (t2 + 1))},{(X . t2)}} is non empty finite V40() set
a3 is Element of the carrier of T
(T,a3) is Element of bool the of T
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . a3 is set
v2 is Element of the carrier of T
c12 is Element of the of T
(T,a3,c12) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,c12) is directed lower Element of bool the carrier of T
downarrow a3 is non empty directed lower Element of bool the carrier of T
{a3} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {a3} is non empty lower Element of bool the carrier of T
(T,c12) /\ (downarrow a3) is Element of bool the carrier of T
"\/" (((T,c12) /\ (downarrow a3)),T) is Element of the carrier of T
t1 is Relation-like Function-like set
dom t1 is set
rng t1 is set
t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
len t2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
Rev t2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
(T,a,(Rev t2)) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len (Rev t2) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
a3 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
1 + a3 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(Rev X) . (1 + a3) is set
(T,a,(Rev t2)) . (1 + a3) is set
a3 + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
1 + (a3 + 1) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
c12 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
(a3 + 1) + c12 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
y + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(y + 1) - (a3 + 1) is V15() ext-real V173() set
a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
a + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
dom (Rev X) is finite Element of bool NAT
(Rev X) . (a3 + 1) is set
(a + 1) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
X . ((a + 1) + 1) is set
(y + 1) - (1 + (a3 + 1)) is V15() ext-real V173() set
(Rev X) . (1 + (a3 + 1)) is set
X . (a + 1) is set
(a + 1) + a3 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
t2 . (a + 1) is set
k is Element of the of T
s is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
k is Element of the carrier of T
(T,k,k) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,k) is directed lower Element of bool the carrier of T
downarrow k is non empty directed lower Element of bool the carrier of T
{k} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {k} is non empty lower Element of bool the carrier of T
(T,k) /\ (downarrow k) is Element of bool the carrier of T
"\/" (((T,k) /\ (downarrow k)),T) is Element of the carrier of T
X . s is set
s + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
X . (s + 1) is set
dom (Rev t2) is finite Element of bool NAT
(Rev t2) . (a3 + 1) is set
(len t2) - (a3 + 1) is V15() ext-real V173() set
((len t2) - (a3 + 1)) + 1 is V15() ext-real V173() set
t2 . (((len t2) - (a3 + 1)) + 1) is set
(T,a,(Rev t2)) . (1 + (a3 + 1)) is set
rng t2 is finite Element of bool the of T
a3 is finite Element of bool the of T
(T,a,a3) is Element of the carrier of T
(T,a3) is directed lower Element of bool the carrier of T
downarrow a is non empty directed lower Element of bool the carrier of T
{a} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {a} is non empty lower Element of bool the carrier of T
(T,a3) /\ (downarrow a) is Element of bool the carrier of T
"\/" (((T,a3) /\ (downarrow a)),T) is Element of the carrier of T
len (T,a,(Rev t2)) is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(len (Rev t2)) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(Rev X) . 1 is set
1 + 0 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(Rev X) . (1 + 0) is set
(T,a,(Rev t2)) . (1 + 0) is set
c12 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
a is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
1 + a is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(Rev X) . c12 is set
(T,a,(Rev t2)) . c12 is set
Rev (T,a,(Rev t2)) is Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
c12 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
(Rev t2) . c12 is set
(T,a,(Rev t2)) . c12 is set
a is Element of the of T
s is Element of the carrier of T
k is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
c12 + k is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() set
k is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
k + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(len t2) - c12 is V15() ext-real V173() set
((len t2) - c12) + 1 is V15() ext-real V173() set
t2 . (((len t2) - c12) + 1) is set
b is Element of the of T
o is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
u is Element of the carrier of T
(T,u,b) is Element of the carrier of T
(T,b) is directed lower Element of bool the carrier of T
downarrow u is non empty directed lower Element of bool the carrier of T
{u} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {u} is non empty lower Element of bool the carrier of T
(T,b) /\ (downarrow u) is Element of bool the carrier of T
"\/" (((T,b) /\ (downarrow u)),T) is Element of the carrier of T
X . o is set
o + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
X . (o + 1) is set
(k + 1) + c12 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(len (T,a,(Rev t2))) - (o + 1) is V15() ext-real V173() set
((len (T,a,(Rev t2))) - (o + 1)) + 1 is V15() ext-real V173() set
rng (Rev t2) is finite Element of bool the of T
rng (Rev t2) is finite Element of bool the of T
(T,a,(Rev t2)) is Element of the carrier of T
(T,a,(Rev t2)) . ((len (Rev t2)) + 1) is set
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () () ()
(T) is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
the carrier of T is non empty set
[: the carrier of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
a is set
t2 is set
[a,t2] is set
{a,t2} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,t2},{a}} is non empty finite V40() set
X is set
[a,X] is set
{a,X} is non empty finite set
{{a,X},{a}} is non empty finite V40() set
the of T is non empty set
y is Element of the carrier of T
(T,y) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . y is set
x is Element of the carrier of T
t2 is Element of the of T
(T,y,t2) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,t2) is directed lower Element of bool the carrier of T
downarrow y is non empty directed lower Element of bool the carrier of T
{y} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {y} is non empty lower Element of bool the carrier of T
(T,t2) /\ (downarrow y) is Element of bool the carrier of T
"\/" (((T,t2) /\ (downarrow y)),T) is Element of the carrier of T
t1 is Element of the carrier of T
y "\/" t1 is Element of the carrier of T
(T,t1) is Element of bool the of T
the of T . t1 is set
a3 is Element of the of T
(T,t1,a3) is Element of the carrier of T
(T,a3) is directed lower Element of bool the carrier of T
downarrow t1 is non empty directed lower Element of bool the carrier of T
{t1} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t1} is non empty lower Element of bool the carrier of T
(T,a3) /\ (downarrow t1) is Element of bool the carrier of T
"\/" (((T,a3) /\ (downarrow t1)),T) is Element of the carrier of T
c12 is finite Element of bool the of T
(T,(y "\/" t1),c12) is Element of the carrier of T
(T,c12) is directed lower Element of bool the carrier of T
downarrow (y "\/" t1) is non empty directed lower Element of bool the carrier of T
{(y "\/" t1)} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {(y "\/" t1)} is non empty lower Element of bool the carrier of T
(T,c12) /\ (downarrow (y "\/" t1)) is Element of bool the carrier of T
"\/" (((T,c12) /\ (downarrow (y "\/" t1))),T) is Element of the carrier of T
a is finite Element of bool the of T
(T,(y "\/" t1),a) is Element of the carrier of T
(T,a) is directed lower Element of bool the carrier of T
(T,a) /\ (downarrow (y "\/" t1)) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow (y "\/" t1))),T) is Element of the carrier of T
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () () ()
the carrier of T is non empty set
(T) is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
[: the carrier of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
nf (t,(T)) is set
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () () ()
the carrier of T is non empty set
(T) is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
[: the carrier of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
(T,t) is Element of the carrier of T
nf (t,(T)) is set
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () () ()
the carrier of T is non empty set
t is Element of the carrier of T
(T,t) is Element of the carrier of T
(T) is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
[: the carrier of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
nf (t,(T)) is set
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () () ()
the carrier of T is non empty set
the of T is non empty set
bool the of T is non empty cup-closed diff-closed preBoolean set
t is Element of the carrier of T
{ b1 where b1 is Element of the carrier of T : ex b2 being finite Element of bool the of T st
( (T,b1,b2) & (T,b1,b2) = t ) } is set
(T,t) is Element of the carrier of T
(T) is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
[: the carrier of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
nf (t,(T)) is set
X is Element of the carrier of T
x is Element of the carrier of T
y is finite Element of bool the of T
(T,x,y) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,y) is directed lower Element of bool the carrier of T
downarrow x is non empty directed lower Element of bool the carrier of T
{x} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {x} is non empty lower Element of bool the carrier of T
(T,y) /\ (downarrow x) is Element of bool the carrier of T
"\/" (((T,y) /\ (downarrow x)),T) is Element of the carrier of T
nf (X,(T)) is set
X is finite Element of bool the of T
(T,(T,t),X) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,X) is directed lower Element of bool the carrier of T
downarrow (T,t) is non empty directed lower Element of bool the carrier of T
{(T,t)} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {(T,t)} is non empty lower Element of bool the carrier of T
(T,X) /\ (downarrow (T,t)) is Element of bool the carrier of T
"\/" (((T,X) /\ (downarrow (T,t))),T) is Element of the carrier of T
X is Element of the carrier of T
X is set
"\/" (X,T) is Element of the carrier of T
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
a is Element of the carrier of T
(T,a) is Element of the carrier of T
(T) is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
[: the carrier of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
nf (a,(T)) is set
t2 is Element of the of T
(T,t,t2) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,t2) is directed lower Element of bool the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,t2) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,t2) /\ (downarrow t)),T) is Element of the carrier of T
bool the of T is non empty cup-closed diff-closed preBoolean set
{ b1 where b1 is Element of the carrier of T : ex b2 being finite Element of bool the of T st
( (T,b1,b2) & (T,b1,b2) = a ) } is set
t "\/" (T,a) is Element of the carrier of T
y is finite Element of bool the of T
(T,(t "\/" (T,a)),y) is Element of the carrier of T
(T,y) is directed lower Element of bool the carrier of T
downarrow (t "\/" (T,a)) is non empty directed lower Element of bool the carrier of T
{(t "\/" (T,a))} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {(t "\/" (T,a))} is non empty lower Element of bool the carrier of T
(T,y) /\ (downarrow (t "\/" (T,a))) is Element of bool the carrier of T
"\/" (((T,y) /\ (downarrow (t "\/" (T,a)))),T) is Element of the carrier of T
t1 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
rng t1 is finite Element of bool the of T
t2 is finite Element of bool the of T
(T,(T,a),t2) is Element of the carrier of T
(T,t2) is directed lower Element of bool the carrier of T
downarrow (T,a) is non empty directed lower Element of bool the carrier of T
{(T,a)} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {(T,a)} is non empty lower Element of bool the carrier of T
(T,t2) /\ (downarrow (T,a)) is Element of bool the carrier of T
"\/" (((T,t2) /\ (downarrow (T,a))),T) is Element of the carrier of T
v2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
rng v2 is finite Element of bool the of T
t1 ^ v2 is Relation-like NAT -defined the of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the of T
rng (t1 ^ v2) is finite Element of bool the of T
y \/ t2 is finite Element of bool the of T
(T,(t "\/" (T,a)),t1) is Element of the carrier of T
(T,(t "\/" (T,a)),t1) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len t1 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len t1) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,(t "\/" (T,a)),t1) . ((len t1) + 1) is set
(T,(t "\/" (T,a)),(y \/ t2)) is Element of the carrier of T
(T,(y \/ t2)) is directed lower Element of bool the carrier of T
(T,(y \/ t2)) /\ (downarrow (t "\/" (T,a))) is Element of bool the carrier of T
"\/" (((T,(y \/ t2)) /\ (downarrow (t "\/" (T,a)))),T) is Element of the carrier of T
(T,(t "\/" (T,a)),(t1 ^ v2)) is Element of the carrier of T
(T,(t "\/" (T,a)),(t1 ^ v2)) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len (t1 ^ v2) is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len (t1 ^ v2)) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,(t "\/" (T,a)),(t1 ^ v2)) . ((len (t1 ^ v2)) + 1) is set
(T,(T,a),v2) is Element of the carrier of T
(T,(T,a),v2) is non empty Relation-like NAT -defined the carrier of T -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of T
len v2 is V8() V9() V10() V14() V15() ext-real non negative finite cardinal V173() Element of NAT
(len v2) + 1 is non empty V8() V9() V10() V14() V15() ext-real positive non negative finite cardinal V173() Element of NAT
(T,(T,a),v2) . ((len v2) + 1) is set
"\/" ( { b1 where b1 is Element of the carrier of T : ex b2 being finite Element of bool the of T st
( (T,b1,b2) & (T,b1,b2) = a ) } ,T) is Element of the carrier of T
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () () ()
the carrier of T is non empty set
(T) is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
[: the carrier of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
a is Element of the carrier of T
t2 is Element of the carrier of T
(T,a) is Element of the carrier of T
nf (a,(T)) is set
(T,t2) is Element of the carrier of T
nf (t2,(T)) is set
x is Element of the carrier of T
y is Element of the carrier of T
t1 is Element of the carrier of T
x is Element of the carrier of T
y is Element of the carrier of T
[x,y] is Element of [: the carrier of T, the carrier of T:]
{x,y} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,y},{x}} is non empty finite V40() set
the of T is non empty set
t2 is Element of the carrier of T
(T,t2) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . t2 is set
t1 is Element of the carrier of T
v2 is Element of the of T
(T,t2,v2) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,v2) is directed lower Element of bool the carrier of T
downarrow t2 is non empty directed lower Element of bool the carrier of T
{t2} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t2} is non empty lower Element of bool the carrier of T
(T,v2) /\ (downarrow t2) is Element of bool the carrier of T
"\/" (((T,v2) /\ (downarrow t2)),T) is Element of the carrier of T
x is Element of the carrier of T
T is non empty reflexive transitive antisymmetric with_suprema upper-bounded () () () () () ()
the carrier of T is non empty set
the of T is non empty set
t is Element of the carrier of T
(T,t) is Element of the carrier of T
(T) is Relation-like the carrier of T -defined the carrier of T -valued Element of bool [: the carrier of T, the carrier of T:]
[: the carrier of T, the carrier of T:] is non empty Relation-like set
bool [: the carrier of T, the carrier of T:] is non empty cup-closed diff-closed preBoolean set
nf (t,(T)) is set
a is Element of the of T
(T,t,a) is Element of the carrier of T
bool the carrier of T is non empty cup-closed diff-closed preBoolean set
(T,a) is directed lower Element of bool the carrier of T
downarrow t is non empty directed lower Element of bool the carrier of T
{t} is non empty trivial finite 1 -element Element of bool the carrier of T
downarrow {t} is non empty lower Element of bool the carrier of T
(T,a) /\ (downarrow t) is Element of bool the carrier of T
"\/" (((T,a) /\ (downarrow t)),T) is Element of the carrier of T
(T,(T,t,a)) is Element of the carrier of T
nf ((T,t,a),(T)) is set
(T,t) is Element of bool the of T
bool the of T is non empty cup-closed diff-closed preBoolean set
the of T is non empty Relation-like the carrier of T -defined Fin the of T -valued Function-like V29( the carrier of T) V33( the carrier of T, Fin the of T) Element of bool [: the carrier of T,(Fin the of T):]
Fin the of T is non empty cup-closed diff-closed preBoolean set
[: the carrier of T,(Fin the of T):] is non empty Relation-like set
bool [: the carrier of T,(Fin the of T):] is non empty cup-closed diff-closed preBoolean set
the of T . t is set
[(T,t,a),t] is Element of [: the carrier of T, the carrier of T:]
{(T,t,a),t} is non empty finite set
{(T,t,a)} is non empty trivial finite 1 -element set
{{(T,t,a),t},{(T,t,a)}} is non empty finite V40() set