MODELC_3

:: MODELC_3 semantic presentation

REAL is non empty non trivial non finite set
NAT is epsilon-transitive epsilon-connected ordinal non empty non trivial non finite cardinal limit_cardinal Element of bool REAL
bool REAL is non empty non trivial non finite set
omega is epsilon-transitive epsilon-connected ordinal non empty non trivial non finite cardinal limit_cardinal set
bool omega is non empty non trivial non finite set
bool NAT is non empty non trivial non finite set
K372() is set
CTL_WFF is non empty set
bool CTL_WFF is non empty set
LTL_WFF is non empty set
bool LTL_WFF is non empty set
AtomicFamily is non empty set
atomic_LTL is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : b₁ is atomic } is set
bool atomic_LTL is non empty set
Inf_seq AtomicFamily is non empty set
K86(NAT,AtomicFamily) is functional non empty M4( NAT , AtomicFamily )
ModelSP (Inf_seq AtomicFamily) is set
bool (ModelSP (Inf_seq AtomicFamily)) is non empty set
AtomicBasicAsgn is non empty Element of bool (ModelSP (Inf_seq AtomicFamily))
{ b₁ where b₁ is Element of ModelSP (Inf_seq AtomicFamily) : ex b₂ being set st b₁ = AtomicAsgn b₂ } is set
Inf_seqModel (AtomicFamily,AtomicBasicAsgn) is non empty strict with_basic LTLModelStr
And_ AtomicFamily is Relation-like [:(ModelSP (Inf_seq AtomicFamily)),(ModelSP (Inf_seq AtomicFamily)):] -defined ModelSP (Inf_seq AtomicFamily) -valued Function-like V25([:(ModelSP (Inf_seq AtomicFamily)),(ModelSP (Inf_seq AtomicFamily)):], ModelSP (Inf_seq AtomicFamily)) Element of bool [:[:(ModelSP (Inf_seq AtomicFamily)),(ModelSP (Inf_seq AtomicFamily)):],(ModelSP (Inf_seq AtomicFamily)):]
[:(ModelSP (Inf_seq AtomicFamily)),(ModelSP (Inf_seq AtomicFamily)):] is Relation-like set
[:[:(ModelSP (Inf_seq AtomicFamily)),(ModelSP (Inf_seq AtomicFamily)):],(ModelSP (Inf_seq AtomicFamily)):] is Relation-like set
bool [:[:(ModelSP (Inf_seq AtomicFamily)),(ModelSP (Inf_seq AtomicFamily)):],(ModelSP (Inf_seq AtomicFamily)):] is non empty set
Or_ AtomicFamily is Relation-like [:(ModelSP (Inf_seq AtomicFamily)),(ModelSP (Inf_seq AtomicFamily)):] -defined ModelSP (Inf_seq AtomicFamily) -valued Function-like V25([:(ModelSP (Inf_seq AtomicFamily)),(ModelSP (Inf_seq AtomicFamily)):], ModelSP (Inf_seq AtomicFamily)) Element of bool [:[:(ModelSP (Inf_seq AtomicFamily)),(ModelSP (Inf_seq AtomicFamily)):],(ModelSP (Inf_seq AtomicFamily)):]
Not_ AtomicFamily is Relation-like ModelSP (Inf_seq AtomicFamily) -defined ModelSP (Inf_seq AtomicFamily) -valued Function-like V21( ModelSP (Inf_seq AtomicFamily)) V25( ModelSP (Inf_seq AtomicFamily), ModelSP (Inf_seq AtomicFamily)) Element of bool [:(ModelSP (Inf_seq AtomicFamily)),(ModelSP (Inf_seq AtomicFamily)):]
bool [:(ModelSP (Inf_seq AtomicFamily)),(ModelSP (Inf_seq AtomicFamily)):] is non empty set
Next_ AtomicFamily is Relation-like ModelSP (Inf_seq AtomicFamily) -defined ModelSP (Inf_seq AtomicFamily) -valued Function-like V21( ModelSP (Inf_seq AtomicFamily)) V25( ModelSP (Inf_seq AtomicFamily), ModelSP (Inf_seq AtomicFamily)) Element of bool [:(ModelSP (Inf_seq AtomicFamily)),(ModelSP (Inf_seq AtomicFamily)):]
Until_ AtomicFamily is Relation-like [:(ModelSP (Inf_seq AtomicFamily)),(ModelSP (Inf_seq AtomicFamily)):] -defined ModelSP (Inf_seq AtomicFamily) -valued Function-like V25([:(ModelSP (Inf_seq AtomicFamily)),(ModelSP (Inf_seq AtomicFamily)):], ModelSP (Inf_seq AtomicFamily)) Element of bool [:[:(ModelSP (Inf_seq AtomicFamily)),(ModelSP (Inf_seq AtomicFamily)):],(ModelSP (Inf_seq AtomicFamily)):]
Release_ AtomicFamily is Relation-like [:(ModelSP (Inf_seq AtomicFamily)),(ModelSP (Inf_seq AtomicFamily)):] -defined ModelSP (Inf_seq AtomicFamily) -valued Function-like V25([:(ModelSP (Inf_seq AtomicFamily)),(ModelSP (Inf_seq AtomicFamily)):], ModelSP (Inf_seq AtomicFamily)) Element of bool [:[:(ModelSP (Inf_seq AtomicFamily)),(ModelSP (Inf_seq AtomicFamily)):],(ModelSP (Inf_seq AtomicFamily)):]
LTLModelStr(# (ModelSP (Inf_seq AtomicFamily)),AtomicBasicAsgn,(And_ AtomicFamily),(Or_ AtomicFamily),(Not_ AtomicFamily),(Next_ AtomicFamily),(Until_ AtomicFamily),(Release_ AtomicFamily) #) is strict LTLModelStr
the BasicAssign of (Inf_seqModel (AtomicFamily,AtomicBasicAsgn)) is non empty Element of bool the carrier of (Inf_seqModel (AtomicFamily,AtomicBasicAsgn))
the carrier of (Inf_seqModel (AtomicFamily,AtomicBasicAsgn)) is set
bool the carrier of (Inf_seqModel (AtomicFamily,AtomicBasicAsgn)) is non empty set
[:atomic_LTL, the BasicAssign of (Inf_seqModel (AtomicFamily,AtomicBasicAsgn)):] is Relation-like set
bool [:atomic_LTL, the BasicAssign of (Inf_seqModel (AtomicFamily,AtomicBasicAsgn)):] is non empty set
COMPLEX is non empty non trivial non finite set
RAT is non empty non trivial non finite set
INT is non empty non trivial non finite set
[:NAT,REAL:] is Relation-like non empty non trivial non finite set
bool [:NAT,REAL:] is non empty non trivial non finite set
ExtREAL is non empty set
{} is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty real integer finite finite-yielding V42() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative V257() V258() V259() V260() V261() set
1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
2 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
3 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
0 is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty real integer finite finite-yielding V42() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative V257() V258() V259() V260() V261() Element of NAT
Seg 1 is non empty trivial finite 1 -element Element of bool NAT
{1} is non empty trivial finite V42() 1 -element set
Seg 2 is non empty finite 2 -element Element of bool NAT
{1,2} is non empty finite V42() set
{{}} is functional non empty trivial finite V42() 1 -element set
atom. 0 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
6 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
6 + 0 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
<*(6 + 0)*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
card {} is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty real integer finite finite-yielding V42() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative V257() V258() V259() V260() V261() set
w is set
v is set
LS is set
v \/ LS is set
LT is set
(v \/ LS) \/ LT is set
w is set
v is set
LS is set
v \ LS is Element of bool v
bool v is non empty set
LT is set
IS is set
LT \ IS is Element of bool LT
bool LT is non empty set
(v \ LS) \/ (LT \ IS) is set
[:NAT,NAT:] is Relation-like non empty non trivial non finite set
bool [:NAT,NAT:] is non empty non trivial non finite set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*w*> is Relation-like NAT -defined bool [:NAT,NAT:] -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of bool [:NAT,NAT:]
<*w*> . 1 is set
rng <*w*> is non empty trivial finite 1 -element Element of bool (bool [:NAT,NAT:])
bool (bool [:NAT,NAT:]) is non empty non trivial non finite set
{w} is functional non empty trivial finite V42() 1 -element set
dom <*w*> is non empty trivial finite 1 -element Element of bool NAT
w is real ext-real V257() set
v is real ext-real V257() set
[\w/] is real integer ext-real V257() set
[\v/] is real integer ext-real V257() set
[\v/] + 1 is real integer ext-real V257() Element of REAL
w is real ext-real V257() set
v is real ext-real V257() set
v - 1 is real ext-real V257() Element of REAL
[\w/] is real integer ext-real V257() set
[\v/] is real integer ext-real V257() set
[\v/] - 1 is real integer ext-real V257() Element of REAL
w + 1 is real ext-real V257() Element of REAL
(v - 1) + 1 is real ext-real V257() Element of REAL
[\(w + 1)/] is real integer ext-real V257() set
[\w/] + 1 is real integer ext-real V257() Element of REAL
([\w/] + 1) - 1 is real integer ext-real V257() Element of REAL
w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
0 + w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_left_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_right_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{w} is functional non empty trivial finite V42() 1 -element set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae v is non empty set
bool (Subformulae v) is non empty set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae v is non empty set
bool (Subformulae v) is non empty set
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{w,LS} is functional non empty finite V42() set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_left_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_right_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{(the_left_argument_of w),(the_right_argument_of w)} is functional non empty finite V42() set
Subformulae w is non empty set
bool (Subformulae w) is non empty set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_left_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{(the_left_argument_of w)} is functional non empty trivial finite V42() 1 -element set
Subformulae w is non empty set
bool (Subformulae w) is non empty set
the_right_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{(the_right_argument_of w)} is functional non empty trivial finite V42() 1 -element set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{w} is functional non empty trivial finite V42() 1 -element set
Subformulae w is non empty set
bool (Subformulae w) is non empty set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{(the_argument_of w)} is functional non empty trivial finite V42() 1 -element set
Subformulae w is non empty set
bool (Subformulae w) is non empty set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae w is non empty set
bool (Subformulae w) is non empty set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_left_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_right_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{(the_left_argument_of w),(the_right_argument_of w)} is functional non empty finite V42() set
(w) is non empty Element of bool LTL_WFF
bool (w) is non empty set
{(the_left_argument_of w)} is functional non empty trivial finite V42() 1 -element set
{(the_right_argument_of w)} is functional non empty trivial finite V42() 1 -element set
v is Element of bool (w)
LS is Element of bool (w)
LT is Element of bool (w)
IS is Element of bool (w)
FS is Element of bool (w)
chf is Element of bool (w)
run is Element of bool (w)
FSet is Element of bool (w)
FK is Element of bool (w)
x is Element of bool (w)
v is Element of bool (w)
LS is Element of bool (w)
LT is Element of bool (w)
IS is Element of bool (w)
FS is Element of bool (w)
chf is Element of bool (w)
run is Element of bool (w)
FSet is Element of bool (w)
FK is Element of bool (w)
x is Element of bool (w)
the_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{(the_argument_of w)} is functional non empty trivial finite V42() 1 -element set
{w} is functional non empty trivial finite V42() 1 -element set
v is Element of bool (w)
LS is Element of bool (w)
LT is Element of bool (w)
IS is Element of bool (w)
FS is Element of bool (w)
chf is Element of bool (w)
run is Element of bool (w)
FSet is Element of bool (w)
FK is Element of bool (w)
x is Element of bool (w)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is (w)
the of v is Element of bool (w)
(w) is non empty Element of bool LTL_WFF
bool (w) is non empty set
the of v is Element of bool (w)
{LS} is functional non empty trivial finite V42() 1 -element set
the of v \/ {LS} is non empty set
the of v \ {LS} is Element of bool (w)
(LS) is non empty Element of bool LTL_WFF
(LS) is Element of bool (LS)
bool (LS) is non empty set
(LS) \ the of v is Element of bool (LS)
( the of v \ {LS}) \/ ((LS) \ the of v) is set
the of v is Element of bool (w)
(LS) is Element of bool (LS)
the of v \/ (LS) is set
FK is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
FSet is Element of bool (w)
FK is Element of bool (w)
x is Element of bool (w)
(w,FSet,FK,x) is (w) (w)
the of (w,FSet,FK,x) is Element of bool (w)
the of (w,FSet,FK,x) is Element of bool (w)
the of (w,FSet,FK,x) is Element of bool (w)
LT is (w) (w)
the of LT is Element of bool (w)
the of LT is Element of bool (w)
the of LT is Element of bool (w)
IS is (w) (w)
the of IS is Element of bool (w)
the of IS is Element of bool (w)
the of IS is Element of bool (w)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is (w)
the of v is Element of bool (w)
(w) is non empty Element of bool LTL_WFF
bool (w) is non empty set
the of v is Element of bool (w)
{LS} is functional non empty trivial finite V42() 1 -element set
the of v \/ {LS} is non empty set
the of v \ {LS} is Element of bool (w)
(LS) is non empty Element of bool LTL_WFF
(LS) is Element of bool (LS)
bool (LS) is non empty set
(LS) \ the of v is Element of bool (LS)
( the of v \ {LS}) \/ ((LS) \ the of v) is set
the of v is Element of bool (w)
FK is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
FSet is Element of bool (w)
FK is Element of bool (w)
(w,FSet,FK, the of v) is (w) (w)
the of (w,FSet,FK, the of v) is Element of bool (w)
the of (w,FSet,FK, the of v) is Element of bool (w)
the of (w,FSet,FK, the of v) is Element of bool (w)
LT is (w) (w)
the of LT is Element of bool (w)
the of LT is Element of bool (w)
the of LT is Element of bool (w)
IS is (w) (w)
the of IS is Element of bool (w)
the of IS is Element of bool (w)
the of IS is Element of bool (w)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty Element of bool LTL_WFF
bool (w) is non empty set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{w} is functional non empty trivial finite V42() 1 -element set
(w) is non empty Element of bool LTL_WFF
bool (w) is non empty set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is Element of bool (w)
(w) is non empty Element of bool LTL_WFF
bool (w) is non empty set
(w,(w),(w),(w)) is (w) (w)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is Element of bool (w)
(w) is non empty Element of bool LTL_WFF
bool (w) is non empty set
(w,(w),(w),(w)) is (w) (w)
w is set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(v) is Element of bool (v)
(v) is non empty Element of bool LTL_WFF
bool (v) is non empty set
(v,(v),(v),(v)) is (v) (v)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is Element of bool (w)
(w) is non empty Element of bool LTL_WFF
bool (w) is non empty set
(w) is Element of bool (w)
{w} is functional non empty trivial finite V42() 1 -element set
(w,(w),(w),(w)) is (w) (w)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is Element of bool (w)
(w) is non empty Element of bool LTL_WFF
bool (w) is non empty set
v is (w)
the of v is Element of bool (w)
(w,(w), the of v,(w)) is (w) (w)
w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
w - 1 is real integer ext-real V257() Element of REAL
v is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len v is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
v . w is set
(len v) - (w - 1) is real integer ext-real V257() Element of REAL
v . (len v) is set
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(len v) - 0 is real integer ext-real non negative V257() Element of REAL
IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Seg IS is finite IS -element Element of bool NAT
v | (Seg IS) is Relation-like NAT -defined Seg IS -defined NAT -defined Function-like finite FinSubsequence-like set
chf is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
run is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
chf ^ run is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
len run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(len chf) + (len run) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(len v) - (len chf) is real integer ext-real V257() Element of REAL
(len v) - IS is real integer ext-real V257() Element of REAL
w - w is real integer ext-real V257() set
(len v) - w is real integer ext-real V257() Element of REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
((len v) - w) + 1 is real integer ext-real V257() Element of REAL
dom run is finite Element of bool NAT
run . 1 is set
(len chf) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
v . ((len chf) + 1) is set
IS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
v . (IS + 1) is set
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . FSet is set
FSet + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run . (FSet + 1) is set
FSet + IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
1 + 0 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
((len v) - IS) + IS is real integer ext-real V257() Element of REAL
v . (FSet + IS) is set
(FSet + IS) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
v . ((FSet + IS) + 1) is set
F is (LS) (LS)
F2 is (LS) (LS)
IS + (FSet + 1) is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
v . (IS + (FSet + 1)) is set
run . (len run) is set
v . ((len chf) + (len run)) is set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty Element of bool LTL_WFF
bool (w) is non empty set
v is Element of bool (w)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty Element of bool LTL_WFF
v is (w) (w)
the of v is Element of bool (w)
bool (w) is non empty set
the of v is Element of bool (w)
the of v \/ the of v is Element of bool (w)
the of v is Element of bool (w)
(w, the of v) is Element of bool LTL_WFF
'X' (w, the of v) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of v) & b₁ = 'X' b₂ ) } is set
( the of v \/ the of v) \/ ('X' (w, the of v)) is set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is (v) (v)
the of LS is Element of bool (v)
(v) is non empty Element of bool LTL_WFF
bool (v) is non empty set
(v,LS) is Element of bool LTL_WFF
the of LS is Element of bool (v)
the of LS \/ the of LS is Element of bool (v)
the of LS is Element of bool (v)
(v, the of LS) is Element of bool LTL_WFF
'X' (v, the of LS) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of LS) & b₁ = 'X' b₂ ) } is set
( the of LS \/ the of LS) \/ ('X' (v, the of LS)) is set
(v,LS,w) is (v) (v)
(v,(v,LS,w)) is Element of bool LTL_WFF
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) \/ the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
(v, the of (v,LS,w)) is Element of bool LTL_WFF
'X' (v, the of (v,LS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,LS,w)) & b₁ = 'X' b₂ ) } is set
( the of (v,LS,w) \/ the of (v,LS,w)) \/ ('X' (v, the of (v,LS,w))) is set
(w) is Element of bool (w)
(w) is non empty Element of bool LTL_WFF
bool (w) is non empty set
the of LS \/ (w) is set
{w} is functional non empty trivial finite V42() 1 -element set
the of LS \/ {w} is non empty set
(w) is Element of bool (w)
the of LS \ {w} is Element of bool (v)
(w) \ the of LS is Element of bool (w)
( the of LS \ {w}) \/ ((w) \ the of LS) is set
x is set
x is set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is (v) (v)
the of LS is Element of bool (v)
(v) is non empty Element of bool LTL_WFF
bool (v) is non empty set
(v,LS) is Element of bool LTL_WFF
the of LS is Element of bool (v)
the of LS \/ the of LS is Element of bool (v)
the of LS is Element of bool (v)
(v, the of LS) is Element of bool LTL_WFF
'X' (v, the of LS) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of LS) & b₁ = 'X' b₂ ) } is set
( the of LS \/ the of LS) \/ ('X' (v, the of LS)) is set
(v,LS,w) is (v) (v)
(v,(v,LS,w)) is Element of bool LTL_WFF
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) \/ the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
(v, the of (v,LS,w)) is Element of bool LTL_WFF
'X' (v, the of (v,LS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,LS,w)) & b₁ = 'X' b₂ ) } is set
( the of (v,LS,w) \/ the of (v,LS,w)) \/ ('X' (v, the of (v,LS,w))) is set
LT is Element of Inf_seq AtomicFamily
F1 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{w} is functional non empty trivial finite V42() 1 -element set
the of LS \/ {w} is non empty set
{w} is functional non empty trivial finite V42() 1 -element set
the of LS \ {w} is Element of bool (v)
(w) is non empty Element of bool LTL_WFF
(w) is Element of bool (w)
bool (w) is non empty set
(w) \ the of LS is Element of bool (w)
( the of LS \ {w}) \/ ((w) \ the of LS) is set
the_left_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_right_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{(the_left_argument_of w),(the_right_argument_of w)} is functional non empty finite V42() set
(the_left_argument_of w) '&' (the_right_argument_of w) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*1*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*1*> ^ (the_left_argument_of w) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(<*1*> ^ (the_left_argument_of w)) ^ (the_right_argument_of w) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
m is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w1 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
'X' w1 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*3*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*3*> ^ w1 is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
w1 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
'X' w1 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*3*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*3*> ^ w1 is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(w) is Element of bool (w)
(w) is non empty Element of bool LTL_WFF
bool (w) is non empty set
the of LS \/ (w) is set
the_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{(the_argument_of w)} is functional non empty trivial finite V42() 1 -element set
F1 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{w} is functional non empty trivial finite V42() 1 -element set
the of LS \/ {w} is non empty set
{w} is functional non empty trivial finite V42() 1 -element set
the of LS \/ {w} is non empty set
{w} is functional non empty trivial finite V42() 1 -element set
the of LS \ {w} is Element of bool (v)
(w) is non empty Element of bool LTL_WFF
(w) is Element of bool (w)
bool (w) is non empty set
(w) \ the of LS is Element of bool (w)
( the of LS \ {w}) \/ ((w) \ the of LS) is set
(w) is Element of bool (w)
(w) is non empty Element of bool LTL_WFF
bool (w) is non empty set
the of LS \/ (w) is set
m is Element of bool (v)
(v,m) is Element of bool LTL_WFF
h is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
m2 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
'X' m2 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*3*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*3*> ^ m2 is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
m2 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
'X' m2 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*3*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*3*> ^ m2 is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
'X' (v,m) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v,m) & b₁ = 'X' b₂ ) } is set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is (v) (v)
the of LS is Element of bool (v)
(v) is non empty Element of bool LTL_WFF
bool (v) is non empty set
LT is Element of Inf_seq AtomicFamily
(v,LS) is Element of bool LTL_WFF
the of LS is Element of bool (v)
the of LS \/ the of LS is Element of bool (v)
the of LS is Element of bool (v)
(v, the of LS) is Element of bool LTL_WFF
'X' (v, the of LS) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of LS) & b₁ = 'X' b₂ ) } is set
( the of LS \/ the of LS) \/ ('X' (v, the of LS)) is set
(v,LS,w) is (v) (v)
(v,(v,LS,w)) is Element of bool LTL_WFF
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) \/ the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
(v, the of (v,LS,w)) is Element of bool LTL_WFF
'X' (v, the of (v,LS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,LS,w)) & b₁ = 'X' b₂ ) } is set
( the of (v,LS,w) \/ the of (v,LS,w)) \/ ('X' (v, the of (v,LS,w))) is set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is (v) (v)
the of LS is Element of bool (v)
(v) is non empty Element of bool LTL_WFF
bool (v) is non empty set
(v,LS) is Element of bool LTL_WFF
the of LS is Element of bool (v)
the of LS \/ the of LS is Element of bool (v)
the of LS is Element of bool (v)
(v, the of LS) is Element of bool LTL_WFF
'X' (v, the of LS) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of LS) & b₁ = 'X' b₂ ) } is set
( the of LS \/ the of LS) \/ ('X' (v, the of LS)) is set
(v,LS,w) is (v) (v)
(v,(v,LS,w)) is Element of bool LTL_WFF
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) \/ the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
(v, the of (v,LS,w)) is Element of bool LTL_WFF
'X' (v, the of (v,LS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,LS,w)) & b₁ = 'X' b₂ ) } is set
( the of (v,LS,w) \/ the of (v,LS,w)) \/ ('X' (v, the of (v,LS,w))) is set
(v,LS,w) is (v) (v)
(v,(v,LS,w)) is Element of bool LTL_WFF
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) \/ the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
(v, the of (v,LS,w)) is Element of bool LTL_WFF
'X' (v, the of (v,LS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,LS,w)) & b₁ = 'X' b₂ ) } is set
( the of (v,LS,w) \/ the of (v,LS,w)) \/ ('X' (v, the of (v,LS,w))) is set
LT is Element of Inf_seq AtomicFamily
(w) is Element of bool (w)
(w) is non empty Element of bool LTL_WFF
bool (w) is non empty set
the of LS \/ {} is set
the_left_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{w} is functional non empty trivial finite V42() 1 -element set
the of LS \/ {w} is non empty set
(w) is Element of bool (w)
{(the_left_argument_of w)} is functional non empty trivial finite V42() 1 -element set
the of LS \ {w} is Element of bool (v)
{(the_left_argument_of w)} \ the of LS is functional trivial finite V42() Element of bool {(the_left_argument_of w)}
bool {(the_left_argument_of w)} is non empty finite V42() set
( the of LS \ {w}) \/ ({(the_left_argument_of w)} \ the of LS) is set
L is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_right_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is Element of bool (w)
{(the_right_argument_of w)} is functional non empty trivial finite V42() 1 -element set
{(the_right_argument_of w)} \ the of LS is functional trivial finite V42() Element of bool {(the_right_argument_of w)}
bool {(the_right_argument_of w)} is non empty finite V42() set
( the of LS \ {w}) \/ ({(the_right_argument_of w)} \ the of LS) is set
m3 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(the_left_argument_of w) 'or' (the_right_argument_of w) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*2*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*2*> ^ (the_left_argument_of w) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(<*2*> ^ (the_left_argument_of w)) ^ (the_right_argument_of w) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
m3 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
m3 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
m3 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
m3 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is (v) (v)
the of LS is Element of bool (v)
(v) is non empty Element of bool LTL_WFF
bool (v) is non empty set
(v,LS) is Element of bool LTL_WFF
the of LS is Element of bool (v)
the of LS \/ the of LS is Element of bool (v)
the of LS is Element of bool (v)
(v, the of LS) is Element of bool LTL_WFF
'X' (v, the of LS) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of LS) & b₁ = 'X' b₂ ) } is set
( the of LS \/ the of LS) \/ ('X' (v, the of LS)) is set
(v,LS,w) is (v) (v)
(v,(v,LS,w)) is Element of bool LTL_WFF
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) \/ the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
(v, the of (v,LS,w)) is Element of bool LTL_WFF
'X' (v, the of (v,LS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,LS,w)) & b₁ = 'X' b₂ ) } is set
( the of (v,LS,w) \/ the of (v,LS,w)) \/ ('X' (v, the of (v,LS,w))) is set
(v,LS,w) is (v) (v)
(v,(v,LS,w)) is Element of bool LTL_WFF
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) \/ the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
(v, the of (v,LS,w)) is Element of bool LTL_WFF
'X' (v, the of (v,LS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,LS,w)) & b₁ = 'X' b₂ ) } is set
( the of (v,LS,w) \/ the of (v,LS,w)) \/ ('X' (v, the of (v,LS,w))) is set
LT is Element of Inf_seq AtomicFamily
(w) is Element of bool (w)
(w) is non empty Element of bool LTL_WFF
bool (w) is non empty set
{w} is functional non empty trivial finite V42() 1 -element set
the of LS \/ {w} is non empty set
the_right_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is Element of bool (w)
{(the_right_argument_of w)} is functional non empty trivial finite V42() 1 -element set
the of LS \ {w} is Element of bool (v)
{(the_right_argument_of w)} \ the of LS is functional trivial finite V42() Element of bool {(the_right_argument_of w)}
bool {(the_right_argument_of w)} is non empty finite V42() set
( the of LS \ {w}) \/ ({(the_right_argument_of w)} \ the of LS) is set
the_left_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the of LS \/ {w} is non empty set
(w) is Element of bool (w)
{(the_left_argument_of w)} is functional non empty trivial finite V42() 1 -element set
{(the_left_argument_of w)} \ the of LS is functional trivial finite V42() Element of bool {(the_left_argument_of w)}
bool {(the_left_argument_of w)} is non empty finite V42() set
( the of LS \ {w}) \/ ({(the_left_argument_of w)} \ the of LS) is set
'X' w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*3*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*3*> ^ w is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
m1 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
h is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
m2 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
'X' m2 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*3*> ^ m2 is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
m2 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
'X' m2 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*3*> ^ m2 is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
m3 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(the_left_argument_of w) 'U' (the_right_argument_of w) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
4 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
<*4*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*4*> ^ (the_left_argument_of w) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(<*4*> ^ (the_left_argument_of w)) ^ (the_right_argument_of w) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(the_left_argument_of w) '&' ('X' w) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*1*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*1*> ^ (the_left_argument_of w) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(<*1*> ^ (the_left_argument_of w)) ^ ('X' w) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(the_right_argument_of w) 'or' ((the_left_argument_of w) '&' ('X' w)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*2*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*2*> ^ (the_right_argument_of w) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(<*2*> ^ (the_right_argument_of w)) ^ ((the_left_argument_of w) '&' ('X' w)) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
m3 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
m3 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
m3 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
natMAX is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
k is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
'X' k is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*3*> ^ k is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
k is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
'X' k is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*3*> ^ k is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
m3 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is (v) (v)
the of LS is Element of bool (v)
(v) is non empty Element of bool LTL_WFF
bool (v) is non empty set
(v,LS) is Element of bool LTL_WFF
the of LS is Element of bool (v)
the of LS \/ the of LS is Element of bool (v)
the of LS is Element of bool (v)
(v, the of LS) is Element of bool LTL_WFF
'X' (v, the of LS) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of LS) & b₁ = 'X' b₂ ) } is set
( the of LS \/ the of LS) \/ ('X' (v, the of LS)) is set
(v,LS,w) is (v) (v)
(v,(v,LS,w)) is Element of bool LTL_WFF
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) \/ the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
(v, the of (v,LS,w)) is Element of bool LTL_WFF
'X' (v, the of (v,LS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,LS,w)) & b₁ = 'X' b₂ ) } is set
( the of (v,LS,w) \/ the of (v,LS,w)) \/ ('X' (v, the of (v,LS,w))) is set
(v,LS,w) is (v) (v)
(v,(v,LS,w)) is Element of bool LTL_WFF
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) \/ the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
(v, the of (v,LS,w)) is Element of bool LTL_WFF
'X' (v, the of (v,LS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,LS,w)) & b₁ = 'X' b₂ ) } is set
( the of (v,LS,w) \/ the of (v,LS,w)) \/ ('X' (v, the of (v,LS,w))) is set
LT is Element of Inf_seq AtomicFamily
(w) is Element of bool (w)
(w) is non empty Element of bool LTL_WFF
bool (w) is non empty set
{w} is functional non empty trivial finite V42() 1 -element set
the of LS \/ {w} is non empty set
the_right_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_left_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is Element of bool (w)
{(the_left_argument_of w),(the_right_argument_of w)} is functional non empty finite V42() set
the of LS \ {w} is Element of bool (v)
{(the_left_argument_of w),(the_right_argument_of w)} \ the of LS is functional finite V42() Element of bool {(the_left_argument_of w),(the_right_argument_of w)}
bool {(the_left_argument_of w),(the_right_argument_of w)} is non empty finite V42() set
( the of LS \ {w}) \/ ({(the_left_argument_of w),(the_right_argument_of w)} \ the of LS) is set
the of LS \/ {w} is non empty set
(w) is Element of bool (w)
{(the_right_argument_of w)} is functional non empty trivial finite V42() 1 -element set
{(the_right_argument_of w)} \ the of LS is functional trivial finite V42() Element of bool {(the_right_argument_of w)}
bool {(the_right_argument_of w)} is non empty finite V42() set
( the of LS \ {w}) \/ ({(the_right_argument_of w)} \ the of LS) is set
'X' w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*3*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*3*> ^ w is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
m1 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
h is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
m2 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
'X' m2 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*3*> ^ m2 is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
m2 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
'X' m2 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*3*> ^ m2 is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
m3 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(the_left_argument_of w) 'R' (the_right_argument_of w) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
5 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
<*5*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*5*> ^ (the_left_argument_of w) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(<*5*> ^ (the_left_argument_of w)) ^ (the_right_argument_of w) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(the_left_argument_of w) '&' (the_right_argument_of w) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*1*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*1*> ^ (the_left_argument_of w) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(<*1*> ^ (the_left_argument_of w)) ^ (the_right_argument_of w) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(the_right_argument_of w) '&' ('X' w) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*1*> ^ (the_right_argument_of w) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(<*1*> ^ (the_right_argument_of w)) ^ ('X' w) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
((the_left_argument_of w) '&' (the_right_argument_of w)) 'or' ((the_right_argument_of w) '&' ('X' w)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*2*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*2*> ^ ((the_left_argument_of w) '&' (the_right_argument_of w)) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(<*2*> ^ ((the_left_argument_of w) '&' (the_right_argument_of w))) ^ ((the_right_argument_of w) '&' ('X' w)) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
m3 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
m3 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
m3 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
natMAX is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
k is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
'X' k is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*3*> ^ k is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
k is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
'X' k is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*3*> ^ k is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
m3 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is (v) (v)
the of LS is Element of bool (v)
(v) is non empty Element of bool LTL_WFF
bool (v) is non empty set
LT is Element of Inf_seq AtomicFamily
(v,LS) is Element of bool LTL_WFF
the of LS is Element of bool (v)
the of LS \/ the of LS is Element of bool (v)
the of LS is Element of bool (v)
(v, the of LS) is Element of bool LTL_WFF
'X' (v, the of LS) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of LS) & b₁ = 'X' b₂ ) } is set
( the of LS \/ the of LS) \/ ('X' (v, the of LS)) is set
(v,LS,w) is (v) (v)
(v,(v,LS,w)) is Element of bool LTL_WFF
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) \/ the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
(v, the of (v,LS,w)) is Element of bool LTL_WFF
'X' (v, the of (v,LS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,LS,w)) & b₁ = 'X' b₂ ) } is set
( the of (v,LS,w) \/ the of (v,LS,w)) \/ ('X' (v, the of (v,LS,w))) is set
(v,LS,w) is (v) (v)
(v,(v,LS,w)) is Element of bool LTL_WFF
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) \/ the of (v,LS,w) is Element of bool (v)
the of (v,LS,w) is Element of bool (v)
(v, the of (v,LS,w)) is Element of bool LTL_WFF
'X' (v, the of (v,LS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,LS,w)) & b₁ = 'X' b₂ ) } is set
( the of (v,LS,w) \/ the of (v,LS,w)) \/ ('X' (v, the of (v,LS,w))) is set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty Element of bool LTL_WFF
the_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
((the_argument_of w)) is non empty Element of bool LTL_WFF
{w} is functional non empty trivial finite V42() 1 -element set
((the_argument_of w)) \/ {w} is non empty set
LS is set
LT is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty Element of bool LTL_WFF
the_left_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
((the_left_argument_of w)) is non empty Element of bool LTL_WFF
the_right_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
((the_right_argument_of w)) is non empty Element of bool LTL_WFF
((the_left_argument_of w)) \/ ((the_right_argument_of w)) is non empty Element of bool LTL_WFF
{w} is functional non empty trivial finite V42() 1 -element set
(((the_left_argument_of w)) \/ ((the_right_argument_of w))) \/ {w} is non empty set
IS is set
FS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty Element of bool LTL_WFF
{w} is functional non empty trivial finite V42() 1 -element set
len w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
v is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
atom. v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
6 + v is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
<*(6 + v)*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
v is set
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
len LS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
v is set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae w is non empty set
bool (Subformulae w) is non empty set
v is Element of bool (Subformulae w)
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty Element of bool LTL_WFF
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_argument_of v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
((the_argument_of v)) is non empty Element of bool LTL_WFF
(v) is non empty Element of bool LTL_WFF
LS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng LS is finite set
LS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng LS is finite set
<*v*> is Relation-like NAT -defined bool [:NAT,NAT:] -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of bool [:NAT,NAT:]
LS ^ <*v*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
rng (LS ^ <*v*>) is non empty finite set
rng <*v*> is non empty trivial finite 1 -element Element of bool (bool [:NAT,NAT:])
bool (bool [:NAT,NAT:]) is non empty non trivial non finite set
(rng LS) \/ (rng <*v*>) is non empty finite set
{v} is functional non empty trivial finite V42() 1 -element set
((the_argument_of v)) \/ {v} is non empty set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_left_argument_of v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
((the_left_argument_of v)) is non empty Element of bool LTL_WFF
the_right_argument_of v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
((the_right_argument_of v)) is non empty Element of bool LTL_WFF
(v) is non empty Element of bool LTL_WFF
LS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng LS is finite set
LS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng LS is finite set
LT is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng LT is finite set
LT is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng LT is finite set
LS ^ LT is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng (LS ^ LT) is finite set
((the_left_argument_of v)) \/ ((the_right_argument_of v)) is non empty Element of bool LTL_WFF
<*v*> is Relation-like NAT -defined bool [:NAT,NAT:] -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of bool [:NAT,NAT:]
(LS ^ LT) ^ <*v*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
rng ((LS ^ LT) ^ <*v*>) is non empty finite set
rng <*v*> is non empty trivial finite 1 -element Element of bool (bool [:NAT,NAT:])
bool (bool [:NAT,NAT:]) is non empty non trivial non finite set
(rng (LS ^ LT)) \/ (rng <*v*>) is non empty finite set
{v} is functional non empty trivial finite V42() 1 -element set
(((the_left_argument_of v)) \/ ((the_right_argument_of v))) \/ {v} is non empty set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(v) is non empty Element of bool LTL_WFF
<*v*> is Relation-like NAT -defined bool [:NAT,NAT:] -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of bool [:NAT,NAT:]
rng <*v*> is non empty trivial finite 1 -element set
rng <*v*> is non empty trivial finite 1 -element Element of bool (bool [:NAT,NAT:])
bool (bool [:NAT,NAT:]) is non empty non trivial non finite set
{v} is functional non empty trivial finite V42() 1 -element set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty Element of bool LTL_WFF
v is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng v is finite set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae w is non empty finite set
bool (Subformulae w) is non empty finite V42() set
LS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
LT is set
LS . LT is set
v is finite Element of bool (Subformulae w)
CastLTL (LS . LT) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
len (CastLTL (LS . LT)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae w is non empty finite set
bool (Subformulae w) is non empty finite V42() set
LS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
v is finite Element of bool (Subformulae w)
LT is set
(w,v,LS,LT) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS . IS is set
LT . IS is real ext-real V257() Element of REAL
CastLTL (LS . IS) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
len (CastLTL (LS . IS)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(w,v,LS,IS) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(w,v,LS,IS) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS . IS is set
LT . IS is real ext-real V257() Element of REAL
CastLTL (LS . IS) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
len (CastLTL (LS . IS)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS . FS is set
LT . FS is real ext-real V257() Element of REAL
LT is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
IS is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
FS is set
LT . FS is real ext-real V257() Element of REAL
IS . FS is real ext-real V257() Element of REAL
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS . chf is set
LT . chf is real ext-real V257() Element of REAL
CastLTL (LS . chf) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
len (CastLTL (LS . chf)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS . chf is set
LT . chf is real ext-real V257() Element of REAL
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS . chf is set
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS . FS is set
LT . FS is real ext-real V257() Element of REAL
CastLTL (LS . FS) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
len (CastLTL (LS . FS)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS . chf is set
LT . chf is real ext-real V257() Element of REAL
run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS . run is set
IS . run is real ext-real V257() Element of REAL
CastLTL (LS . run) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
len (CastLTL (LS . run)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS . FSet is set
IS . FSet is real ext-real V257() Element of REAL
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae w is non empty finite set
bool (Subformulae w) is non empty finite V42() set
v is finite Element of bool (Subformulae w)
LS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(w,v,LS) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
len LS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
Sum ((w,v,LS),(len LS)) is real ext-real V257() Element of REAL
Partial_Sums (w,v,LS) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (w,v,LS)) . (len LS) is real ext-real V257() Element of REAL
w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
v is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
Sum (v,w) is real ext-real V257() Element of REAL
Partial_Sums v is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums v) . w is real ext-real V257() Element of REAL
LS is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
Sum (LS,w) is real ext-real V257() Element of REAL
Partial_Sums LS is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums LS) . w is real ext-real V257() Element of REAL
CastNat w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
CastNat LT is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Sum (v,(CastNat LT)) is real ext-real V257() Element of REAL
(Partial_Sums v) . (CastNat LT) is real ext-real V257() Element of REAL
Sum (LS,(CastNat LT)) is real ext-real V257() Element of REAL
(Partial_Sums LS) . (CastNat LT) is real ext-real V257() Element of REAL
LT + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
CastNat (LT + 1) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Sum (v,(CastNat (LT + 1))) is real ext-real V257() Element of REAL
(Partial_Sums v) . (CastNat (LT + 1)) is real ext-real V257() Element of REAL
Sum (LS,(CastNat (LT + 1))) is real ext-real V257() Element of REAL
(Partial_Sums LS) . (CastNat (LT + 1)) is real ext-real V257() Element of REAL
v . (LT + 1) is real ext-real V257() Element of REAL
LS . (LT + 1) is real ext-real V257() Element of REAL
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
v . FS is real ext-real V257() Element of REAL
LS . FS is real ext-real V257() Element of REAL
Sum (v,(LT + 1)) is real ext-real V257() Element of REAL
(Partial_Sums v) . (LT + 1) is real ext-real V257() Element of REAL
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
Sum (LS,FS) is real ext-real V257() Element of REAL
(Partial_Sums LS) . FS is real ext-real V257() Element of REAL
(Sum (LS,FS)) + (LS . (LT + 1)) is real ext-real V257() Element of REAL
Sum (LS,(LT + 1)) is real ext-real V257() Element of REAL
(Partial_Sums LS) . (LT + 1) is real ext-real V257() Element of REAL
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
v . chf is real ext-real V257() Element of REAL
LS . chf is real ext-real V257() Element of REAL
IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
v . IS is real ext-real V257() Element of REAL
LS . IS is real ext-real V257() Element of REAL
CastNat 0 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Sum (v,(CastNat 0)) is real ext-real V257() Element of REAL
(Partial_Sums v) . (CastNat 0) is real ext-real V257() Element of REAL
Sum (LS,(CastNat 0)) is real ext-real V257() Element of REAL
(Partial_Sums LS) . (CastNat 0) is real ext-real V257() Element of REAL
Sum (v,0) is real ext-real V257() Element of REAL
(Partial_Sums v) . 0 is real ext-real V257() Element of REAL
v . 0 is real ext-real V257() Element of REAL
LS . 0 is real ext-real V257() Element of REAL
Sum (LS,0) is real ext-real V257() Element of REAL
(Partial_Sums LS) . 0 is real ext-real V257() Element of REAL
w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
v is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
Sum (LS,w) is real ext-real V257() Element of REAL
Partial_Sums LS is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums LS) . w is real ext-real V257() Element of REAL
LS . v is real ext-real V257() Element of REAL
(Sum (LS,w)) - (LS . v) is real ext-real V257() Element of REAL
LT is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
Sum (LT,w) is real ext-real V257() Element of REAL
Partial_Sums LT is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums LT) . w is real ext-real V257() Element of REAL
LT . v is real ext-real V257() Element of REAL
(Sum (LT,w)) - (LT . v) is real ext-real V257() Element of REAL
CastNat w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
CastNat IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Sum (LS,(CastNat IS)) is real ext-real V257() Element of REAL
(Partial_Sums LS) . (CastNat IS) is real ext-real V257() Element of REAL
(Sum (LS,(CastNat IS))) - (LS . v) is real ext-real V257() Element of REAL
Sum (LT,(CastNat IS)) is real ext-real V257() Element of REAL
(Partial_Sums LT) . (CastNat IS) is real ext-real V257() Element of REAL
(Sum (LT,(CastNat IS))) - (LT . v) is real ext-real V257() Element of REAL
IS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
CastNat (IS + 1) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Sum (LS,(CastNat (IS + 1))) is real ext-real V257() Element of REAL
(Partial_Sums LS) . (CastNat (IS + 1)) is real ext-real V257() Element of REAL
(Sum (LS,(CastNat (IS + 1)))) - (LS . v) is real ext-real V257() Element of REAL
Sum (LT,(CastNat (IS + 1))) is real ext-real V257() Element of REAL
(Partial_Sums LT) . (CastNat (IS + 1)) is real ext-real V257() Element of REAL
(Sum (LT,(CastNat (IS + 1)))) - (LT . v) is real ext-real V257() Element of REAL
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
Sum (LS,(IS + 1)) is real ext-real V257() Element of REAL
(Partial_Sums LS) . (IS + 1) is real ext-real V257() Element of REAL
(Sum (LS,(IS + 1))) - (LS . v) is real ext-real V257() Element of REAL
Sum (LS,chf) is real ext-real V257() Element of REAL
(Partial_Sums LS) . chf is real ext-real V257() Element of REAL
LS . (IS + 1) is real ext-real V257() Element of REAL
(Sum (LS,chf)) + (LS . (IS + 1)) is real ext-real V257() Element of REAL
((Sum (LS,chf)) + (LS . (IS + 1))) - (LS . v) is real ext-real V257() Element of REAL
(Sum (LS,chf)) - (LS . v) is real ext-real V257() Element of REAL
((Sum (LS,chf)) - (LS . v)) + (LS . (IS + 1)) is real ext-real V257() Element of REAL
Sum (LT,chf) is real ext-real V257() Element of REAL
(Partial_Sums LT) . chf is real ext-real V257() Element of REAL
(Sum (LT,chf)) - (LT . v) is real ext-real V257() Element of REAL
LT . (IS + 1) is real ext-real V257() Element of REAL
((Sum (LT,chf)) - (LT . v)) + (LT . (IS + 1)) is real ext-real V257() Element of REAL
(Sum (LT,chf)) + (LT . (IS + 1)) is real ext-real V257() Element of REAL
((Sum (LT,chf)) + (LT . (IS + 1))) - (LT . v) is real ext-real V257() Element of REAL
Sum (LT,(IS + 1)) is real ext-real V257() Element of REAL
(Partial_Sums LT) . (IS + 1) is real ext-real V257() Element of REAL
(Sum (LT,(IS + 1))) - (LT . v) is real ext-real V257() Element of REAL
run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS . run is real ext-real V257() Element of REAL
LT . run is real ext-real V257() Element of REAL
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
chf + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS . run is real ext-real V257() Element of REAL
LT . run is real ext-real V257() Element of REAL
Sum (LS,(IS + 1)) is real ext-real V257() Element of REAL
(Partial_Sums LS) . (IS + 1) is real ext-real V257() Element of REAL
(Sum (LS,(IS + 1))) - (LS . v) is real ext-real V257() Element of REAL
Sum (LS,chf) is real ext-real V257() Element of REAL
(Partial_Sums LS) . chf is real ext-real V257() Element of REAL
LS . (IS + 1) is real ext-real V257() Element of REAL
(Sum (LS,chf)) + (LS . (IS + 1)) is real ext-real V257() Element of REAL
((Sum (LS,chf)) + (LS . (IS + 1))) - (LS . v) is real ext-real V257() Element of REAL
Sum (LT,chf) is real ext-real V257() Element of REAL
(Partial_Sums LT) . chf is real ext-real V257() Element of REAL
LT . (IS + 1) is real ext-real V257() Element of REAL
(Sum (LT,chf)) + (LT . (IS + 1)) is real ext-real V257() Element of REAL
((Sum (LT,chf)) + (LT . (IS + 1))) - (LT . v) is real ext-real V257() Element of REAL
Sum (LT,(IS + 1)) is real ext-real V257() Element of REAL
(Partial_Sums LT) . (IS + 1) is real ext-real V257() Element of REAL
(Sum (LT,(IS + 1))) - (LT . v) is real ext-real V257() Element of REAL
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
chf + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS . FS is real ext-real V257() Element of REAL
LT . FS is real ext-real V257() Element of REAL
CastNat 0 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Sum (LS,(CastNat 0)) is real ext-real V257() Element of REAL
(Partial_Sums LS) . (CastNat 0) is real ext-real V257() Element of REAL
(Sum (LS,(CastNat 0))) - (LS . v) is real ext-real V257() Element of REAL
Sum (LT,(CastNat 0)) is real ext-real V257() Element of REAL
(Partial_Sums LT) . (CastNat 0) is real ext-real V257() Element of REAL
(Sum (LT,(CastNat 0))) - (LT . v) is real ext-real V257() Element of REAL
Sum (LT,0) is real ext-real V257() Element of REAL
(Partial_Sums LT) . 0 is real ext-real V257() Element of REAL
LT . 0 is real ext-real V257() Element of REAL
Sum (LS,0) is real ext-real V257() Element of REAL
(Partial_Sums LS) . 0 is real ext-real V257() Element of REAL
LS . 0 is real ext-real V257() Element of REAL
w is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(v) is finite Element of bool (v)
(v) is non empty finite Element of bool LTL_WFF
bool (v) is non empty finite V42() set
(v,(v),w) is real ext-real V257() Element of REAL
(v,(v),w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
len w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
Sum ((v,(v),w),(len w)) is real ext-real V257() Element of REAL
Partial_Sums (v,(v),w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (v,(v),w)) . (len w) is real ext-real V257() Element of REAL
LT is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(v,(v),w) . LT is real ext-real V257() Element of REAL
0 * LT is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty real integer finite finite-yielding V42() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative V257() V258() V259() V260() V261() Element of NAT
(0 * LT) + 0 is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty real integer finite finite-yielding V42() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative V257() V258() V259() V260() V261() Element of NAT
LT is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(Partial_Sums (v,(v),w)) . LT is real ext-real V257() Element of REAL
(v,(v),w) . 0 is real ext-real V257() Element of REAL
IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(Partial_Sums (v,(v),w)) . IS is real ext-real V257() Element of REAL
IS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
(v,(v),w) . IS is real ext-real V257() Element of REAL
((v,(v),w) . 0) + ((v,(v),w) . IS) is real ext-real V257() Element of REAL
(IS + 1) * (((v,(v),w) . 0) + ((v,(v),w) . IS)) is real ext-real V257() Element of REAL
((IS + 1) * (((v,(v),w) . 0) + ((v,(v),w) . IS))) / 2 is real ext-real V257() Element of REAL
0 + 0 is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty real integer finite finite-yielding V42() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative V257() V258() V259() V260() V261() Element of NAT
(IS + 1) * (0 + 0) is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty real integer finite finite-yielding V42() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative V257() V258() V259() V260() V261() Element of NAT
((IS + 1) * (0 + 0)) / 2 is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty real integer finite finite-yielding V42() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative V257() V258() V259() V260() V261() Element of REAL
w is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae v is non empty finite set
bool (Subformulae v) is non empty finite V42() set
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{LS} is functional non empty trivial finite V42() 1 -element set
LT is finite Element of bool (Subformulae v)
LT \ {LS} is finite Element of bool (Subformulae v)
(v,(LT \ {LS}),w) is real ext-real V257() Element of REAL
(v,(LT \ {LS}),w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
len w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
Sum ((v,(LT \ {LS}),w),(len w)) is real ext-real V257() Element of REAL
Partial_Sums (v,(LT \ {LS}),w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (v,(LT \ {LS}),w)) . (len w) is real ext-real V257() Element of REAL
(v,LT,w) is real ext-real V257() Element of REAL
(v,LT,w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
Sum ((v,LT,w),(len w)) is real ext-real V257() Element of REAL
Partial_Sums (v,LT,w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (v,LT,w)) . (len w) is real ext-real V257() Element of REAL
IS is set
IS is set
w is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng w is finite set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae v is non empty finite set
bool (Subformulae v) is non empty finite V42() set
(v) is non empty finite Element of bool LTL_WFF
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{LS} is functional non empty trivial finite V42() 1 -element set
len LS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LT is finite Element of bool (Subformulae v)
LT \ {LS} is finite Element of bool (Subformulae v)
(v,(LT \ {LS}),w) is real ext-real V257() Element of REAL
(v,(LT \ {LS}),w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
len w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
Sum ((v,(LT \ {LS}),w),(len w)) is real ext-real V257() Element of REAL
Partial_Sums (v,(LT \ {LS}),w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (v,(LT \ {LS}),w)) . (len w) is real ext-real V257() Element of REAL
(v,LT,w) is real ext-real V257() Element of REAL
(v,LT,w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
Sum ((v,LT,w),(len w)) is real ext-real V257() Element of REAL
Partial_Sums (v,LT,w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (v,LT,w)) . (len w) is real ext-real V257() Element of REAL
(v,LT,w) - (len LS) is real ext-real V257() Element of REAL
dom w is finite Element of bool NAT
IS is set
w . IS is set
Seg (len w) is finite len w -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT : ( 1 <= b₁ & b₁ <= len w ) } is set
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
w . FK is set
(v,(LT \ {LS}),w) . FK is real ext-real V257() Element of REAL
x is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(v,LT,w) . x is real ext-real V257() Element of REAL
(v,(LT \ {LS}),w) . x is real ext-real V257() Element of REAL
w . x is set
w . x is set
CastLTL (w . x) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
len (CastLTL (w . x)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(v,LT,w) . FK is real ext-real V257() Element of REAL
(Sum ((v,LT,w),(len w))) - ((v,LT,w) . FK) is real ext-real V257() Element of REAL
(Sum ((v,(LT \ {LS}),w),(len w))) - ((v,(LT \ {LS}),w) . FK) is real ext-real V257() Element of REAL
CastLTL (w . FK) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
len (CastLTL (w . FK)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
w is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng w is finite set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae v is non empty finite set
bool (Subformulae v) is non empty finite V42() set
(v) is non empty finite Element of bool LTL_WFF
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{LS} is functional non empty trivial finite V42() 1 -element set
len LS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LT is finite Element of bool (Subformulae v)
LT \/ {LS} is non empty finite set
(v,LT,w) is real ext-real V257() Element of REAL
(v,LT,w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
len w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
Sum ((v,LT,w),(len w)) is real ext-real V257() Element of REAL
Partial_Sums (v,LT,w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (v,LT,w)) . (len w) is real ext-real V257() Element of REAL
(v,LT,w) + (len LS) is real ext-real V257() Element of REAL
IS is finite Element of bool (Subformulae v)
(v,IS,w) is real ext-real V257() Element of REAL
(v,IS,w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
Sum ((v,IS,w),(len w)) is real ext-real V257() Element of REAL
Partial_Sums (v,IS,w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (v,IS,w)) . (len w) is real ext-real V257() Element of REAL
IS \ {LS} is finite Element of bool (Subformulae v)
FS is set
FS is set
(v,IS,w) - (len LS) is real ext-real V257() Element of REAL
w is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng w is finite set
v is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng v is finite set
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae LS is non empty finite set
bool (Subformulae LS) is non empty finite V42() set
(LS) is non empty finite Element of bool LTL_WFF
LT is finite Element of bool (Subformulae LS)
(LS,LT,w) is real ext-real V257() Element of REAL
(LS,LT,w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
len w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
Sum ((LS,LT,w),(len w)) is real ext-real V257() Element of REAL
Partial_Sums (LS,LT,w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (LS,LT,w)) . (len w) is real ext-real V257() Element of REAL
(LS,LT,v) is real ext-real V257() Element of REAL
(LS,LT,v) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
len v is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
Sum ((LS,LT,v),(len v)) is real ext-real V257() Element of REAL
Partial_Sums (LS,LT,v) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (LS,LT,v)) . (len v) is real ext-real V257() Element of REAL
card LT is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of omega
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
chf is finite Element of bool (Subformulae LS)
card chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of omega
(LS,chf,w) is real ext-real V257() Element of REAL
(LS,chf,w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
Sum ((LS,chf,w),(len w)) is real ext-real V257() Element of REAL
Partial_Sums (LS,chf,w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (LS,chf,w)) . (len w) is real ext-real V257() Element of REAL
(LS,chf,v) is real ext-real V257() Element of REAL
(LS,chf,v) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
Sum ((LS,chf,v),(len v)) is real ext-real V257() Element of REAL
Partial_Sums (LS,chf,v) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (LS,chf,v)) . (len v) is real ext-real V257() Element of REAL
run is set
FSet is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{FSet} is functional non empty trivial finite V42() 1 -element set
chf \ {FSet} is finite Element of bool (Subformulae LS)
card (chf \ {FSet}) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of omega
card {FSet} is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of omega
(card chf) - (card {FSet}) is real integer ext-real V257() set
(card chf) - 1 is real integer ext-real V257() Element of REAL
len FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(LS,chf,w) - (len FSet) is real ext-real V257() Element of REAL
((LS,chf,w) - (len FSet)) + (len FSet) is real ext-real V257() Element of REAL
(LS,(chf \ {FSet}),w) is real ext-real V257() Element of REAL
(LS,(chf \ {FSet}),w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
Sum ((LS,(chf \ {FSet}),w),(len w)) is real ext-real V257() Element of REAL
Partial_Sums (LS,(chf \ {FSet}),w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (LS,(chf \ {FSet}),w)) . (len w) is real ext-real V257() Element of REAL
(LS,(chf \ {FSet}),w) + (len FSet) is real ext-real V257() Element of REAL
(LS,chf,v) - (len FSet) is real ext-real V257() Element of REAL
((LS,chf,v) - (len FSet)) + (len FSet) is real ext-real V257() Element of REAL
(LS,(chf \ {FSet}),v) is real ext-real V257() Element of REAL
(LS,(chf \ {FSet}),v) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
Sum ((LS,(chf \ {FSet}),v),(len v)) is real ext-real V257() Element of REAL
Partial_Sums (LS,(chf \ {FSet}),v) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (LS,(chf \ {FSet}),v)) . (len v) is real ext-real V257() Element of REAL
(LS,(chf \ {FSet}),v) + (len FSet) is real ext-real V257() Element of REAL
chf is finite Element of bool (Subformulae LS)
card chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of omega
(LS,chf,w) is real ext-real V257() Element of REAL
(LS,chf,w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
Sum ((LS,chf,w),(len w)) is real ext-real V257() Element of REAL
Partial_Sums (LS,chf,w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (LS,chf,w)) . (len w) is real ext-real V257() Element of REAL
(LS,chf,v) is real ext-real V257() Element of REAL
(LS,chf,v) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
Sum ((LS,chf,v),(len v)) is real ext-real V257() Element of REAL
Partial_Sums (LS,chf,v) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (LS,chf,v)) . (len v) is real ext-real V257() Element of REAL
FS is finite Element of bool (Subformulae LS)
card FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of omega
(LS,FS,w) is real ext-real V257() Element of REAL
(LS,FS,w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
Sum ((LS,FS,w),(len w)) is real ext-real V257() Element of REAL
Partial_Sums (LS,FS,w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (LS,FS,w)) . (len w) is real ext-real V257() Element of REAL
(LS,FS,v) is real ext-real V257() Element of REAL
(LS,FS,v) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
Sum ((LS,FS,v),(len v)) is real ext-real V257() Element of REAL
Partial_Sums (LS,FS,v) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (LS,FS,v)) . (len v) is real ext-real V257() Element of REAL
(LS) is finite Element of bool (LS)
bool (LS) is non empty finite V42() set
FS is finite Element of bool (Subformulae LS)
card FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of omega
(LS,FS,w) is real ext-real V257() Element of REAL
(LS,FS,w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
Sum ((LS,FS,w),(len w)) is real ext-real V257() Element of REAL
Partial_Sums (LS,FS,w) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (LS,FS,w)) . (len w) is real ext-real V257() Element of REAL
(LS,FS,v) is real ext-real V257() Element of REAL
(LS,FS,v) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
Sum ((LS,FS,v),(len v)) is real ext-real V257() Element of REAL
Partial_Sums (LS,FS,v) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (LS,FS,v)) . (len v) is real ext-real V257() Element of REAL
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae w is non empty finite set
bool (Subformulae w) is non empty finite V42() set
(w) is non empty finite Element of bool LTL_WFF
v is finite Element of bool (Subformulae w)
LS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng LS is finite set
(w,v,LS) is real ext-real V257() Element of REAL
(w,v,LS) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
len LS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
Sum ((w,v,LS),(len LS)) is real ext-real V257() Element of REAL
Partial_Sums (w,v,LS) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (w,v,LS)) . (len LS) is real ext-real V257() Element of REAL
IS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng IS is finite set
LS is real ext-real V257() Element of REAL
(w,v,IS) is real ext-real V257() Element of REAL
(w,v,IS) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
len IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
Sum ((w,v,IS),(len IS)) is real ext-real V257() Element of REAL
Partial_Sums (w,v,IS) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (w,v,IS)) . (len IS) is real ext-real V257() Element of REAL
FS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng FS is finite set
LT is real ext-real V257() Element of REAL
(w,v,FS) is real ext-real V257() Element of REAL
(w,v,FS) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
len FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
Sum ((w,v,FS),(len FS)) is real ext-real V257() Element of REAL
Partial_Sums (w,v,FS) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (w,v,FS)) . (len FS) is real ext-real V257() Element of REAL
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae w is non empty finite set
bool (Subformulae w) is non empty finite V42() set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{v} is functional non empty trivial finite V42() 1 -element set
LS is finite Element of bool (Subformulae w)
LS \ {v} is finite Element of bool (Subformulae w)
(w,(LS \ {v})) is real ext-real V257() Element of REAL
(w,LS) is real ext-real V257() Element of REAL
(w) is non empty finite Element of bool LTL_WFF
LT is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng LT is finite set
(w,(LS \ {v}),LT) is real ext-real V257() Element of REAL
(w,(LS \ {v}),LT) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
len LT is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
Sum ((w,(LS \ {v}),LT),(len LT)) is real ext-real V257() Element of REAL
Partial_Sums (w,(LS \ {v}),LT) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (w,(LS \ {v}),LT)) . (len LT) is real ext-real V257() Element of REAL
(w,LS,LT) is real ext-real V257() Element of REAL
(w,LS,LT) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
Sum ((w,LS,LT),(len LT)) is real ext-real V257() Element of REAL
Partial_Sums (w,LS,LT) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (w,LS,LT)) . (len LT) is real ext-real V257() Element of REAL
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae w is non empty finite set
bool (Subformulae w) is non empty finite V42() set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{v} is functional non empty trivial finite V42() 1 -element set
len v is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LS is finite Element of bool (Subformulae w)
LS \ {v} is finite Element of bool (Subformulae w)
(w,(LS \ {v})) is real ext-real V257() Element of REAL
(w,LS) is real ext-real V257() Element of REAL
(w,LS) - (len v) is real ext-real V257() Element of REAL
(w) is non empty finite Element of bool LTL_WFF
LT is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng LT is finite set
(w,(LS \ {v}),LT) is real ext-real V257() Element of REAL
(w,(LS \ {v}),LT) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
len LT is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
Sum ((w,(LS \ {v}),LT),(len LT)) is real ext-real V257() Element of REAL
Partial_Sums (w,(LS \ {v}),LT) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (w,(LS \ {v}),LT)) . (len LT) is real ext-real V257() Element of REAL
(w,LS,LT) is real ext-real V257() Element of REAL
(w,LS,LT) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
Sum ((w,LS,LT),(len LT)) is real ext-real V257() Element of REAL
Partial_Sums (w,LS,LT) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (w,LS,LT)) . (len LT) is real ext-real V257() Element of REAL
(w,LS,LT) - (len v) is real ext-real V257() Element of REAL
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae w is non empty finite set
bool (Subformulae w) is non empty finite V42() set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{v} is functional non empty trivial finite V42() 1 -element set
len v is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LS is finite Element of bool (Subformulae w)
LS \/ {v} is non empty finite set
(w,LS) is real ext-real V257() Element of REAL
(w,LS) + (len v) is real ext-real V257() Element of REAL
LT is finite Element of bool (Subformulae w)
(w,LT) is real ext-real V257() Element of REAL
(w) is non empty finite Element of bool LTL_WFF
IS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng IS is finite set
(w,LT,IS) is real ext-real V257() Element of REAL
(w,LT,IS) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
len IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
Sum ((w,LT,IS),(len IS)) is real ext-real V257() Element of REAL
Partial_Sums (w,LT,IS) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (w,LT,IS)) . (len IS) is real ext-real V257() Element of REAL
(w,LS,IS) is real ext-real V257() Element of REAL
(w,LS,IS) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
Sum ((w,LS,IS),(len IS)) is real ext-real V257() Element of REAL
Partial_Sums (w,LS,IS) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (w,LS,IS)) . (len IS) is real ext-real V257() Element of REAL
(w,LS,IS) + (len v) is real ext-real V257() Element of REAL
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae w is non empty finite set
bool (Subformulae w) is non empty finite V42() set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{v} is functional non empty trivial finite V42() 1 -element set
len v is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LS is finite Element of bool (Subformulae w)
(w,LS) is real ext-real V257() Element of REAL
LT is finite Element of bool (Subformulae w)
LT \/ {v} is non empty finite set
(w,LT) is real ext-real V257() Element of REAL
(w,LT) + (len v) is real ext-real V257() Element of REAL
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
(w,(w)) is real ext-real V257() Element of REAL
v is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng v is finite set
(w,(w),v) is real ext-real V257() Element of REAL
(w,(w),v) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
len v is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
Sum ((w,(w),v),(len v)) is real ext-real V257() Element of REAL
Partial_Sums (w,(w),v) is Relation-like NAT -defined REAL -valued Function-like non empty V21( NAT ) V25( NAT , REAL ) V258() V259() V260() Element of bool [:NAT,REAL:]
(Partial_Sums (w,(w),v)) . (len v) is real ext-real V257() Element of REAL
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae w is non empty finite set
bool (Subformulae w) is non empty finite V42() set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{v} is functional non empty trivial finite V42() 1 -element set
len v is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LS is finite Element of bool (Subformulae w)
(w,LS) is real ext-real V257() Element of REAL
LS \ {v} is finite Element of bool (Subformulae w)
LT is set
LT is set
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
(w,LS) - (len v) is real ext-real V257() Element of REAL
((w,LS) - (len v)) + (len v) is real ext-real V257() Element of REAL
(w,(LS \ {v})) is real ext-real V257() Element of REAL
(w,(LS \ {v})) + (len v) is real ext-real V257() Element of REAL
0 + (len v) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae w is non empty finite set
bool (Subformulae w) is non empty finite V42() set
v is finite Element of bool (Subformulae w)
LS is finite Element of bool (Subformulae w)
LT is set
{LT} is non empty trivial finite 1 -element set
LS \ {LT} is finite Element of bool (Subformulae w)
v \ {LT} is finite Element of bool (Subformulae w)
IS is set
IS is set
LT is set
{LT} is non empty trivial finite 1 -element set
LS \ {LT} is finite Element of bool (Subformulae w)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae w is non empty finite set
bool (Subformulae w) is non empty finite V42() set
v is finite Element of bool (Subformulae w)
(w,v) is real ext-real V257() Element of REAL
LS is finite Element of bool (Subformulae w)
(w,LS) is real ext-real V257() Element of REAL
card LS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of omega
IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
FS is finite Element of bool (Subformulae w)
card FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of omega
(w,FS) is real ext-real V257() Element of REAL
chf is set
{chf} is non empty trivial finite 1 -element set
FS \ {chf} is finite Element of bool (Subformulae w)
chf is set
{chf} is non empty trivial finite 1 -element set
FS \ {chf} is finite Element of bool (Subformulae w)
(w) is non empty finite Element of bool LTL_WFF
run is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{run} is functional non empty trivial finite V42() 1 -element set
FS \ {run} is finite Element of bool (Subformulae w)
card (FS \ {run}) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of omega
card {run} is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of omega
(card FS) - (card {run}) is real integer ext-real V257() set
(card FS) - 1 is real integer ext-real V257() Element of REAL
(card (FS \ {run})) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
(w,(FS \ {run})) is real ext-real V257() Element of REAL
len run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(w,FS) - (len run) is real ext-real V257() Element of REAL
FS is finite Element of bool (Subformulae w)
card FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of omega
(w,FS) is real ext-real V257() Element of REAL
IS is finite Element of bool (Subformulae w)
card IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of omega
(w,IS) is real ext-real V257() Element of REAL
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
IS is finite Element of bool (Subformulae w)
card IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of omega
(w,IS) is real ext-real V257() Element of REAL
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae w is non empty finite set
bool (Subformulae w) is non empty finite V42() set
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
v is finite Element of bool (Subformulae w)
(w,v) is real ext-real V257() Element of REAL
LS is set
LT is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{LT} is functional non empty trivial finite V42() 1 -element set
FS is finite Element of bool (w)
(w,FS) is real ext-real V257() Element of REAL
len LT is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae w is non empty finite set
bool (Subformulae w) is non empty finite V42() set
v is finite Element of bool (Subformulae w)
(w,v) is real ext-real V257() Element of REAL
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
Subformulae w is non empty finite set
bool (Subformulae w) is non empty finite V42() set
v is finite Element of bool (Subformulae w)
(w,v) is real ext-real V257() Element of REAL
LS is finite Element of bool (Subformulae w)
(w,LS) is real ext-real V257() Element of REAL
LT is finite Element of bool (Subformulae w)
LS \/ LT is finite Element of bool (Subformulae w)
(w,LT) is real ext-real V257() Element of REAL
(w,LS) + (w,LT) is real ext-real V257() Element of REAL
card LS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of omega
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
chf is finite Element of bool (Subformulae w)
(w,chf) is real ext-real V257() Element of REAL
run is finite Element of bool (Subformulae w)
card run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of omega
(w,run) is real ext-real V257() Element of REAL
FSet is finite Element of bool (Subformulae w)
run \/ FSet is finite Element of bool (Subformulae w)
(w,FSet) is real ext-real V257() Element of REAL
(w,run) + (w,FSet) is real ext-real V257() Element of REAL
FK is set
(w) is non empty finite Element of bool LTL_WFF
x is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{x} is functional non empty trivial finite V42() 1 -element set
run \ {x} is finite Element of bool (Subformulae w)
(run \ {x}) \/ FSet is finite Element of bool (Subformulae w)
card (run \ {x}) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of omega
card {x} is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of omega
(card run) - (card {x}) is real integer ext-real V257() set
(card run) - 1 is real integer ext-real V257() Element of REAL
(card (run \ {x})) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
(w,((run \ {x}) \/ FSet)) is real ext-real V257() Element of REAL
(w,(run \ {x})) is real ext-real V257() Element of REAL
(w,(run \ {x})) + (w,FSet) is real ext-real V257() Element of REAL
len x is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(w,run) - (len x) is real ext-real V257() Element of REAL
((w,run) - (len x)) + (w,FSet) is real ext-real V257() Element of REAL
((w,run) + (w,FSet)) - (len x) is real ext-real V257() Element of REAL
(w,((run \ {x}) \/ FSet)) + (len x) is real ext-real V257() Element of REAL
((run \ {x}) \/ FSet) \/ {x} is non empty finite set
(run \ {x}) \/ {x} is non empty finite set
((run \ {x}) \/ {x}) \/ FSet is non empty finite set
run is finite Element of bool (Subformulae w)
card run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of omega
chf is finite Element of bool (Subformulae w)
FSet is finite Element of bool (Subformulae w)
run \/ FSet is finite Element of bool (Subformulae w)
(w,chf) is real ext-real V257() Element of REAL
(w,run) is real ext-real V257() Element of REAL
(w,FSet) is real ext-real V257() Element of REAL
(w,run) + (w,FSet) is real ext-real V257() Element of REAL
FS is finite Element of bool (Subformulae w)
(w,FS) is real ext-real V257() Element of REAL
chf is finite Element of bool (Subformulae w)
card chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of omega
(w,chf) is real ext-real V257() Element of REAL
run is finite Element of bool (Subformulae w)
chf \/ run is finite Element of bool (Subformulae w)
(w,run) is real ext-real V257() Element of REAL
(w,chf) + (w,run) is real ext-real V257() Element of REAL
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
chf is finite Element of bool (Subformulae w)
card chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of omega
FS is finite Element of bool (Subformulae w)
run is finite Element of bool (Subformulae w)
chf \/ run is finite Element of bool (Subformulae w)
(w,FS) is real ext-real V257() Element of REAL
(w,chf) is real ext-real V257() Element of REAL
(w,run) is real ext-real V257() Element of REAL
(w,chf) + (w,run) is real ext-real V257() Element of REAL
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty finite Element of bool LTL_WFF
(v) is finite Element of bool (v)
(v) is non empty finite Element of bool LTL_WFF
bool (v) is non empty finite V42() set
bool (w) is non empty finite V42() set
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(v) is finite Element of bool (v)
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
len w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(len w) - 1 is real integer ext-real V257() Element of REAL
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(v) is non empty finite Element of bool LTL_WFF
(v,w) is finite Element of bool (v)
bool (v) is non empty finite V42() set
(v,(v,w)) is real ext-real V257() Element of REAL
the_left_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{(the_left_argument_of w)} is functional non empty trivial finite V42() 1 -element set
the_right_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{(the_right_argument_of w)} is functional non empty trivial finite V42() 1 -element set
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
FS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{(the_left_argument_of w),(the_right_argument_of w)} is functional non empty finite V42() set
chf is finite Element of bool (v)
FS is finite Element of bool (v)
chf \/ FS is finite Element of bool (v)
(v,chf) is real ext-real V257() Element of REAL
(v,FS) is real ext-real V257() Element of REAL
(v,chf) + (v,FS) is real ext-real V257() Element of REAL
len (the_left_argument_of w) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
1 + (len (the_left_argument_of w)) is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
len (the_right_argument_of w) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(1 + (len (the_left_argument_of w))) + (len (the_right_argument_of w)) is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
len (the_left_argument_of w) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(v,(v,w)) + 0 is real ext-real V257() Element of REAL
len (the_right_argument_of w) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(len (the_left_argument_of w)) + (len (the_right_argument_of w)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
1 + (len (the_left_argument_of w)) is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
(1 + (len (the_left_argument_of w))) + (len (the_right_argument_of w)) is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
1 - 1 is real integer ext-real V257() Element of REAL
(v) is finite Element of bool (v)
len (the_right_argument_of w) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(v,(v,w)) + 0 is real ext-real V257() Element of REAL
len (the_left_argument_of w) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(len (the_left_argument_of w)) + (len (the_right_argument_of w)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
1 + (len (the_left_argument_of w)) is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
(1 + (len (the_left_argument_of w))) + (len (the_right_argument_of w)) is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
1 - 1 is real integer ext-real V257() Element of REAL
(v) is finite Element of bool (v)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
len w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(len w) - 1 is real integer ext-real V257() Element of REAL
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(v) is non empty finite Element of bool LTL_WFF
(v,w) is finite Element of bool (v)
bool (v) is non empty finite V42() set
(v,(v,w)) is real ext-real V257() Element of REAL
the_left_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{(the_left_argument_of w)} is functional non empty trivial finite V42() 1 -element set
the_right_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{(the_right_argument_of w)} is functional non empty trivial finite V42() 1 -element set
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
FS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{(the_left_argument_of w),(the_right_argument_of w)} is functional non empty finite V42() set
chf is finite Element of bool (v)
FS is finite Element of bool (v)
chf \/ FS is finite Element of bool (v)
(v,chf) is real ext-real V257() Element of REAL
(v,FS) is real ext-real V257() Element of REAL
(v,chf) + (v,FS) is real ext-real V257() Element of REAL
len (the_left_argument_of w) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
1 + (len (the_left_argument_of w)) is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
len (the_right_argument_of w) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(1 + (len (the_left_argument_of w))) + (len (the_right_argument_of w)) is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
len (the_right_argument_of w) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(v,(v,w)) + 0 is real ext-real V257() Element of REAL
len (the_left_argument_of w) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(len (the_left_argument_of w)) + (len (the_right_argument_of w)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
1 + (len (the_left_argument_of w)) is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
(1 + (len (the_left_argument_of w))) + (len (the_right_argument_of w)) is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
1 - 1 is real integer ext-real V257() Element of REAL
(v) is finite Element of bool (v)
1 - 1 is real integer ext-real V257() Element of REAL
(v) is finite Element of bool (v)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is (w) (w)
the of v is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
(w, the of v) is real ext-real V257() Element of REAL
LS is (w) (w)
the of LS is finite Element of bool (w)
(w, the of LS) is real ext-real V257() Element of REAL
(w, the of LS) - 1 is real ext-real V257() Element of REAL
FS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w,LS,FS) is (w) (w)
{FS} is functional non empty trivial finite V42() 1 -element set
the of LS \ {FS} is finite Element of bool (w)
(w,FS) is finite Element of bool (w)
the of LS is finite Element of bool (w)
(w,FS) \ the of LS is finite Element of bool (w)
(FS) is finite Element of bool (FS)
(FS) is non empty finite Element of bool LTL_WFF
bool (FS) is non empty finite V42() set
FK is finite Element of bool (w)
x is finite Element of bool (w)
FK \/ x is finite Element of bool (w)
(w,FK) is real ext-real V257() Element of REAL
(w,x) is real ext-real V257() Element of REAL
(w,FK) + (w,x) is real ext-real V257() Element of REAL
(w,(w,FS)) is real ext-real V257() Element of REAL
len FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(len FS) - 1 is real integer ext-real V257() Element of REAL
(w,FK) + ((len FS) - 1) is real ext-real V257() Element of REAL
F is finite Element of bool (w)
(w,F) is real ext-real V257() Element of REAL
(w,F) - (len FS) is real ext-real V257() Element of REAL
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is (w) (w)
the of v is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
(w, the of v) is real ext-real V257() Element of REAL
LS is (w) (w)
the of LS is finite Element of bool (w)
(w, the of LS) is real ext-real V257() Element of REAL
(w, the of LS) - 1 is real ext-real V257() Element of REAL
FS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w,LS,FS) is (w) (w)
{FS} is functional non empty trivial finite V42() 1 -element set
the of LS \ {FS} is finite Element of bool (w)
(w,FS) is finite Element of bool (w)
the of LS is finite Element of bool (w)
(w,FS) \ the of LS is finite Element of bool (w)
(FS) is finite Element of bool (FS)
(FS) is non empty finite Element of bool LTL_WFF
bool (FS) is non empty finite V42() set
FK is finite Element of bool (w)
x is finite Element of bool (w)
FK \/ x is finite Element of bool (w)
(w,FK) is real ext-real V257() Element of REAL
(w,x) is real ext-real V257() Element of REAL
(w,FK) + (w,x) is real ext-real V257() Element of REAL
(w,(w,FS)) is real ext-real V257() Element of REAL
len FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(len FS) - 1 is real integer ext-real V257() Element of REAL
(w,FK) + ((len FS) - 1) is real ext-real V257() Element of REAL
F is finite Element of bool (w)
(w,F) is real ext-real V257() Element of REAL
(w,F) - (len FS) is real ext-real V257() Element of REAL
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is (w) (w)
the of v is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
(w, the of v) is real ext-real V257() Element of REAL
[\(w, the of v)/] is real integer ext-real V257() set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is (w) (w)
(w,v) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of v is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
(w, the of v) is real ext-real V257() Element of REAL
[\(w, the of v)/] is real integer ext-real V257() set
LS is (w) (w)
(w,LS) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of LS is finite Element of bool (w)
(w, the of LS) is real ext-real V257() Element of REAL
[\(w, the of LS)/] is real integer ext-real V257() set
(w,LS) - 1 is real integer ext-real V257() Element of REAL
(w, the of LS) - 1 is real ext-real V257() Element of REAL
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
v is (w) (w)
(w,v) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of v is finite Element of bool (w)
(w, the of v) is real ext-real V257() Element of REAL
[\(w, the of v)/] is real integer ext-real V257() set
(w, the of v) - 1 is real ext-real V257() Element of REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
((w, the of v) - 1) + 1 is real ext-real V257() Element of REAL
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
v is (w) (w)
(w,v) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of v is finite Element of bool (w)
(w, the of v) is real ext-real V257() Element of REAL
[\(w, the of v)/] is real integer ext-real V257() set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
v is (w) (w)
LS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LT is (w) (w)
(w,LT) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of LT is finite Element of bool (w)
(w, the of LT) is real ext-real V257() Element of REAL
[\(w, the of LT)/] is real integer ext-real V257() set
FS is set
chf is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w,LT,chf) is (w) (w)
(w,(w,LT,chf)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of (w,LT,chf) is finite Element of bool (w)
(w, the of (w,LT,chf)) is real ext-real V257() Element of REAL
[\(w, the of (w,LT,chf))/] is real integer ext-real V257() set
(w,LT) - 1 is real integer ext-real V257() Element of REAL
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FK is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
FK . 1 is set
FK . FSet is set
x is (w) (w)
the of x is finite Element of bool (w)
<*LT*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
<*LT*> ^ FK is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
FSet + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
len (<*LT*> ^ FK) is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
len <*LT*> is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
(len <*LT*>) + (len FK) is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
F1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(<*LT*> ^ FK) . F1 is set
F1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
(<*LT*> ^ FK) . (F1 + 1) is set
2 - 1 is real integer ext-real V257() Element of REAL
FK . (2 - 1) is set
w1 is (w) (w)
m1 is (w) (w)
F1 - 1 is real integer ext-real V257() Element of REAL
m1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
m1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
F1 - (len <*LT*>) is real integer ext-real V257() Element of REAL
FK . (F1 - (len <*LT*>)) is set
FK . m1 is set
(F1 + 1) - (len <*LT*>) is real integer ext-real V257() Element of REAL
FK . ((F1 + 1) - (len <*LT*>)) is set
(F1 + 1) - 1 is real integer ext-real V257() Element of REAL
FK . ((F1 + 1) - 1) is set
FK . (m1 + 1) is set
(FSet + 1) - 1 is real integer ext-real V257() Element of REAL
m2 is (w) (w)
m3 is (w) (w)
m3 is (w) (w)
natMAX is (w) (w)
h is (w) (w)
m2 is (w) (w)
h is (w) (w)
m2 is (w) (w)
L is (w) (w)
m is (w) (w)
(<*LT*> ^ FK) . 1 is set
(<*LT*> ^ FK) . (FSet + 1) is set
(FSet + 1) - 1 is real integer ext-real V257() Element of REAL
FK . ((FSet + 1) - 1) is set
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
chf is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
chf . 1 is set
chf . FS is set
run is (w) (w)
the of run is finite Element of bool (w)
IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
FS . 1 is set
FS . IS is set
chf is (w) (w)
the of chf is finite Element of bool (w)
IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
FS . 1 is set
FS . IS is set
chf is (w) (w)
the of chf is finite Element of bool (w)
LT is (w) (w)
(w,LT) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of LT is finite Element of bool (w)
(w, the of LT) is real ext-real V257() Element of REAL
[\(w, the of LT)/] is real integer ext-real V257() set
(w,v) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of v is finite Element of bool (w)
(w, the of v) is real ext-real V257() Element of REAL
[\(w, the of v)/] is real integer ext-real V257() set
IS is (w) (w)
(w,IS) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of IS is finite Element of bool (w)
(w, the of IS) is real ext-real V257() Element of REAL
[\(w, the of IS)/] is real integer ext-real V257() set
<*IS*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
len <*IS*> is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
<*IS*> . 1 is set
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
<*IS*> . FSet is set
FSet + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
<*IS*> . (FSet + 1) is set
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
chf is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
chf . 1 is set
chf . FS is set
run is (w) (w)
the of run is finite Element of bool (w)
LT is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS is (w) (w)
(w,IS) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of IS is finite Element of bool (w)
(w, the of IS) is real ext-real V257() Element of REAL
[\(w, the of IS)/] is real integer ext-real V257() set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is (w) (w)
the of v is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
the of v is finite Element of bool (w)
LS is (w) (w)
the of LS is finite Element of bool (w)
the of LS is finite Element of bool (w)
the of LS is finite Element of bool (w)
LT is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w,LS,LT) is (w) (w)
{LT} is functional non empty trivial finite V42() 1 -element set
the of LS \/ {LT} is non empty finite set
(LT) is finite Element of bool (LT)
(LT) is non empty finite Element of bool LTL_WFF
bool (LT) is non empty finite V42() set
the of LS \/ (LT) is finite set
the of LS is finite Element of bool (w)
LT is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w,LS,LT) is (w) (w)
{LT} is functional non empty trivial finite V42() 1 -element set
the of LS \/ {LT} is non empty finite set
w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Seg w is finite w -element Element of bool NAT
v is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len v is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
v | (Seg w) is Relation-like NAT -defined Seg w -defined NAT -defined Function-like finite FinSubsequence-like set
LS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
LT is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
IS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
dom IS is finite Element of bool NAT
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS . FS is set
FS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
IS . (FS + 1) is set
v . FS is set
v . (FS + 1) is set
w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
v is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
v . 1 is set
len v is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
v . w is set
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LT is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
((v . 1),LT) is (LT) (LT)
the of ((v . 1),LT) is finite Element of bool (LT)
(LT) is non empty finite Element of bool LTL_WFF
bool (LT) is non empty finite V42() set
((v . w),LT) is (LT) (LT)
the of ((v . w),LT) is finite Element of bool (LT)
IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
FS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
run . 1 is set
((run . 1),LT) is (LT) (LT)
the of ((run . 1),LT) is finite Element of bool (LT)
run . chf is set
((run . chf),LT) is (LT) (LT)
the of ((run . chf),LT) is finite Element of bool (LT)
Seg IS is finite IS -element Element of bool NAT
run | (Seg IS) is Relation-like NAT -defined Seg IS -defined NAT -defined Function-like finite FinSubsequence-like set
IS + 0 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
FK is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom FK is finite Element of bool NAT
FK . chf is set
FK . 1 is set
((FK . 1),LT) is (LT) (LT)
the of ((FK . 1),LT) is finite Element of bool (LT)
len FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
x is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FK . x is set
((FK . x),LT) is (LT) (LT)
the of ((FK . x),LT) is finite Element of bool (LT)
x + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
FK . (x + 1) is set
((FK . (x + 1)),LT) is (LT) (LT)
the of ((FK . (x + 1)),LT) is finite Element of bool (LT)
run . (x + 1) is set
run . x is set
IS + 0 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
run . IS is set
((run . IS),LT) is (LT) (LT)
the of ((run . IS),LT) is finite Element of bool (LT)
run . IS is set
((run . IS),LT) is (LT) (LT)
the of ((run . IS),LT) is finite Element of bool (LT)
1 - IS is real integer ext-real V257() Element of REAL
IS - 1 is real integer ext-real V257() Element of REAL
(IS - 1) + (1 - IS) is real integer ext-real V257() Element of REAL
1 - 1 is real integer ext-real V257() Element of REAL
Seg IS is finite IS -element Element of bool NAT
run | (Seg IS) is Relation-like NAT -defined Seg IS -defined NAT -defined Function-like finite FinSubsequence-like set
FK is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom FK is finite Element of bool NAT
FK . IS is set
((FK . IS),LT) is (LT) (LT)
the of ((FK . IS),LT) is finite Element of bool (LT)
FK . 1 is set
((FK . 1),LT) is (LT) (LT)
the of ((FK . 1),LT) is finite Element of bool (LT)
len FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
x is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FK . x is set
((FK . x),LT) is (LT) (LT)
the of ((FK . x),LT) is finite Element of bool (LT)
x + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
FK . (x + 1) is set
((FK . (x + 1)),LT) is (LT) (LT)
the of ((FK . (x + 1)),LT) is finite Element of bool (LT)
run . x is set
((run . x),LT) is (LT) (LT)
the of ((run . x),LT) is finite Element of bool (LT)
run . (x + 1) is set
run . IS is set
((run . IS),LT) is (LT) (LT)
the of ((run . IS),LT) is finite Element of bool (LT)
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . FSet is set
((run . FSet),LT) is (LT) (LT)
the of ((run . FSet),LT) is finite Element of bool (LT)
FSet + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run . (FSet + 1) is set
((run . (FSet + 1)),LT) is (LT) (LT)
the of ((run . (FSet + 1)),LT) is finite Element of bool (LT)
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . FSet is set
((run . FSet),LT) is (LT) (LT)
the of ((run . FSet),LT) is finite Element of bool (LT)
FSet + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run . (FSet + 1) is set
((run . (FSet + 1)),LT) is (LT) (LT)
the of ((run . (FSet + 1)),LT) is finite Element of bool (LT)
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . FSet is set
((run . FSet),LT) is (LT) (LT)
the of ((run . FSet),LT) is finite Element of bool (LT)
FSet + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run . (FSet + 1) is set
((run . (FSet + 1)),LT) is (LT) (LT)
the of ((run . (FSet + 1)),LT) is finite Element of bool (LT)
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . FSet is set
((run . FSet),LT) is (LT) (LT)
the of ((run . FSet),LT) is finite Element of bool (LT)
FSet + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run . (FSet + 1) is set
((run . (FSet + 1)),LT) is (LT) (LT)
the of ((run . (FSet + 1)),LT) is finite Element of bool (LT)
run is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
FS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
run . 1 is set
((run . 1),LT) is (LT) (LT)
the of ((run . 1),LT) is finite Element of bool (LT)
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . chf is set
((run . chf),LT) is (LT) (LT)
the of ((run . chf),LT) is finite Element of bool (LT)
chf is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
IS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
chf . 1 is set
((chf . 1),LT) is (LT) (LT)
the of ((chf . 1),LT) is finite Element of bool (LT)
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
chf . FS is set
((chf . FS),LT) is (LT) (LT)
the of ((chf . FS),LT) is finite Element of bool (LT)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is (v) (v)
the of LS is finite Element of bool (v)
(v) is non empty finite Element of bool LTL_WFF
bool (v) is non empty finite V42() set
LT is (v) (v)
the of LT is finite Element of bool (v)
the of LT is finite Element of bool (v)
IS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(v,LT,IS) is (v) (v)
{IS} is functional non empty trivial finite V42() 1 -element set
the of LT \/ {IS} is non empty finite set
the of LT is finite Element of bool (v)
IS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(v,LT,IS) is (v) (v)
{IS} is functional non empty trivial finite V42() 1 -element set
the of LT \/ {IS} is non empty finite set
w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
v is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
v . 1 is set
len v is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
v . w is set
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LT is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
((v . 1),LT) is (LT) (LT)
the of ((v . 1),LT) is finite Element of bool (LT)
(LT) is non empty finite Element of bool LTL_WFF
bool (LT) is non empty finite V42() set
((v . w),LT) is (LT) (LT)
the of ((v . w),LT) is finite Element of bool (LT)
IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
FS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
run . 1 is set
((run . 1),LT) is (LT) (LT)
the of ((run . 1),LT) is finite Element of bool (LT)
run . chf is set
((run . chf),LT) is (LT) (LT)
the of ((run . chf),LT) is finite Element of bool (LT)
Seg IS is finite IS -element Element of bool NAT
run | (Seg IS) is Relation-like NAT -defined Seg IS -defined NAT -defined Function-like finite FinSubsequence-like set
IS + 0 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
FK is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom FK is finite Element of bool NAT
FK . chf is set
FK . 1 is set
((FK . 1),LT) is (LT) (LT)
the of ((FK . 1),LT) is finite Element of bool (LT)
len FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
x is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FK . x is set
((FK . x),LT) is (LT) (LT)
the of ((FK . x),LT) is finite Element of bool (LT)
x + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
FK . (x + 1) is set
((FK . (x + 1)),LT) is (LT) (LT)
the of ((FK . (x + 1)),LT) is finite Element of bool (LT)
run . (x + 1) is set
run . x is set
IS + 0 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
run . IS is set
((run . IS),LT) is (LT) (LT)
the of ((run . IS),LT) is finite Element of bool (LT)
run . IS is set
((run . IS),LT) is (LT) (LT)
the of ((run . IS),LT) is finite Element of bool (LT)
1 - IS is real integer ext-real V257() Element of REAL
IS - 1 is real integer ext-real V257() Element of REAL
(IS - 1) + (1 - IS) is real integer ext-real V257() Element of REAL
1 - 1 is real integer ext-real V257() Element of REAL
Seg IS is finite IS -element Element of bool NAT
run | (Seg IS) is Relation-like NAT -defined Seg IS -defined NAT -defined Function-like finite FinSubsequence-like set
FK is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom FK is finite Element of bool NAT
FK . IS is set
((FK . IS),LT) is (LT) (LT)
the of ((FK . IS),LT) is finite Element of bool (LT)
FK . 1 is set
((FK . 1),LT) is (LT) (LT)
the of ((FK . 1),LT) is finite Element of bool (LT)
len FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
x is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FK . x is set
((FK . x),LT) is (LT) (LT)
the of ((FK . x),LT) is finite Element of bool (LT)
x + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
FK . (x + 1) is set
((FK . (x + 1)),LT) is (LT) (LT)
the of ((FK . (x + 1)),LT) is finite Element of bool (LT)
run . x is set
((run . x),LT) is (LT) (LT)
the of ((run . x),LT) is finite Element of bool (LT)
run . (x + 1) is set
run . IS is set
((run . IS),LT) is (LT) (LT)
the of ((run . IS),LT) is finite Element of bool (LT)
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . FSet is set
((run . FSet),LT) is (LT) (LT)
the of ((run . FSet),LT) is finite Element of bool (LT)
FSet + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run . (FSet + 1) is set
((run . (FSet + 1)),LT) is (LT) (LT)
the of ((run . (FSet + 1)),LT) is finite Element of bool (LT)
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . FSet is set
((run . FSet),LT) is (LT) (LT)
the of ((run . FSet),LT) is finite Element of bool (LT)
FSet + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run . (FSet + 1) is set
((run . (FSet + 1)),LT) is (LT) (LT)
the of ((run . (FSet + 1)),LT) is finite Element of bool (LT)
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . FSet is set
((run . FSet),LT) is (LT) (LT)
the of ((run . FSet),LT) is finite Element of bool (LT)
FSet + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run . (FSet + 1) is set
((run . (FSet + 1)),LT) is (LT) (LT)
the of ((run . (FSet + 1)),LT) is finite Element of bool (LT)
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . FSet is set
((run . FSet),LT) is (LT) (LT)
the of ((run . FSet),LT) is finite Element of bool (LT)
FSet + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run . (FSet + 1) is set
((run . (FSet + 1)),LT) is (LT) (LT)
the of ((run . (FSet + 1)),LT) is finite Element of bool (LT)
run is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
FS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
run . 1 is set
((run . 1),LT) is (LT) (LT)
the of ((run . 1),LT) is finite Element of bool (LT)
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . chf is set
((run . chf),LT) is (LT) (LT)
the of ((run . chf),LT) is finite Element of bool (LT)
chf is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
IS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
chf . 1 is set
((chf . 1),LT) is (LT) (LT)
the of ((chf . 1),LT) is finite Element of bool (LT)
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
chf . FS is set
((chf . FS),LT) is (LT) (LT)
the of ((chf . FS),LT) is finite Element of bool (LT)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is (v) (v)
the of LS is finite Element of bool (v)
(v) is non empty finite Element of bool LTL_WFF
bool (v) is non empty finite V42() set
LT is (v) (v)
the of LT is finite Element of bool (v)
IS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(v,LT,IS) is (v) (v)
{IS} is functional non empty trivial finite V42() 1 -element set
the of LT \ {IS} is finite Element of bool (v)
(IS) is non empty finite Element of bool LTL_WFF
(IS) is finite Element of bool (IS)
bool (IS) is non empty finite V42() set
the of LT is finite Element of bool (v)
(IS) \ the of LT is finite Element of bool (IS)
( the of LT \ {IS}) \/ ((IS) \ the of LT) is finite set
IS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(v,LT,IS) is (v) (v)
{IS} is functional non empty trivial finite V42() 1 -element set
the of LT \ {IS} is finite Element of bool (v)
(IS) is non empty finite Element of bool LTL_WFF
(IS) is finite Element of bool (IS)
bool (IS) is non empty finite V42() set
the of LT is finite Element of bool (v)
(IS) \ the of LT is finite Element of bool (IS)
( the of LT \ {IS}) \/ ((IS) \ the of LT) is finite set
w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
v is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len LS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LS . w is set
LS . v is set
LT is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
((LS . w),LT) is (LT) (LT)
the of ((LS . w),LT) is finite Element of bool (LT)
(LT) is non empty finite Element of bool LTL_WFF
bool (LT) is non empty finite V42() set
((LS . v),LT) is (LT) (LT)
the of ((LS . v),LT) is finite Element of bool (LT)
the of ((LS . w),LT) is finite Element of bool (LT)
the of ((LS . v),LT) is finite Element of bool (LT)
IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
run . chf is set
((run . chf),LT) is (LT) (LT)
the of ((run . chf),LT) is finite Element of bool (LT)
run . FS is set
((run . FS),LT) is (LT) (LT)
the of ((run . FS),LT) is finite Element of bool (LT)
the of ((run . chf),LT) is finite Element of bool (LT)
the of ((run . FS),LT) is finite Element of bool (LT)
Seg IS is finite IS -element Element of bool NAT
run | (Seg IS) is Relation-like NAT -defined Seg IS -defined NAT -defined Function-like finite FinSubsequence-like set
IS + 0 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
FK is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom FK is finite Element of bool NAT
FK . FS is set
FK . chf is set
len FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
Seg IS is finite IS -element Element of bool NAT
run | (Seg IS) is Relation-like NAT -defined Seg IS -defined NAT -defined Function-like finite FinSubsequence-like set
IS + 0 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
FK is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom FK is finite Element of bool NAT
FK . chf is set
FK . IS is set
run . IS is set
len FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
((run . IS),LT) is (LT) (LT)
the of ((run . IS),LT) is finite Element of bool (LT)
the of ((run . IS),LT) is finite Element of bool (LT)
run . (IS + 1) is set
x is (LT) (LT)
F is (LT) (LT)
(x,LT) is (LT) (LT)
(F,LT) is (LT) (LT)
the of x is finite Element of bool (LT)
the of F is finite Element of bool (LT)
the of x is finite Element of bool (LT)
the of F is finite Element of bool (LT)
run is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . chf is set
((run . chf),LT) is (LT) (LT)
the of ((run . chf),LT) is finite Element of bool (LT)
run . FS is set
((run . FS),LT) is (LT) (LT)
the of ((run . FS),LT) is finite Element of bool (LT)
the of ((run . chf),LT) is finite Element of bool (LT)
the of ((run . FS),LT) is finite Element of bool (LT)
chf is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
chf . FS is set
((chf . FS),LT) is (LT) (LT)
the of ((chf . FS),LT) is finite Element of bool (LT)
chf . IS is set
((chf . IS),LT) is (LT) (LT)
the of ((chf . IS),LT) is finite Element of bool (LT)
the of ((chf . FS),LT) is finite Element of bool (LT)
the of ((chf . IS),LT) is finite Element of bool (LT)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is (v) (v)
the of LS is finite Element of bool (v)
(v) is non empty finite Element of bool LTL_WFF
bool (v) is non empty finite V42() set
LT is (v) (v)
the of LT is finite Element of bool (v)
(v,LT,w) is (v) (v)
the of LT is finite Element of bool (v)
{w} is functional non empty trivial finite V42() 1 -element set
the of LT \/ {w} is non empty finite set
the of LT is finite Element of bool (v)
(v,LT,w) is (v) (v)
the of LT is finite Element of bool (v)
{w} is functional non empty trivial finite V42() 1 -element set
the of LT \/ {w} is non empty finite set
the of LT is finite Element of bool (v)
(v,LT,w) is (v) (v)
(v,LT,w) is (v) (v)
w is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
w . (len w) is set
w . 1 is set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
((w . (len w)),v) is (v) (v)
the of ((w . (len w)),v) is finite Element of bool (v)
(v) is non empty finite Element of bool LTL_WFF
bool (v) is non empty finite V42() set
(v) is finite Element of bool (v)
((w . 1),v) is (v) (v)
the of ((w . 1),v) is finite Element of bool (v)
the of ((w . (len w)),v) is finite Element of bool (v)
LT is set
IS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
w . FS is set
((w . FS),v) is (v) (v)
the of ((w . FS),v) is finite Element of bool (v)
FS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
w . (FS + 1) is set
((w . (FS + 1)),v) is (v) (v)
the of ((w . (FS + 1)),v) is finite Element of bool (v)
the of ((w . (FS + 1)),v) is finite Element of bool (v)
run is (v) (v)
FSet is (v) (v)
the of FSet is finite Element of bool (v)
w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
v is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len v is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
v . (len v) is set
v . w is set
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
((v . (len v)),LS) is (LS) (LS)
the of ((v . (len v)),LS) is finite Element of bool (LS)
(LS) is non empty finite Element of bool LTL_WFF
bool (LS) is non empty finite V42() set
(LS) is finite Element of bool (LS)
((v . w),LS) is (LS) (LS)
the of ((v . w),LS) is finite Element of bool (LS)
the of ((v . (len v)),LS) is finite Element of bool (LS)
w - 1 is real integer ext-real V257() Element of REAL
(len v) - (w - 1) is real integer ext-real V257() Element of REAL
IS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
LT is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
LT ^ IS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
IS . 1 is set
len IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
IS . (len IS) is set
w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
w + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
v is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len v is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
v . w is set
v . (w + 1) is set
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
((v . w),LS) is (LS) (LS)
((v . (w + 1)),LS) is (LS) (LS)
LT is (LS) (LS)
IS is (LS) (LS)
w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
v is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len v is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
v . w is set
v . 1 is set
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
((v . w),LS) is (LS) (LS)
(LS,((v . w),LS)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of ((v . w),LS) is finite Element of bool (LS)
(LS) is non empty finite Element of bool LTL_WFF
bool (LS) is non empty finite V42() set
(LS, the of ((v . w),LS)) is real ext-real V257() Element of REAL
[\(LS, the of ((v . w),LS))/] is real integer ext-real V257() set
((v . 1),LS) is (LS) (LS)
(LS,((v . 1),LS)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of ((v . 1),LS) is finite Element of bool (LS)
(LS, the of ((v . 1),LS)) is real ext-real V257() Element of REAL
[\(LS, the of ((v . 1),LS))/] is real integer ext-real V257() set
(LS,((v . 1),LS)) - w is real integer ext-real V257() set
((LS,((v . 1),LS)) - w) + 1 is real integer ext-real V257() Element of REAL
LT is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
IS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
IS . 1 is set
((IS . 1),LS) is (LS) (LS)
(LS,((IS . 1),LS)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of ((IS . 1),LS) is finite Element of bool (LS)
(LS, the of ((IS . 1),LS)) is real ext-real V257() Element of REAL
[\(LS, the of ((IS . 1),LS))/] is real integer ext-real V257() set
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS . FS is set
((IS . FS),LS) is (LS) (LS)
(LS,((IS . FS),LS)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of ((IS . FS),LS) is finite Element of bool (LS)
(LS, the of ((IS . FS),LS)) is real ext-real V257() Element of REAL
[\(LS, the of ((IS . FS),LS))/] is real integer ext-real V257() set
(LS,((IS . 1),LS)) - FS is real integer ext-real V257() set
((LS,((IS . 1),LS)) - FS) + 1 is real integer ext-real V257() Element of REAL
Seg LT is finite LT -element Element of bool NAT
IS | (Seg LT) is Relation-like NAT -defined Seg LT -defined NAT -defined Function-like finite FinSubsequence-like set
run is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
dom run is finite Element of bool NAT
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . FSet is set
IS . FSet is set
0 + LT is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
run . 1 is set
run . FS is set
IS . LT is set
((IS . LT),LS) is (LS) (LS)
(LS,((IS . LT),LS)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of ((IS . LT),LS) is finite Element of bool (LS)
(LS, the of ((IS . LT),LS)) is real ext-real V257() Element of REAL
[\(LS, the of ((IS . LT),LS))/] is real integer ext-real V257() set
(LS,((IS . LT),LS)) - 1 is real integer ext-real V257() Element of REAL
(LS,((IS . FS),LS)) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
((LS,((IS . LT),LS)) - 1) + 1 is real integer ext-real V257() Element of REAL
run . LT is set
run . 1 is set
(LS,((IS . 1),LS)) - LT is real integer ext-real V257() set
((LS,((IS . 1),LS)) - LT) + 1 is real integer ext-real V257() Element of REAL
IS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
IS . 1 is set
((IS . 1),LS) is (LS) (LS)
(LS,((IS . 1),LS)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of ((IS . 1),LS) is finite Element of bool (LS)
(LS, the of ((IS . 1),LS)) is real ext-real V257() Element of REAL
[\(LS, the of ((IS . 1),LS))/] is real integer ext-real V257() set
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS . FS is set
((IS . FS),LS) is (LS) (LS)
(LS,((IS . FS),LS)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of ((IS . FS),LS) is finite Element of bool (LS)
(LS, the of ((IS . FS),LS)) is real ext-real V257() Element of REAL
[\(LS, the of ((IS . FS),LS))/] is real integer ext-real V257() set
(LS,((IS . 1),LS)) - FS is real integer ext-real V257() set
((LS,((IS . 1),LS)) - FS) + 1 is real integer ext-real V257() Element of REAL
IS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS . FS is set
((IS . FS),LS) is (LS) (LS)
(LS,((IS . FS),LS)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of ((IS . FS),LS) is finite Element of bool (LS)
(LS, the of ((IS . FS),LS)) is real ext-real V257() Element of REAL
[\(LS, the of ((IS . FS),LS))/] is real integer ext-real V257() set
IS . 1 is set
((IS . 1),LS) is (LS) (LS)
(LS,((IS . 1),LS)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of ((IS . 1),LS) is finite Element of bool (LS)
(LS, the of ((IS . 1),LS)) is real ext-real V257() Element of REAL
[\(LS, the of ((IS . 1),LS))/] is real integer ext-real V257() set
(LS,((IS . 1),LS)) - FS is real integer ext-real V257() set
((LS,((IS . 1),LS)) - FS) + 1 is real integer ext-real V257() Element of REAL
LT is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len LT is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT . IS is set
((LT . IS),LS) is (LS) (LS)
(LS,((LT . IS),LS)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of ((LT . IS),LS) is finite Element of bool (LS)
(LS, the of ((LT . IS),LS)) is real ext-real V257() Element of REAL
[\(LS, the of ((LT . IS),LS))/] is real integer ext-real V257() set
LT . 1 is set
((LT . 1),LS) is (LS) (LS)
(LS,((LT . 1),LS)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of ((LT . 1),LS) is finite Element of bool (LS)
(LS, the of ((LT . 1),LS)) is real ext-real V257() Element of REAL
[\(LS, the of ((LT . 1),LS))/] is real integer ext-real V257() set
(LS,((LT . 1),LS)) - IS is real integer ext-real V257() set
((LS,((LT . 1),LS)) - IS) + 1 is real integer ext-real V257() Element of REAL
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is (w) (w) (w)
the of v is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
LS is (w) (w) (w)
the of LS is finite Element of bool (w)
(w,LS) is (w) (w)
(w) is finite Element of bool (w)
(w,(w), the of LS,(w)) is (w) (w)
the of v is finite Element of bool (w)
IS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
IS . 1 is set
IS . (len IS) is set
((IS . (len IS)),w) is (w) (w)
((IS . 1),w) is (w) (w)
chf is set
run is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS . FSet is set
((IS . FSet),w) is (w) (w)
the of ((IS . FSet),w) is finite Element of bool (w)
FSet + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
IS . (FSet + 1) is set
((IS . (FSet + 1)),w) is (w) (w)
the of ((IS . (FSet + 1)),w) is finite Element of bool (w)
x is (w) (w)
F is (w) (w)
the of F is finite Element of bool (w)
the of ((IS . (len IS)),w) is finite Element of bool (w)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is (v) (v) (v)
the of LS is finite Element of bool (v)
(v) is non empty finite Element of bool LTL_WFF
bool (v) is non empty finite V42() set
LT is (v) (v) (v)
(v,LT) is (v) (v)
(v) is finite Element of bool (v)
the of LT is finite Element of bool (v)
(v,(v), the of LT,(v)) is (v) (v)
FS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
FS . 1 is set
FS . (len FS) is set
((FS . 1),v) is (v) (v)
((FS . (len FS)),v) is (v) (v)
run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FS . run is set
((FS . run),v) is (v) (v)
the of ((FS . run),v) is finite Element of bool (v)
run + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
FS . (run + 1) is set
((FS . (run + 1)),v) is (v) (v)
the of ((FS . (run + 1)),v) is finite Element of bool (v)
FK is (v) (v)
x is (v) (v)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_left_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_right_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is (v) (v) (v)
the of LS is finite Element of bool (v)
(v) is non empty finite Element of bool LTL_WFF
bool (v) is non empty finite V42() set
the of LS is finite Element of bool (v)
LT is (v) (v) (v)
(v,LT) is (v) (v)
(v) is finite Element of bool (v)
the of LT is finite Element of bool (v)
(v,(v), the of LT,(v)) is (v) (v)
run is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
run . 1 is set
run . (len run) is set
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . FSet is set
((run . FSet),v) is (v) (v)
FSet + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run . (FSet + 1) is set
((run . (FSet + 1)),v) is (v) (v)
((run . (len run)),v) is (v) (v)
the of ((run . FSet),v) is finite Element of bool (v)
the of ((run . (FSet + 1)),v) is finite Element of bool (v)
the of LS is finite Element of bool (v)
the of ((run . (FSet + 1)),v) is finite Element of bool (v)
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
{(the_left_argument_of w),(the_right_argument_of w)} is functional non empty finite V42() set
the of ((run . FSet),v) is finite Element of bool (v)
(w) \ the of ((run . FSet),v) is finite Element of bool (w)
{w} is functional non empty trivial finite V42() 1 -element set
the of ((run . FSet),v) \ {w} is finite Element of bool (v)
( the of ((run . FSet),v) \ {w}) \/ ((w) \ the of ((run . FSet),v)) is finite set
(v,((run . FSet),v),w) is (v) (v)
(w) is finite Element of bool (w)
{(the_right_argument_of w)} is functional non empty trivial finite V42() 1 -element set
(v,((run . FSet),v),w) is (v) (v)
the of ((run . (FSet + 1)),v) is finite Element of bool (v)
(w) \ the of ((run . FSet),v) is finite Element of bool (w)
( the of ((run . FSet),v) \ {w}) \/ ((w) \ the of ((run . FSet),v)) is finite set
the of ((run . FSet),v) \/ {w} is non empty finite set
(w) is finite Element of bool (w)
the of ((run . FSet),v) is finite Element of bool (v)
the of ((run . FSet),v) \/ (w) is finite set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_right_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is (v) (v) (v)
the of LS is finite Element of bool (v)
(v) is non empty finite Element of bool LTL_WFF
bool (v) is non empty finite V42() set
LT is (v) (v) (v)
the of LT is finite Element of bool (v)
the_left_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(v,LT) is (v) (v)
(v) is finite Element of bool (v)
(v,(v), the of LT,(v)) is (v) (v)
run is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
run . 1 is set
run . (len run) is set
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . FSet is set
((run . FSet),v) is (v) (v)
FSet + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run . (FSet + 1) is set
((run . (FSet + 1)),v) is (v) (v)
the of LS is finite Element of bool (v)
((run . (len run)),v) is (v) (v)
the of ((run . (FSet + 1)),v) is finite Element of bool (v)
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
{(the_left_argument_of w),(the_right_argument_of w)} is functional non empty finite V42() set
(w) is finite Element of bool (w)
{(the_right_argument_of w)} is functional non empty trivial finite V42() 1 -element set
the of ((run . FSet),v) is finite Element of bool (v)
the of ((run . FSet),v) is finite Element of bool (v)
(v,((run . FSet),v),w) is (v) (v)
(w) \ the of ((run . FSet),v) is finite Element of bool (w)
{w} is functional non empty trivial finite V42() 1 -element set
the of ((run . FSet),v) \ {w} is finite Element of bool (v)
( the of ((run . FSet),v) \ {w}) \/ ((w) \ the of ((run . FSet),v)) is finite set
the of ((run . FSet),v) is finite Element of bool (v)
(v,((run . FSet),v),w) is (v) (v)
(w) \ the of ((run . FSet),v) is finite Element of bool (w)
{w} is functional non empty trivial finite V42() 1 -element set
the of ((run . FSet),v) \ {w} is finite Element of bool (v)
( the of ((run . FSet),v) \ {w}) \/ ((w) \ the of ((run . FSet),v)) is finite set
the of ((run . FSet),v) is finite Element of bool (v)
(v,((run . FSet),v),w) is (v) (v)
(v,((run . FSet),v),w) is (v) (v)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_left_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_right_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is (v) (v) (v)
the of LS is finite Element of bool (v)
(v) is non empty finite Element of bool LTL_WFF
bool (v) is non empty finite V42() set
the of LS is finite Element of bool (v)
LT is (v) (v) (v)
(v,LT) is (v) (v)
(v) is finite Element of bool (v)
the of LT is finite Element of bool (v)
(v,(v), the of LT,(v)) is (v) (v)
IS is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
IS . 1 is set
IS . (len IS) is set
((IS . 1),v) is (v) (v)
((IS . (len IS)),v) is (v) (v)
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS . chf is set
((IS . chf),v) is (v) (v)
the of ((IS . chf),v) is finite Element of bool (v)
chf + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
IS . (chf + 1) is set
((IS . (chf + 1)),v) is (v) (v)
the of ((IS . (chf + 1)),v) is finite Element of bool (v)
run is (v) (v)
FSet is (v) (v)
the of run is finite Element of bool (v)
the of ((IS . (len IS)),v) is finite Element of bool (v)
the of FSet is finite Element of bool (v)
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
{(the_left_argument_of w),(the_right_argument_of w)} is functional non empty finite V42() set
the of run is finite Element of bool (v)
(v,run,w) is (v) (v)
{w} is functional non empty trivial finite V42() 1 -element set
the of run \ {w} is finite Element of bool (v)
(w) \ the of run is finite Element of bool (w)
( the of run \ {w}) \/ ((w) \ the of run) is finite set
the of run is finite Element of bool (v)
(v,run,w) is (v) (v)
the of run is finite Element of bool (v)
(v,run,w) is (v) (v)
(v,run,w) is (v) (v)
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
{(the_left_argument_of w),(the_right_argument_of w)} is functional non empty finite V42() set
(w) is finite Element of bool (w)
{(the_right_argument_of w)} is functional non empty trivial finite V42() 1 -element set
the of run is finite Element of bool (v)
(v,run,w) is (v) (v)
{w} is functional non empty trivial finite V42() 1 -element set
the of run \ {w} is finite Element of bool (v)
(w) \ the of run is finite Element of bool (w)
( the of run \ {w}) \/ ((w) \ the of run) is finite set
the of run is finite Element of bool (v)
(v,run,w) is (v) (v)
{w} is functional non empty trivial finite V42() 1 -element set
the of run \ {w} is finite Element of bool (v)
(w) \ the of run is finite Element of bool (w)
( the of run \ {w}) \/ ((w) \ the of run) is finite set
the of run is finite Element of bool (v)
(v,run,w) is (v) (v)
(v,run,w) is (v) (v)
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
{(the_right_argument_of w)} is functional non empty trivial finite V42() 1 -element set
(w) is finite Element of bool (w)
{(the_left_argument_of w)} is functional non empty trivial finite V42() 1 -element set
the of run is finite Element of bool (v)
(v,run,w) is (v) (v)
{w} is functional non empty trivial finite V42() 1 -element set
the of run \ {w} is finite Element of bool (v)
(w) \ the of run is finite Element of bool (w)
( the of run \ {w}) \/ ((w) \ the of run) is finite set
the of run is finite Element of bool (v)
(v,run,w) is (v) (v)
{w} is functional non empty trivial finite V42() 1 -element set
the of run \ {w} is finite Element of bool (v)
(w) \ the of run is finite Element of bool (w)
( the of run \ {w}) \/ ((w) \ the of run) is finite set
the of run is finite Element of bool (v)
(v,run,w) is (v) (v)
(v,run,w) is (v) (v)
the of FSet is finite Element of bool (v)
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
{(the_argument_of w)} is functional non empty trivial finite V42() 1 -element set
the of run is finite Element of bool (v)
(v,run,w) is (v) (v)
the of run is finite Element of bool (v)
the of run \/ (w) is finite set
the of run is finite Element of bool (v)
(v,run,w) is (v) (v)
the of run is finite Element of bool (v)
(v,run,w) is (v) (v)
(v,run,w) is (v) (v)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w 'U' v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
4 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
<*4*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*4*> ^ w is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(<*4*> ^ w) ^ v is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LT is (LS) (LS) (LS)
the of LT is finite Element of bool (LS)
(LS) is non empty finite Element of bool LTL_WFF
bool (LS) is non empty finite V42() set
IS is (LS) (LS) (LS)
FS is (LS) (LS) (LS)
the of FS is finite Element of bool (LS)
(LS,IS) is (LS) (LS)
(LS) is finite Element of bool (LS)
the of IS is finite Element of bool (LS)
(LS,(LS), the of IS,(LS)) is (LS) (LS)
run is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
run . 1 is set
run . (len run) is set
((run . 1),LS) is (LS) (LS)
((run . (len run)),LS) is (LS) (LS)
FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . FK is set
((run . FK),LS) is (LS) (LS)
the of ((run . FK),LS) is finite Element of bool (LS)
FK + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run . (FK + 1) is set
((run . (FK + 1)),LS) is (LS) (LS)
the of ((run . (FK + 1)),LS) is finite Element of bool (LS)
x is (LS) (LS)
F is (LS) (LS)
((w 'U' v)) is finite Element of bool ((w 'U' v))
((w 'U' v)) is non empty finite Element of bool LTL_WFF
bool ((w 'U' v)) is non empty finite V42() set
{(w 'U' v)} is functional non empty trivial finite V42() 1 -element set
the_right_argument_of (w 'U' v) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
((w 'U' v)) is finite Element of bool ((w 'U' v))
{v} is functional non empty trivial finite V42() 1 -element set
the_left_argument_of (w 'U' v) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
((w 'U' v)) is finite Element of bool ((w 'U' v))
{w} is functional non empty trivial finite V42() 1 -element set
the of x is finite Element of bool (LS)
the of F is finite Element of bool (LS)
the of LT is finite Element of bool (LS)
the of ((run . (len run)),LS) is finite Element of bool (LS)
the of F is finite Element of bool (LS)
the of x is finite Element of bool (LS)
(LS,x,(w 'U' v)) is (LS) (LS)
the of x \ {(w 'U' v)} is finite Element of bool (LS)
((w 'U' v)) \ the of x is finite Element of bool ((w 'U' v))
( the of x \ {(w 'U' v)}) \/ (((w 'U' v)) \ the of x) is finite set
the of x is finite Element of bool (LS)
the of x \/ ((w 'U' v)) is finite set
the of x is finite Element of bool (LS)
(LS,x,(w 'U' v)) is (LS) (LS)
the of x \ {(w 'U' v)} is finite Element of bool (LS)
((w 'U' v)) \ the of x is finite Element of bool ((w 'U' v))
( the of x \ {(w 'U' v)}) \/ (((w 'U' v)) \ the of x) is finite set
the of x is finite Element of bool (LS)
(LS,x,(w 'U' v)) is (LS) (LS)
(LS,x,(w 'U' v)) is (LS) (LS)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_right_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_left_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is (v) (v) (v)
the of LS is finite Element of bool (v)
(v) is non empty finite Element of bool LTL_WFF
bool (v) is non empty finite V42() set
LT is (v) (v) (v)
IS is (v) (v) (v)
the of IS is finite Element of bool (v)
(the_left_argument_of w) 'U' (the_right_argument_of w) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
4 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
<*4*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*4*> ^ (the_left_argument_of w) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(<*4*> ^ (the_left_argument_of w)) ^ (the_right_argument_of w) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
[:(bool (w)),(bool (w)),(bool (w)):] is non empty finite set
LT is set
IS is set
FS is set
chf is finite Element of bool (w)
run is finite Element of bool (w)
[chf,run] is set
{chf,run} is non empty finite V42() set
{chf} is non empty trivial finite V42() 1 -element set
{{chf,run},{chf}} is non empty finite V42() set
FSet is finite Element of bool (w)
[[chf,run],FSet] is set
{[chf,run],FSet} is non empty finite set
{[chf,run]} is Relation-like Function-like constant non empty trivial finite 1 -element set
{{[chf,run],FSet},{[chf,run]}} is non empty finite V42() set
FK is (w) (w)
the of FK is finite Element of bool (w)
the of FK is finite Element of bool (w)
the of FK is finite Element of bool (w)
chf is finite Element of bool (w)
run is finite Element of bool (w)
[chf,run] is set
{chf,run} is non empty finite V42() set
{chf} is non empty trivial finite V42() 1 -element set
{{chf,run},{chf}} is non empty finite V42() set
FSet is finite Element of bool (w)
[[chf,run],FSet] is set
{[chf,run],FSet} is non empty finite set
{[chf,run]} is Relation-like Function-like constant non empty trivial finite 1 -element set
{{[chf,run],FSet},{[chf,run]}} is non empty finite V42() set
FK is (w) (w)
the of FK is finite Element of bool (w)
the of FK is finite Element of bool (w)
the of FK is finite Element of bool (w)
x is finite Element of bool (w)
F is finite Element of bool (w)
[x,F] is set
{x,F} is non empty finite V42() set
{x} is non empty trivial finite V42() 1 -element set
{{x,F},{x}} is non empty finite V42() set
F2 is finite Element of bool (w)
[[x,F],F2] is set
{[x,F],F2} is non empty finite set
{[x,F]} is Relation-like Function-like constant non empty trivial finite 1 -element set
{{[x,F],F2},{[x,F]}} is non empty finite V42() set
F1 is (w) (w)
the of F1 is finite Element of bool (w)
the of F1 is finite Element of bool (w)
the of F1 is finite Element of bool (w)
x is finite Element of bool (w)
F is finite Element of bool (w)
[x,F] is set
{x,F} is non empty finite V42() set
{x} is non empty trivial finite V42() 1 -element set
{{x,F},{x}} is non empty finite V42() set
F2 is finite Element of bool (w)
[[x,F],F2] is set
{[x,F],F2} is non empty finite set
{[x,F]} is Relation-like Function-like constant non empty trivial finite 1 -element set
{{[x,F],F2},{[x,F]}} is non empty finite V42() set
F1 is (w) (w)
the of F1 is finite Element of bool (w)
the of F1 is finite Element of bool (w)
the of F1 is finite Element of bool (w)
LT is set
(w) is finite Element of bool (w)
(w,(w),(w),(w)) is (w) (w)
[(w),(w)] is set
{(w),(w)} is non empty finite V42() set
{(w)} is non empty trivial finite V42() 1 -element set
{{(w),(w)},{(w)}} is non empty finite V42() set
[[(w),(w)],(w)] is set
{[(w),(w)],(w)} is non empty finite set
{[(w),(w)]} is Relation-like Function-like constant non empty trivial finite 1 -element set
{{[(w),(w)],(w)},{[(w),(w)]}} is non empty finite V42() set
[:(bool (w)),(bool (w)):] is Relation-like non empty finite set
[:[:(bool (w)),(bool (w)):],(bool (w)):] is Relation-like non empty finite set
run is finite Element of bool (w)
FSet is finite Element of bool (w)
[run,FSet] is set
{run,FSet} is non empty finite V42() set
{run} is non empty trivial finite V42() 1 -element set
{{run,FSet},{run}} is non empty finite V42() set
FK is finite Element of bool (w)
[[run,FSet],FK] is set
{[run,FSet],FK} is non empty finite set
{[run,FSet]} is Relation-like Function-like constant non empty trivial finite 1 -element set
{{[run,FSet],FK},{[run,FSet]}} is non empty finite V42() set
x is (w) (w)
the of x is finite Element of bool (w)
the of x is finite Element of bool (w)
the of x is finite Element of bool (w)
IS is non empty set
FS is set
chf is (w) (w)
chf is (w) (w)
the of chf is finite Element of bool (w)
the of chf is finite Element of bool (w)
the of chf is finite Element of bool (w)
[ the of chf, the of chf] is set
{ the of chf, the of chf} is non empty finite V42() set
{ the of chf} is non empty trivial finite V42() 1 -element set
{{ the of chf, the of chf},{ the of chf}} is non empty finite V42() set
[[ the of chf, the of chf], the of chf] is set
{[ the of chf, the of chf], the of chf} is non empty finite set
{[ the of chf, the of chf]} is Relation-like Function-like constant non empty trivial finite 1 -element set
{{[ the of chf, the of chf], the of chf},{[ the of chf, the of chf]}} is non empty finite V42() set
[:(bool (w)),(bool (w)):] is Relation-like non empty finite set
[:[:(bool (w)),(bool (w)):],(bool (w)):] is Relation-like non empty finite set
FS is set
chf is set
run is finite Element of bool (w)
FSet is finite Element of bool (w)
[run,FSet] is set
{run,FSet} is non empty finite V42() set
{run} is non empty trivial finite V42() 1 -element set
{{run,FSet},{run}} is non empty finite V42() set
FK is finite Element of bool (w)
[[run,FSet],FK] is set
{[run,FSet],FK} is non empty finite set
{[run,FSet]} is Relation-like Function-like constant non empty trivial finite 1 -element set
{{[run,FSet],FK},{[run,FSet]}} is non empty finite V42() set
x is (w) (w)
the of x is finite Element of bool (w)
the of x is finite Element of bool (w)
the of x is finite Element of bool (w)
FS is set
chf is set
run is (w) (w)
v is non empty set
LS is non empty set
LT is set
IS is (w) (w)
IS is (w) (w)
LT is set
IS is set
FS is (w) (w)
chf is set
run is set
FSet is (w) (w)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty set
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
[:(bool (w)),(bool (w)),(bool (w)):] is non empty finite set
IS is set
(IS,w) is (w) (w)
the of (IS,w) is finite Element of bool (w)
the of (IS,w) is finite Element of bool (w)
[ the of (IS,w), the of (IS,w)] is set
{ the of (IS,w), the of (IS,w)} is non empty finite V42() set
{ the of (IS,w)} is non empty trivial finite V42() 1 -element set
{{ the of (IS,w), the of (IS,w)},{ the of (IS,w)}} is non empty finite V42() set
the of (IS,w) is finite Element of bool (w)
[[ the of (IS,w), the of (IS,w)], the of (IS,w)] is set
{[ the of (IS,w), the of (IS,w)], the of (IS,w)} is non empty finite set
{[ the of (IS,w), the of (IS,w)]} is Relation-like Function-like constant non empty trivial finite 1 -element set
{{[ the of (IS,w), the of (IS,w)], the of (IS,w)},{[ the of (IS,w), the of (IS,w)]}} is non empty finite V42() set
[:(bool (w)),(bool (w)):] is Relation-like non empty finite set
[:[:(bool (w)),(bool (w)):],(bool (w)):] is Relation-like non empty finite set
[:(w),[:(bool (w)),(bool (w)),(bool (w)):]:] is Relation-like non empty set
bool [:(w),[:(bool (w)),(bool (w)),(bool (w)):]:] is non empty set
IS is Relation-like (w) -defined [:(bool (w)),(bool (w)),(bool (w)):] -valued Function-like non empty V21((w)) V25((w),[:(bool (w)),(bool (w)),(bool (w)):]) Element of bool [:(w),[:(bool (w)),(bool (w)),(bool (w)):]:]
IS is Relation-like (w) -defined [:(bool (w)),(bool (w)),(bool (w)):] -valued Function-like non empty V21((w)) V25((w),[:(bool (w)),(bool (w)),(bool (w)):]) Element of bool [:(w),[:(bool (w)),(bool (w)),(bool (w)):]:]
FS is set
chf is set
IS . FS is set
IS . chf is set
(chf,w) is (w) (w)
the of (chf,w) is finite Element of bool (w)
the of (chf,w) is finite Element of bool (w)
the of (chf,w) is finite Element of bool (w)
F is (w) (w)
(FS,w) is (w) (w)
the of (FS,w) is finite Element of bool (w)
the of (FS,w) is finite Element of bool (w)
the of (FS,w) is finite Element of bool (w)
[ the of (FS,w), the of (FS,w)] is set
{ the of (FS,w), the of (FS,w)} is non empty finite V42() set
{ the of (FS,w)} is non empty trivial finite V42() 1 -element set
{{ the of (FS,w), the of (FS,w)},{ the of (FS,w)}} is non empty finite V42() set
[ the of (chf,w), the of (chf,w)] is set
{ the of (chf,w), the of (chf,w)} is non empty finite V42() set
{ the of (chf,w)} is non empty trivial finite V42() 1 -element set
{{ the of (chf,w), the of (chf,w)},{ the of (chf,w)}} is non empty finite V42() set
x is (w) (w)
the of x is finite Element of bool (w)
the of x is finite Element of bool (w)
m1 is (w) (w)
w1 is (w) (w)
IS . w1 is set
[[ the of (FS,w), the of (FS,w)], the of (FS,w)] is set
{[ the of (FS,w), the of (FS,w)], the of (FS,w)} is non empty finite set
{[ the of (FS,w), the of (FS,w)]} is Relation-like Function-like constant non empty trivial finite 1 -element set
{{[ the of (FS,w), the of (FS,w)], the of (FS,w)},{[ the of (FS,w), the of (FS,w)]}} is non empty finite V42() set
IS . x is set
[[ the of (chf,w), the of (chf,w)], the of (chf,w)] is set
{[ the of (chf,w), the of (chf,w)], the of (chf,w)} is non empty finite set
{[ the of (chf,w), the of (chf,w)]} is Relation-like Function-like constant non empty trivial finite 1 -element set
{{[ the of (chf,w), the of (chf,w)], the of (chf,w)},{[ the of (chf,w), the of (chf,w)]}} is non empty finite V42() set
the of w1 is finite Element of bool (w)
the of x is finite Element of bool (w)
the of w1 is finite Element of bool (w)
the of w1 is finite Element of bool (w)
rng IS is non empty finite Element of bool [:(bool (w)),(bool (w)),(bool (w)):]
bool [:(bool (w)),(bool (w)),(bool (w)):] is non empty finite V42() set
IS " is Relation-like Function-like set
dom (IS ") is set
dom IS is non empty Element of bool (w)
bool (w) is non empty set
rng (IS ") is set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty finite set
{ b₁ where b₁ is Element of (w) : b₁ is (w) (w) (w) } is set
(w) is (w) (w) (w)
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
(w) is finite Element of bool (w)
{w} is functional non empty trivial finite V42() 1 -element set
(w,(w),(w),(w)) is (w) (w)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty set
(w) is non empty finite set
{ b₁ where b₁ is Element of (w) : b₁ is (w) (w) (w) } is set
v is set
LS is Element of (w)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is (w) (w) (w)
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
(w) is finite Element of bool (w)
{w} is functional non empty trivial finite V42() 1 -element set
(w,(w),(w),(w)) is (w) (w)
(w) is non empty finite set
(w) is non empty finite set
{ b₁ where b₁ is Element of (w) : b₁ is (w) (w) (w) } is set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty finite set
(w) is non empty finite set
{ b₁ where b₁ is Element of (w) : b₁ is (w) (w) (w) } is set
v is (w) (w) (w)
w is set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(v) is non empty finite set
(v) is non empty finite set
{ b₁ where b₁ is Element of (v) : b₁ is (v) (v) (v) } is set
LS is Element of (v)
LT is (v) (v) (v)
LS is (v) (v) (v)
LT is (v) (v) (v)
w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Seg w is finite w -element Element of bool NAT
v is set
LS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Seg LS is finite LS -element Element of bool NAT
LS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
Seg (LS + 1) is non empty finite LS + 1 -element Element of bool NAT
IS is set
FS is set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT : ( 1 <= b₁ & b₁ <= LS + 1 ) } is set
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
IS is set
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
{(LS + 1)} is non empty trivial finite V42() 1 -element set
IS \ {(LS + 1)} is Element of bool IS
bool IS is non empty set
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS is set
Seg 0 is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty proper real integer finite finite-yielding V42() cardinal 0 -element {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative V257() V258() V259() V260() V261() Element of bool NAT
LS is set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty finite set
[:(w),(w):] is Relation-like non empty finite set
bool [:(w),(w):] is non empty finite V42() set
v is Element of Inf_seq AtomicFamily
LT is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
IS is set
(IS,w) is (w) (w)
(w,(IS,w)) is Element of bool LTL_WFF
(w) is non empty finite Element of bool LTL_WFF
the of (IS,w) is finite Element of bool (w)
bool (w) is non empty finite V42() set
the of (IS,w) is finite Element of bool (w)
the of (IS,w) \/ the of (IS,w) is finite Element of bool (w)
the of (IS,w) is finite Element of bool (w)
(w, the of (IS,w)) is Element of bool LTL_WFF
'X' (w, the of (IS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (IS,w)) & b₁ = 'X' b₂ ) } is set
( the of (IS,w) \/ the of (IS,w)) \/ ('X' (w, the of (IS,w))) is set
LT . IS is set
((LT . IS),w) is (w) (w)
(w,((LT . IS),w)) is Element of bool LTL_WFF
the of ((LT . IS),w) is finite Element of bool (w)
the of ((LT . IS),w) is finite Element of bool (w)
the of ((LT . IS),w) \/ the of ((LT . IS),w) is finite Element of bool (w)
the of ((LT . IS),w) is finite Element of bool (w)
(w, the of ((LT . IS),w)) is Element of bool LTL_WFF
'X' (w, the of ((LT . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of ((LT . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of ((LT . IS),w) \/ the of ((LT . IS),w)) \/ ('X' (w, the of ((LT . IS),w))) is set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty finite set
[:(w),(w):] is Relation-like non empty finite set
bool [:(w),(w):] is non empty finite V42() set
v is Element of Inf_seq AtomicFamily
LT is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
IS is set
(IS,w) is (w) (w)
(w,(IS,w)) is Element of bool LTL_WFF
(w) is non empty finite Element of bool LTL_WFF
the of (IS,w) is finite Element of bool (w)
bool (w) is non empty finite V42() set
the of (IS,w) is finite Element of bool (w)
the of (IS,w) \/ the of (IS,w) is finite Element of bool (w)
the of (IS,w) is finite Element of bool (w)
(w, the of (IS,w)) is Element of bool LTL_WFF
'X' (w, the of (IS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (IS,w)) & b₁ = 'X' b₂ ) } is set
( the of (IS,w) \/ the of (IS,w)) \/ ('X' (w, the of (IS,w))) is set
LT . IS is set
((LT . IS),w) is (w) (w)
(w,((LT . IS),w)) is Element of bool LTL_WFF
the of ((LT . IS),w) is finite Element of bool (w)
the of ((LT . IS),w) is finite Element of bool (w)
the of ((LT . IS),w) \/ the of ((LT . IS),w) is finite Element of bool (w)
the of ((LT . IS),w) is finite Element of bool (w)
(w, the of ((LT . IS),w)) is Element of bool LTL_WFF
'X' (w, the of ((LT . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of ((LT . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of ((LT . IS),w) \/ the of ((LT . IS),w)) \/ ('X' (w, the of ((LT . IS),w))) is set
IS is set
(IS,w) is (w) (w)
(w,(IS,w)) is Element of bool LTL_WFF
(w) is non empty finite Element of bool LTL_WFF
the of (IS,w) is finite Element of bool (w)
bool (w) is non empty finite V42() set
the of (IS,w) is finite Element of bool (w)
the of (IS,w) \/ the of (IS,w) is finite Element of bool (w)
the of (IS,w) is finite Element of bool (w)
(w, the of (IS,w)) is Element of bool LTL_WFF
'X' (w, the of (IS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (IS,w)) & b₁ = 'X' b₂ ) } is set
( the of (IS,w) \/ the of (IS,w)) \/ ('X' (w, the of (IS,w))) is set
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** FS is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** FS) . IS is set
(((LT |** FS) . IS),w) is (w) (w)
(w,(((LT |** FS) . IS),w)) is Element of bool LTL_WFF
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) \/ the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** FS) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** FS) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** FS) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** FS) . IS),w) \/ the of (((LT |** FS) . IS),w)) \/ ('X' (w, the of (((LT |** FS) . IS),w))) is set
FS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LT |** (FS + 1) is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** (FS + 1)) . IS is set
(((LT |** (FS + 1)) . IS),w) is (w) (w)
(w,(((LT |** (FS + 1)) . IS),w)) is Element of bool LTL_WFF
the of (((LT |** (FS + 1)) . IS),w) is finite Element of bool (w)
the of (((LT |** (FS + 1)) . IS),w) is finite Element of bool (w)
the of (((LT |** (FS + 1)) . IS),w) \/ the of (((LT |** (FS + 1)) . IS),w) is finite Element of bool (w)
the of (((LT |** (FS + 1)) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** (FS + 1)) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** (FS + 1)) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** (FS + 1)) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** (FS + 1)) . IS),w) \/ the of (((LT |** (FS + 1)) . IS),w)) \/ ('X' (w, the of (((LT |** (FS + 1)) . IS),w))) is set
LT * (LT |** FS) is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT * (LT |** FS)) . IS is set
LT . ((LT |** FS) . IS) is set
run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** run is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** run) . IS is set
(((LT |** run) . IS),w) is (w) (w)
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** chf is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** chf) . IS is set
(((LT |** chf) . IS),w) is (w) (w)
LT |** 0 is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** 0) . IS is set
(((LT |** 0) . IS),w) is (w) (w)
(w,(((LT |** 0) . IS),w)) is Element of bool LTL_WFF
the of (((LT |** 0) . IS),w) is finite Element of bool (w)
the of (((LT |** 0) . IS),w) is finite Element of bool (w)
the of (((LT |** 0) . IS),w) \/ the of (((LT |** 0) . IS),w) is finite Element of bool (w)
the of (((LT |** 0) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** 0) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** 0) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** 0) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** 0) . IS),w) \/ the of (((LT |** 0) . IS),w)) \/ ('X' (w, the of (((LT |** 0) . IS),w))) is set
id (w) is Relation-like (w) -defined (w) -valued Function-like one-to-one non empty V21((w)) V25((w),(w)) finite being_quasi-order being_partial-order Element of bool [:(w),(w):]
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** FS is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** FS) . IS is set
(((LT |** FS) . IS),w) is (w) (w)
(w,(((LT |** FS) . IS),w)) is Element of bool LTL_WFF
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) \/ the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** FS) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** FS) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** FS) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** FS) . IS),w) \/ the of (((LT |** FS) . IS),w)) \/ ('X' (w, the of (((LT |** FS) . IS),w))) is set
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** FS is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** FS) . IS is set
(((LT |** FS) . IS),w) is (w) (w)
(w,(((LT |** FS) . IS),w)) is Element of bool LTL_WFF
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) \/ the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** FS) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** FS) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** FS) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** FS) . IS),w) \/ the of (((LT |** FS) . IS),w)) \/ ('X' (w, the of (((LT |** FS) . IS),w))) is set
IS is set
(IS,w) is (w) (w)
(w,(IS,w)) is Element of bool LTL_WFF
(w) is non empty finite Element of bool LTL_WFF
the of (IS,w) is finite Element of bool (w)
bool (w) is non empty finite V42() set
the of (IS,w) is finite Element of bool (w)
the of (IS,w) \/ the of (IS,w) is finite Element of bool (w)
the of (IS,w) is finite Element of bool (w)
(w, the of (IS,w)) is Element of bool LTL_WFF
'X' (w, the of (IS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (IS,w)) & b₁ = 'X' b₂ ) } is set
( the of (IS,w) \/ the of (IS,w)) \/ ('X' (w, the of (IS,w))) is set
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** FS is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** FS) . IS is set
(((LT |** FS) . IS),w) is (w) (w)
(w,(((LT |** FS) . IS),w)) is Element of bool LTL_WFF
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) \/ the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** FS) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** FS) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** FS) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** FS) . IS),w) \/ the of (((LT |** FS) . IS),w)) \/ ('X' (w, the of (((LT |** FS) . IS),w))) is set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty finite set
[:(w),(w):] is Relation-like non empty finite set
bool [:(w),(w):] is non empty finite V42() set
v is Element of Inf_seq AtomicFamily
LT is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
IS is set
(IS,w) is (w) (w)
(w,(IS,w)) is Element of bool LTL_WFF
(w) is non empty finite Element of bool LTL_WFF
the of (IS,w) is finite Element of bool (w)
bool (w) is non empty finite V42() set
the of (IS,w) is finite Element of bool (w)
the of (IS,w) \/ the of (IS,w) is finite Element of bool (w)
the of (IS,w) is finite Element of bool (w)
(w, the of (IS,w)) is Element of bool LTL_WFF
'X' (w, the of (IS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (IS,w)) & b₁ = 'X' b₂ ) } is set
( the of (IS,w) \/ the of (IS,w)) \/ ('X' (w, the of (IS,w))) is set
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** FS is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** FS) . IS is set
(((LT |** FS) . IS),w) is (w) (w)
FS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LT |** (FS + 1) is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** (FS + 1)) . IS is set
(((LT |** (FS + 1)) . IS),w) is (w) (w)
(w,(((LT |** FS) . IS),w)) is Element of bool LTL_WFF
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) \/ the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** FS) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** FS) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** FS) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** FS) . IS),w) \/ the of (((LT |** FS) . IS),w)) \/ ('X' (w, the of (((LT |** FS) . IS),w))) is set
LT * (LT |** FS) is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT * (LT |** FS)) . IS is set
LT . ((LT |** FS) . IS) is set
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** FS is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** FS) . IS is set
(((LT |** FS) . IS),w) is (w) (w)
FS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LT |** (FS + 1) is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** (FS + 1)) . IS is set
(((LT |** (FS + 1)) . IS),w) is (w) (w)
(w,(((LT |** FS) . IS),w)) is Element of bool LTL_WFF
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) \/ the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** FS) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** FS) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** FS) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** FS) . IS),w) \/ the of (((LT |** FS) . IS),w)) \/ ('X' (w, the of (((LT |** FS) . IS),w))) is set
IS is set
(IS,w) is (w) (w)
(w,(IS,w)) is Element of bool LTL_WFF
(w) is non empty finite Element of bool LTL_WFF
the of (IS,w) is finite Element of bool (w)
bool (w) is non empty finite V42() set
the of (IS,w) is finite Element of bool (w)
the of (IS,w) \/ the of (IS,w) is finite Element of bool (w)
the of (IS,w) is finite Element of bool (w)
(w, the of (IS,w)) is Element of bool LTL_WFF
'X' (w, the of (IS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (IS,w)) & b₁ = 'X' b₂ ) } is set
( the of (IS,w) \/ the of (IS,w)) \/ ('X' (w, the of (IS,w))) is set
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** FS is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** FS) . IS is set
(((LT |** FS) . IS),w) is (w) (w)
FS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LT |** (FS + 1) is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** (FS + 1)) . IS is set
(((LT |** (FS + 1)) . IS),w) is (w) (w)
(w,(((LT |** FS) . IS),w)) is Element of bool LTL_WFF
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) \/ the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** FS) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** FS) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** FS) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** FS) . IS),w) \/ the of (((LT |** FS) . IS),w)) \/ ('X' (w, the of (((LT |** FS) . IS),w))) is set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty finite set
[:(w),(w):] is Relation-like non empty finite set
bool [:(w),(w):] is non empty finite V42() set
v is Element of Inf_seq AtomicFamily
LT is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
IS is set
(IS,w) is (w) (w)
(w,(IS,w)) is Element of bool LTL_WFF
(w) is non empty finite Element of bool LTL_WFF
the of (IS,w) is finite Element of bool (w)
bool (w) is non empty finite V42() set
the of (IS,w) is finite Element of bool (w)
the of (IS,w) \/ the of (IS,w) is finite Element of bool (w)
the of (IS,w) is finite Element of bool (w)
(w, the of (IS,w)) is Element of bool LTL_WFF
'X' (w, the of (IS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (IS,w)) & b₁ = 'X' b₂ ) } is set
( the of (IS,w) \/ the of (IS,w)) \/ ('X' (w, the of (IS,w))) is set
LT . IS is set
((LT . IS),w) is (w) (w)
(w,((LT . IS),w)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of ((LT . IS),w) is finite Element of bool (w)
(w, the of ((LT . IS),w)) is real ext-real V257() Element of REAL
[\(w, the of ((LT . IS),w))/] is real integer ext-real V257() set
(w,((LT . IS),w)) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
0 + ((w,((LT . IS),w)) + 1) is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
dom run is finite Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT : ( 1 <= b₁ & b₁ <= chf & (((LT |** b₁) . IS),w) is (w) ) } is set
Seg chf is finite chf -element Element of bool NAT
FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . FK is set
LT |** FK is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** FK) . IS is set
CastNat FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** (CastNat FK) is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** (CastNat FK)) . IS is set
FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** FK is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** FK) . IS is set
(((LT |** FK) . IS),w) is (w) (w)
x is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** FK is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** FK) . IS is set
(((LT |** FK) . IS),w) is (w) (w)
FK + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LT |** (FK + 1) is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** (FK + 1)) . IS is set
(((LT |** (FK + 1)) . IS),w) is (w) (w)
x is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** x is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** x) . IS is set
(((LT |** x) . IS),w) is (w) (w)
id (w) is Relation-like (w) -defined (w) -valued Function-like one-to-one non empty V21((w)) V25((w),(w)) finite being_quasi-order being_partial-order Element of bool [:(w),(w):]
FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . FK is set
FK + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run . (FK + 1) is set
LT |** (FK + 1) is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** (FK + 1)) . IS is set
LT |** FK is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** FK) . IS is set
F1 is (w) (w)
L is (w) (w)
F1 is (w) (w)
(F1,w) is (w) (w)
F2 is (w) (w)
(F2,w) is (w) (w)
run . chf is set
((run . chf),w) is (w) (w)
(w,((run . chf),w)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of ((run . chf),w) is finite Element of bool (w)
(w, the of ((run . chf),w)) is real ext-real V257() Element of REAL
[\(w, the of ((run . chf),w))/] is real integer ext-real V257() set
run . 1 is set
((run . 1),w) is (w) (w)
(w,((run . 1),w)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of ((run . 1),w) is finite Element of bool (w)
(w, the of ((run . 1),w)) is real ext-real V257() Element of REAL
[\(w, the of ((run . 1),w))/] is real integer ext-real V257() set
(w,((run . 1),w)) - chf is real integer ext-real V257() set
((w,((run . 1),w)) - chf) + 1 is real integer ext-real V257() Element of REAL
LT |** 1 is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** 1) . IS is set
(((LT |** 1) . IS),w) is (w) (w)
(w,(((LT |** 1) . IS),w)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of (((LT |** 1) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** 1) . IS),w)) is real ext-real V257() Element of REAL
[\(w, the of (((LT |** 1) . IS),w))/] is real integer ext-real V257() set
(w,(((LT |** 1) . IS),w)) - chf is real integer ext-real V257() set
((w,(((LT |** 1) . IS),w)) - chf) + 1 is real integer ext-real V257() Element of REAL
(w,((LT . IS),w)) - chf is real integer ext-real V257() set
((w,((LT . IS),w)) - chf) + 1 is real integer ext-real V257() Element of REAL
LT |** chf is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** chf) . IS is set
(((LT |** chf) . IS),w) is (w) (w)
(w,(((LT |** chf) . IS),w)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
the of (((LT |** chf) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** chf) . IS),w)) is real ext-real V257() Element of REAL
[\(w, the of (((LT |** chf) . IS),w))/] is real integer ext-real V257() set
(w) is finite Element of bool (w)
FK is set
x is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LT |** x is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** x) . IS is set
(((LT |** x) . IS),w) is (w) (w)
FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
x is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** x is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** x) . IS is set
(((LT |** x) . IS),w) is (w) (w)
id (w) is Relation-like (w) -defined (w) -valued Function-like one-to-one non empty V21((w)) V25((w),(w)) finite being_quasi-order being_partial-order Element of bool [:(w),(w):]
F is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LT |** FK is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** FK) . IS is set
(((LT |** FK) . IS),w) is (w) (w)
x is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LT |** x is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** x) . IS is set
(((LT |** x) . IS),w) is (w) (w)
IS is set
(IS,w) is (w) (w)
(w,(IS,w)) is Element of bool LTL_WFF
(w) is non empty finite Element of bool LTL_WFF
the of (IS,w) is finite Element of bool (w)
bool (w) is non empty finite V42() set
the of (IS,w) is finite Element of bool (w)
the of (IS,w) \/ the of (IS,w) is finite Element of bool (w)
the of (IS,w) is finite Element of bool (w)
(w, the of (IS,w)) is Element of bool LTL_WFF
'X' (w, the of (IS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (IS,w)) & b₁ = 'X' b₂ ) } is set
( the of (IS,w) \/ the of (IS,w)) \/ ('X' (w, the of (IS,w))) is set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty finite set
[:(w),(w):] is Relation-like non empty finite set
bool [:(w),(w):] is non empty finite V42() set
v is Element of Inf_seq AtomicFamily
LT is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
IS is set
(IS,w) is (w) (w)
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** FS is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** FS) . IS is set
(((LT |** FS) . IS),w) is (w) (w)
(w,(((LT |** FS) . IS),w)) is Element of bool LTL_WFF
(w) is non empty finite Element of bool LTL_WFF
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
bool (w) is non empty finite V42() set
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) \/ the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** FS) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** FS) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** FS) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** FS) . IS),w) \/ the of (((LT |** FS) . IS),w)) \/ ('X' (w, the of (((LT |** FS) . IS),w))) is set
FS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LT |** (FS + 1) is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** (FS + 1)) . IS is set
(((LT |** (FS + 1)) . IS),w) is (w) (w)
(w,(((LT |** (FS + 1)) . IS),w)) is Element of bool LTL_WFF
the of (((LT |** (FS + 1)) . IS),w) is finite Element of bool (w)
the of (((LT |** (FS + 1)) . IS),w) is finite Element of bool (w)
the of (((LT |** (FS + 1)) . IS),w) \/ the of (((LT |** (FS + 1)) . IS),w) is finite Element of bool (w)
the of (((LT |** (FS + 1)) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** (FS + 1)) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** (FS + 1)) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** (FS + 1)) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** (FS + 1)) . IS),w) \/ the of (((LT |** (FS + 1)) . IS),w)) \/ ('X' (w, the of (((LT |** (FS + 1)) . IS),w))) is set
LT * (LT |** FS) is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT * (LT |** FS)) . IS is set
LT . ((LT |** FS) . IS) is set
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** FS is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** FS) . IS is set
(((LT |** FS) . IS),w) is (w) (w)
(w,(((LT |** FS) . IS),w)) is Element of bool LTL_WFF
(w) is non empty finite Element of bool LTL_WFF
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
bool (w) is non empty finite V42() set
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) \/ the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** FS) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** FS) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** FS) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** FS) . IS),w) \/ the of (((LT |** FS) . IS),w)) \/ ('X' (w, the of (((LT |** FS) . IS),w))) is set
FS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LT |** (FS + 1) is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** (FS + 1)) . IS is set
(((LT |** (FS + 1)) . IS),w) is (w) (w)
(w,(((LT |** (FS + 1)) . IS),w)) is Element of bool LTL_WFF
the of (((LT |** (FS + 1)) . IS),w) is finite Element of bool (w)
the of (((LT |** (FS + 1)) . IS),w) is finite Element of bool (w)
the of (((LT |** (FS + 1)) . IS),w) \/ the of (((LT |** (FS + 1)) . IS),w) is finite Element of bool (w)
the of (((LT |** (FS + 1)) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** (FS + 1)) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** (FS + 1)) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** (FS + 1)) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** (FS + 1)) . IS),w) \/ the of (((LT |** (FS + 1)) . IS),w)) \/ ('X' (w, the of (((LT |** (FS + 1)) . IS),w))) is set
IS is set
(IS,w) is (w) (w)
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** FS is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** FS) . IS is set
(((LT |** FS) . IS),w) is (w) (w)
(w,(((LT |** FS) . IS),w)) is Element of bool LTL_WFF
(w) is non empty finite Element of bool LTL_WFF
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
bool (w) is non empty finite V42() set
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) \/ the of (((LT |** FS) . IS),w) is finite Element of bool (w)
the of (((LT |** FS) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** FS) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** FS) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** FS) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** FS) . IS),w) \/ the of (((LT |** FS) . IS),w)) \/ ('X' (w, the of (((LT |** FS) . IS),w))) is set
FS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LT |** (FS + 1) is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** (FS + 1)) . IS is set
(((LT |** (FS + 1)) . IS),w) is (w) (w)
(w,(((LT |** (FS + 1)) . IS),w)) is Element of bool LTL_WFF
the of (((LT |** (FS + 1)) . IS),w) is finite Element of bool (w)
the of (((LT |** (FS + 1)) . IS),w) is finite Element of bool (w)
the of (((LT |** (FS + 1)) . IS),w) \/ the of (((LT |** (FS + 1)) . IS),w) is finite Element of bool (w)
the of (((LT |** (FS + 1)) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** (FS + 1)) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** (FS + 1)) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** (FS + 1)) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** (FS + 1)) . IS),w) \/ the of (((LT |** (FS + 1)) . IS),w)) \/ ('X' (w, the of (((LT |** (FS + 1)) . IS),w))) is set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty finite set
[:(w),(w):] is Relation-like non empty finite set
bool [:(w),(w):] is non empty finite V42() set
v is Element of Inf_seq AtomicFamily
LT is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
IS is set
(IS,w) is (w) (w)
(w,(IS,w)) is Element of bool LTL_WFF
(w) is non empty finite Element of bool LTL_WFF
the of (IS,w) is finite Element of bool (w)
bool (w) is non empty finite V42() set
the of (IS,w) is finite Element of bool (w)
the of (IS,w) \/ the of (IS,w) is finite Element of bool (w)
the of (IS,w) is finite Element of bool (w)
(w, the of (IS,w)) is Element of bool LTL_WFF
'X' (w, the of (IS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (IS,w)) & b₁ = 'X' b₂ ) } is set
( the of (IS,w) \/ the of (IS,w)) \/ ('X' (w, the of (IS,w))) is set
LT . IS is set
((LT . IS),w) is (w) (w)
(w,((LT . IS),w)) is Element of bool LTL_WFF
the of ((LT . IS),w) is finite Element of bool (w)
the of ((LT . IS),w) is finite Element of bool (w)
the of ((LT . IS),w) \/ the of ((LT . IS),w) is finite Element of bool (w)
the of ((LT . IS),w) is finite Element of bool (w)
(w, the of ((LT . IS),w)) is Element of bool LTL_WFF
'X' (w, the of ((LT . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of ((LT . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of ((LT . IS),w) \/ the of ((LT . IS),w)) \/ ('X' (w, the of ((LT . IS),w))) is set
IS is set
(IS,w) is (w) (w)
(w,(IS,w)) is Element of bool LTL_WFF
(w) is non empty finite Element of bool LTL_WFF
the of (IS,w) is finite Element of bool (w)
bool (w) is non empty finite V42() set
the of (IS,w) is finite Element of bool (w)
the of (IS,w) \/ the of (IS,w) is finite Element of bool (w)
the of (IS,w) is finite Element of bool (w)
(w, the of (IS,w)) is Element of bool LTL_WFF
'X' (w, the of (IS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (IS,w)) & b₁ = 'X' b₂ ) } is set
( the of (IS,w) \/ the of (IS,w)) \/ ('X' (w, the of (IS,w))) is set
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** FS is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** FS) . IS is set
(((LT |** FS) . IS),w) is (w) (w)
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** chf is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** chf) . IS is set
(((LT |** chf) . IS),w) is (w) (w)
chf + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LT |** (chf + 1) is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** (chf + 1)) . IS is set
(((LT |** (chf + 1)) . IS),w) is (w) (w)
run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** run is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** run) . IS is set
(((LT |** run) . IS),w) is (w) (w)
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** chf is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** chf) . IS is set
(((LT |** chf) . IS),w) is (w) (w)
chf + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LT |** (chf + 1) is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** (chf + 1)) . IS is set
(((LT |** (chf + 1)) . IS),w) is (w) (w)
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
chf + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LT |** chf is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** chf) . IS is set
(((LT |** chf) . IS),w) is (w) (w)
run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** run is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** run) . IS is set
(((LT |** run) . IS),w) is (w) (w)
(w,(((LT |** run) . IS),w)) is Element of bool LTL_WFF
the of (((LT |** run) . IS),w) is finite Element of bool (w)
the of (((LT |** run) . IS),w) is finite Element of bool (w)
the of (((LT |** run) . IS),w) \/ the of (((LT |** run) . IS),w) is finite Element of bool (w)
the of (((LT |** run) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** run) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** run) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** run) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** run) . IS),w) \/ the of (((LT |** run) . IS),w)) \/ ('X' (w, the of (((LT |** run) . IS),w))) is set
(w,(((LT |** chf) . IS),w)) is Element of bool LTL_WFF
the of (((LT |** chf) . IS),w) is finite Element of bool (w)
the of (((LT |** chf) . IS),w) is finite Element of bool (w)
the of (((LT |** chf) . IS),w) \/ the of (((LT |** chf) . IS),w) is finite Element of bool (w)
the of (((LT |** chf) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** chf) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** chf) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** chf) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** chf) . IS),w) \/ the of (((LT |** chf) . IS),w)) \/ ('X' (w, the of (((LT |** chf) . IS),w))) is set
LT |** (chf + 1) is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** (chf + 1)) . IS is set
(((LT |** (chf + 1)) . IS),w) is (w) (w)
(w,(((LT |** (chf + 1)) . IS),w)) is Element of bool LTL_WFF
the of (((LT |** (chf + 1)) . IS),w) is finite Element of bool (w)
the of (((LT |** (chf + 1)) . IS),w) is finite Element of bool (w)
the of (((LT |** (chf + 1)) . IS),w) \/ the of (((LT |** (chf + 1)) . IS),w) is finite Element of bool (w)
the of (((LT |** (chf + 1)) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** (chf + 1)) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** (chf + 1)) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** (chf + 1)) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** (chf + 1)) . IS),w) \/ the of (((LT |** (chf + 1)) . IS),w)) \/ ('X' (w, the of (((LT |** (chf + 1)) . IS),w))) is set
run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** run is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** run) . IS is set
(((LT |** run) . IS),w) is (w) (w)
(w,(((LT |** run) . IS),w)) is Element of bool LTL_WFF
the of (((LT |** run) . IS),w) is finite Element of bool (w)
the of (((LT |** run) . IS),w) is finite Element of bool (w)
the of (((LT |** run) . IS),w) \/ the of (((LT |** run) . IS),w) is finite Element of bool (w)
the of (((LT |** run) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** run) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** run) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** run) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** run) . IS),w) \/ the of (((LT |** run) . IS),w)) \/ ('X' (w, the of (((LT |** run) . IS),w))) is set
run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** run is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** run) . IS is set
(((LT |** run) . IS),w) is (w) (w)
(w,(((LT |** run) . IS),w)) is Element of bool LTL_WFF
the of (((LT |** run) . IS),w) is finite Element of bool (w)
the of (((LT |** run) . IS),w) is finite Element of bool (w)
the of (((LT |** run) . IS),w) \/ the of (((LT |** run) . IS),w) is finite Element of bool (w)
the of (((LT |** run) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** run) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** run) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** run) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** run) . IS),w) \/ the of (((LT |** run) . IS),w)) \/ ('X' (w, the of (((LT |** run) . IS),w))) is set
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** chf is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** chf) . IS is set
(((LT |** chf) . IS),w) is (w) (w)
(w,(((LT |** chf) . IS),w)) is Element of bool LTL_WFF
the of (((LT |** chf) . IS),w) is finite Element of bool (w)
the of (((LT |** chf) . IS),w) is finite Element of bool (w)
the of (((LT |** chf) . IS),w) \/ the of (((LT |** chf) . IS),w) is finite Element of bool (w)
the of (((LT |** chf) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** chf) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** chf) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** chf) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** chf) . IS),w) \/ the of (((LT |** chf) . IS),w)) \/ ('X' (w, the of (((LT |** chf) . IS),w))) is set
id (w) is Relation-like (w) -defined (w) -valued Function-like one-to-one non empty V21((w)) V25((w),(w)) finite being_quasi-order being_partial-order Element of bool [:(w),(w):]
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** chf is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** chf) . IS is set
(((LT |** chf) . IS),w) is (w) (w)
(w,(((LT |** chf) . IS),w)) is Element of bool LTL_WFF
the of (((LT |** chf) . IS),w) is finite Element of bool (w)
the of (((LT |** chf) . IS),w) is finite Element of bool (w)
the of (((LT |** chf) . IS),w) \/ the of (((LT |** chf) . IS),w) is finite Element of bool (w)
the of (((LT |** chf) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** chf) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** chf) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** chf) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** chf) . IS),w) \/ the of (((LT |** chf) . IS),w)) \/ ('X' (w, the of (((LT |** chf) . IS),w))) is set
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT |** chf is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(LT |** chf) . IS is set
(((LT |** chf) . IS),w) is (w) (w)
(w,(((LT |** chf) . IS),w)) is Element of bool LTL_WFF
the of (((LT |** chf) . IS),w) is finite Element of bool (w)
the of (((LT |** chf) . IS),w) is finite Element of bool (w)
the of (((LT |** chf) . IS),w) \/ the of (((LT |** chf) . IS),w) is finite Element of bool (w)
the of (((LT |** chf) . IS),w) is finite Element of bool (w)
(w, the of (((LT |** chf) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((LT |** chf) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((LT |** chf) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((LT |** chf) . IS),w) \/ the of (((LT |** chf) . IS),w)) \/ ('X' (w, the of (((LT |** chf) . IS),w))) is set
IS is set
(IS,w) is (w) (w)
(w,(IS,w)) is Element of bool LTL_WFF
(w) is non empty finite Element of bool LTL_WFF
the of (IS,w) is finite Element of bool (w)
bool (w) is non empty finite V42() set
the of (IS,w) is finite Element of bool (w)
the of (IS,w) \/ the of (IS,w) is finite Element of bool (w)
the of (IS,w) is finite Element of bool (w)
(w, the of (IS,w)) is Element of bool LTL_WFF
'X' (w, the of (IS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (IS,w)) & b₁ = 'X' b₂ ) } is set
( the of (IS,w) \/ the of (IS,w)) \/ ('X' (w, the of (IS,w))) is set
w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(v) is non empty finite set
(v) is non empty finite set
{ b₁ where b₁ is Element of (v) : b₁ is (v) (v) (v) } is set
[:NAT,(v):] is Relation-like non empty non trivial non finite set
bool [:NAT,(v):] is non empty non trivial non finite set
LS is Relation-like NAT -defined (v) -valued Function-like non empty V21( NAT ) V25( NAT ,(v)) Element of bool [:NAT,(v):]
LS . w is set
((LS . w),v) is (v) (v)
LT is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LS . LT is Element of (v)
IS is (v) (v) (v)
((LS . LT),v) is (v) (v)
w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v 'U' LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
4 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
<*4*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*4*> ^ v is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(<*4*> ^ v) ^ LS is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
LT is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(LT) is non empty finite set
(LT) is non empty finite set
{ b₁ where b₁ is Element of (LT) : b₁ is (LT) (LT) (LT) } is set
[:NAT,(LT):] is Relation-like non empty non trivial non finite set
bool [:NAT,(LT):] is non empty non trivial non finite set
IS is Relation-like NAT -defined (LT) -valued Function-like non empty V21( NAT ) V25( NAT ,(LT)) Element of bool [:NAT,(LT):]
IS . 1 is Element of (LT)
((IS . 1),LT) is (LT) (LT)
the of ((IS . 1),LT) is finite Element of bool (LT)
(LT) is non empty finite Element of bool LTL_WFF
bool (LT) is non empty finite V42() set
IS . 1 is set
((IS . 1),LT) is (LT) (LT)
the of H₁(1) is finite Element of bool (LT)
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS . run is set
((IS . run),LT) is (LT) (LT)
the of H₁(run) is finite Element of bool (LT)
run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS . run is set
((IS . run),LT) is (LT) (LT)
the of H₁(run) is finite Element of bool (LT)
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS . FSet is set
((IS . FSet),LT) is (LT) (LT)
the of ((IS . FSet),LT) is finite Element of bool (LT)
IS . 0 is set
((IS . 0),LT) is (LT) (LT)
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
IS . (0 + 1) is set
((IS . (0 + 1)),LT) is (LT) (LT)
1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
IS . (1 + 1) is set
((IS . (1 + 1)),LT) is (LT) (LT)
IS . 2 is set
((IS . 2),LT) is (LT) (LT)
FSet is (LT) (LT) (LT)
the of FSet is finite Element of bool (LT)
FK is (LT) (LT) (LT)
x is (LT) (LT) (LT)
FS - 1 is real integer ext-real V257() Element of REAL
FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FK - 1 is real integer ext-real V257() Element of REAL
FK + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
IS . FK is set
((IS . FK),LT) is (LT) (LT)
F2 is (LT) (LT) (LT)
the of F2 is finite Element of bool (LT)
IS . (FS + 1) is set
((IS . (FS + 1)),LT) is (LT) (LT)
IS . (FK + 1) is set
((IS . (FK + 1)),LT) is (LT) (LT)
F is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS . F is set
((IS . F),LT) is (LT) (LT)
F + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
IS . (F + 1) is set
((IS . (F + 1)),LT) is (LT) (LT)
IS . FS is set
((IS . FS),LT) is (LT) (LT)
F1 is (LT) (LT) (LT)
the of F1 is finite Element of bool (LT)
L is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS . L is set
((IS . L),LT) is (LT) (LT)
the of ((IS . L),LT) is finite Element of bool (LT)
L is (LT) (LT) (LT)
L is (LT) (LT) (LT)
run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS . run is set
((IS . run),LT) is (LT) (LT)
the of ((IS . run),LT) is finite Element of bool (LT)
run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS . run is set
((IS . run),LT) is (LT) (LT)
the of ((IS . run),LT) is finite Element of bool (LT)
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS . FSet is set
((IS . FSet),LT) is (LT) (LT)
the of ((IS . FSet),LT) is finite Element of bool (LT)
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS . FS is set
((IS . FS),LT) is (LT) (LT)
the of ((IS . FS),LT) is finite Element of bool (LT)
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS . FS is set
((IS . FS),LT) is (LT) (LT)
the of ((IS . FS),LT) is finite Element of bool (LT)
w is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_right_argument_of v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_left_argument_of v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(LS) is non empty finite set
(LS) is non empty finite set
{ b₁ where b₁ is Element of (LS) : b₁ is (LS) (LS) (LS) } is set
[:NAT,(LS):] is Relation-like non empty non trivial non finite set
bool [:NAT,(LS):] is non empty non trivial non finite set
LT is Relation-like NAT -defined (LS) -valued Function-like non empty V21( NAT ) V25( NAT ,(LS)) Element of bool [:NAT,(LS):]
LT . 1 is Element of (LS)
((LT . 1),LS) is (LS) (LS)
the of ((LT . 1),LS) is finite Element of bool (LS)
(LS) is non empty finite Element of bool LTL_WFF
bool (LS) is non empty finite V42() set
LT . 1 is set
((LT . 1),LS) is (LS) (LS)
the of H₁(1) is finite Element of bool (LS)
(the_left_argument_of v) 'U' (the_right_argument_of v) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
4 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
<*4*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*4*> ^ (the_left_argument_of v) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(<*4*> ^ (the_left_argument_of v)) ^ (the_right_argument_of v) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT . chf is set
((LT . chf),LS) is (LS) (LS)
the of ((LT . chf),LS) is finite Element of bool (LS)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w 'U' v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
4 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
<*4*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*4*> ^ w is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(<*4*> ^ w) ^ v is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(LS) is non empty finite set
(LS) is non empty finite set
{ b₁ where b₁ is Element of (LS) : b₁ is (LS) (LS) (LS) } is set
[:NAT,(LS):] is Relation-like non empty non trivial non finite set
bool [:NAT,(LS):] is non empty non trivial non finite set
LT is Relation-like NAT -defined (LS) -valued Function-like non empty V21( NAT ) V25( NAT ,(LS)) Element of bool [:NAT,(LS):]
LT . 1 is Element of (LS)
((LT . 1),LS) is (LS) (LS)
the of ((LT . 1),LS) is finite Element of bool (LS)
(LS) is non empty finite Element of bool LTL_WFF
bool (LS) is non empty finite V42() set
LT . 1 is set
((LT . 1),LS) is (LS) (LS)
the of H₁(1) is finite Element of bool (LS)
IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT . IS is set
((LT . IS),LS) is (LS) (LS)
the of ((LT . IS),LS) is finite Element of bool (LS)
IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT . IS is set
((LT . IS),LS) is (LS) (LS)
the of H₁(IS) is finite Element of bool (LS)
IS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT . chf is set
((LT . chf),LS) is (LS) (LS)
the of H₁(chf) is finite Element of bool (LS)
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT . chf is set
((LT . chf),LS) is (LS) (LS)
the of ((LT . chf),LS) is finite Element of bool (LS)
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT . chf is set
((LT . chf),LS) is (LS) (LS)
the of ((LT . chf),LS) is finite Element of bool (LS)
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT . chf is set
((LT . chf),LS) is (LS) (LS)
the of ((LT . chf),LS) is finite Element of bool (LS)
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT . chf is set
((LT . chf),LS) is (LS) (LS)
the of H₁(chf) is finite Element of bool (LS)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT : ( 1 <= b₁ & b₁ <= IS & v in the of H₁(b₁) ) } is set
Seg IS is finite IS -element Element of bool NAT
FSet is set
FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LT . FK is set
((LT . FK),LS) is (LS) (LS)
the of ((LT . FK),LS) is finite Element of bool (LS)
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
x is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT . x is set
((LT . x),LS) is (LS) (LS)
the of H₁(x) is finite Element of bool (LS)
F is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
x is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT . x is set
((LT . x),LS) is (LS) (LS)
the of ((LT . x),LS) is finite Element of bool (LS)
LT . FK is set
((LT . FK),LS) is (LS) (LS)
the of H₁(FK) is finite Element of bool (LS)
x is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LT . x is set
((LT . x),LS) is (LS) (LS)
the of ((LT . x),LS) is finite Element of bool (LS)
IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT . IS is set
((LT . IS),LS) is (LS) (LS)
the of ((LT . IS),LS) is finite Element of bool (LS)
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT . FS is set
((LT . FS),LS) is (LS) (LS)
the of ((LT . FS),LS) is finite Element of bool (LS)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_left_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_right_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(v) is non empty finite set
(v) is non empty finite set
{ b₁ where b₁ is Element of (v) : b₁ is (v) (v) (v) } is set
[:NAT,(v):] is Relation-like non empty non trivial non finite set
bool [:NAT,(v):] is non empty non trivial non finite set
LS is Relation-like NAT -defined (v) -valued Function-like non empty V21( NAT ) V25( NAT ,(v)) Element of bool [:NAT,(v):]
LS . 1 is Element of (v)
((LS . 1),v) is (v) (v)
the of ((LS . 1),v) is finite Element of bool (v)
(v) is non empty finite Element of bool LTL_WFF
bool (v) is non empty finite V42() set
LS . 1 is set
((LS . 1),v) is (v) (v)
the of H₁(1) is finite Element of bool (v)
(the_left_argument_of w) 'U' (the_right_argument_of w) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
4 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
<*4*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*4*> ^ (the_left_argument_of w) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(<*4*> ^ (the_left_argument_of w)) ^ (the_right_argument_of w) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS . FS is set
((LS . FS),v) is (v) (v)
the of ((LS . FS),v) is finite Element of bool (v)
w is set
BOOL w is set
union (BOOL w) is set
bool w is non empty set
(bool w) \ {{}} is Element of bool (bool w)
bool (bool w) is non empty set
(BOOL w) \/ {{}} is non empty set
((bool w) \ {{}}) \/ {{}} is non empty set
(bool w) \/ {{}} is non empty set
union (bool w) is set
union {{}} is finite set
(union (BOOL w)) \/ (union {{}}) is set
(union (BOOL w)) \/ {} is set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty finite Element of bool LTL_WFF
BOOL (w) is non empty set
v is (w) (w)
the of v is finite Element of bool (w)
bool (w) is non empty finite V42() set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty finite Element of bool LTL_WFF
BOOL (w) is non empty set
union (BOOL (w)) is set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty finite Element of bool LTL_WFF
BOOL (w) is non empty set
union (BOOL (w)) is non empty set
[:(BOOL (w)),(w):] is Relation-like non empty set
bool [:(BOOL (w)),(w):] is non empty set
LT is set
LT is Relation-like Function-like set
dom LT is set
IS is set
LT . IS is set
bool (w) is non empty finite V42() set
IS is Relation-like BOOL (w) -defined union (BOOL (w)) -valued Function-like non empty V21( BOOL (w)) V25( BOOL (w), union (BOOL (w))) Choice_Function of BOOL (w)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty finite Element of bool LTL_WFF
BOOL (w) is non empty set
union (BOOL (w)) is non empty set
LS is (w) (w)
v is Relation-like BOOL (w) -defined union (BOOL (w)) -valued Function-like non empty V21( BOOL (w)) V25( BOOL (w), union (BOOL (w))) Choice_Function of BOOL (w)
the of LS is finite Element of bool (w)
bool (w) is non empty finite V42() set
v . the of LS is set
FS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty finite Element of bool LTL_WFF
BOOL (w) is non empty set
union (BOOL (w)) is non empty set
v is (w) (w)
the of v is finite Element of bool (w)
bool (w) is non empty finite V42() set
LS is Relation-like BOOL (w) -defined union (BOOL (w)) -valued Function-like non empty V21( BOOL (w)) V25( BOOL (w), union (BOOL (w))) Choice_Function of BOOL (w)
(w,LS,v) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS . the of v is set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(v) is non empty finite Element of bool LTL_WFF
BOOL (v) is non empty set
union (BOOL (v)) is non empty set
LS is Relation-like BOOL (v) -defined union (BOOL (v)) -valued Function-like non empty V21( BOOL (v)) V25( BOOL (v), union (BOOL (v))) Choice_Function of BOOL (v)
LT is (v) (v)
(v,LS,LT) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Element of Inf_seq AtomicFamily
(v,LT,(v,LS,LT)) is (v) (v)
(v,(v,LT,(v,LS,LT))) is Element of bool LTL_WFF
the of (v,LT,(v,LS,LT)) is finite Element of bool (v)
bool (v) is non empty finite V42() set
the of (v,LT,(v,LS,LT)) is finite Element of bool (v)
the of (v,LT,(v,LS,LT)) \/ the of (v,LT,(v,LS,LT)) is finite Element of bool (v)
the of (v,LT,(v,LS,LT)) is finite Element of bool (v)
(v, the of (v,LT,(v,LS,LT))) is Element of bool LTL_WFF
'X' (v, the of (v,LT,(v,LS,LT))) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,LT,(v,LS,LT))) & b₁ = 'X' b₂ ) } is set
( the of (v,LT,(v,LS,LT)) \/ the of (v,LT,(v,LS,LT))) \/ ('X' (v, the of (v,LT,(v,LS,LT)))) is set
the_right_argument_of (v,LS,LT) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(v,LT,(v,LS,LT)) is (v) (v)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty finite Element of bool LTL_WFF
BOOL (w) is non empty set
union (BOOL (w)) is non empty set
v is (w) (w)
(w,v) is Element of bool LTL_WFF
the of v is finite Element of bool (w)
bool (w) is non empty finite V42() set
the of v is finite Element of bool (w)
the of v \/ the of v is finite Element of bool (w)
the of v is finite Element of bool (w)
(w, the of v) is Element of bool LTL_WFF
'X' (w, the of v) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of v) & b₁ = 'X' b₂ ) } is set
( the of v \/ the of v) \/ ('X' (w, the of v)) is set
LS is Element of Inf_seq AtomicFamily
LT is Relation-like BOOL (w) -defined union (BOOL (w)) -valued Function-like non empty V21( BOOL (w)) V25( BOOL (w), union (BOOL (w))) Choice_Function of BOOL (w)
(LS,w,LT,v) is (w) (w)
(w,(LS,w,LT,v)) is Element of bool LTL_WFF
the of (LS,w,LT,v) is finite Element of bool (w)
the of (LS,w,LT,v) is finite Element of bool (w)
the of (LS,w,LT,v) \/ the of (LS,w,LT,v) is finite Element of bool (w)
the of (LS,w,LT,v) is finite Element of bool (w)
(w, the of (LS,w,LT,v)) is Element of bool LTL_WFF
'X' (w, the of (LS,w,LT,v)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (LS,w,LT,v)) & b₁ = 'X' b₂ ) } is set
( the of (LS,w,LT,v) \/ the of (LS,w,LT,v)) \/ ('X' (w, the of (LS,w,LT,v))) is set
(w,LT,v) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_right_argument_of (w,LT,v) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w,v,(w,LT,v)) is (w) (w)
(w,(w,v,(w,LT,v))) is Element of bool LTL_WFF
the of (w,v,(w,LT,v)) is finite Element of bool (w)
the of (w,v,(w,LT,v)) is finite Element of bool (w)
the of (w,v,(w,LT,v)) \/ the of (w,v,(w,LT,v)) is finite Element of bool (w)
the of (w,v,(w,LT,v)) is finite Element of bool (w)
(w, the of (w,v,(w,LT,v))) is Element of bool LTL_WFF
'X' (w, the of (w,v,(w,LT,v))) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (w,v,(w,LT,v))) & b₁ = 'X' b₂ ) } is set
( the of (w,v,(w,LT,v)) \/ the of (w,v,(w,LT,v))) \/ ('X' (w, the of (w,v,(w,LT,v)))) is set
(w,v,(w,LT,v)) is (w) (w)
(w,(w,v,(w,LT,v))) is Element of bool LTL_WFF
the of (w,v,(w,LT,v)) is finite Element of bool (w)
the of (w,v,(w,LT,v)) is finite Element of bool (w)
the of (w,v,(w,LT,v)) \/ the of (w,v,(w,LT,v)) is finite Element of bool (w)
the of (w,v,(w,LT,v)) is finite Element of bool (w)
(w, the of (w,v,(w,LT,v))) is Element of bool LTL_WFF
'X' (w, the of (w,v,(w,LT,v))) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (w,v,(w,LT,v))) & b₁ = 'X' b₂ ) } is set
( the of (w,v,(w,LT,v)) \/ the of (w,v,(w,LT,v))) \/ ('X' (w, the of (w,v,(w,LT,v)))) is set
{(w,LT,v)} is functional non empty trivial finite V42() 1 -element set
the of v \/ {(w,LT,v)} is non empty finite set
((w,LT,v)) is finite Element of bool ((w,LT,v))
((w,LT,v)) is non empty finite Element of bool LTL_WFF
bool ((w,LT,v)) is non empty finite V42() set
{(the_right_argument_of (w,LT,v))} is functional non empty trivial finite V42() 1 -element set
((w,LT,v)) \ the of v is finite Element of bool ((w,LT,v))
the of v \ {(w,LT,v)} is finite Element of bool (w)
( the of v \ {(w,LT,v)}) \/ (((w,LT,v)) \ the of v) is finite set
(w,v,(w,LT,v)) is (w) (w)
(w,(w,v,(w,LT,v))) is Element of bool LTL_WFF
the of (w,v,(w,LT,v)) is finite Element of bool (w)
the of (w,v,(w,LT,v)) is finite Element of bool (w)
the of (w,v,(w,LT,v)) \/ the of (w,v,(w,LT,v)) is finite Element of bool (w)
the of (w,v,(w,LT,v)) is finite Element of bool (w)
(w, the of (w,v,(w,LT,v))) is Element of bool LTL_WFF
'X' (w, the of (w,v,(w,LT,v))) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (w,v,(w,LT,v))) & b₁ = 'X' b₂ ) } is set
( the of (w,v,(w,LT,v)) \/ the of (w,v,(w,LT,v))) \/ ('X' (w, the of (w,v,(w,LT,v)))) is set
(w,v,(w,LT,v)) is (w) (w)
((w,LT,v)) is finite Element of bool ((w,LT,v))
((w,LT,v)) is non empty finite Element of bool LTL_WFF
bool ((w,LT,v)) is non empty finite V42() set
{(the_right_argument_of (w,LT,v))} is functional non empty trivial finite V42() 1 -element set
{(w,LT,v)} is functional non empty trivial finite V42() 1 -element set
the of v \ {(w,LT,v)} is finite Element of bool (w)
{(the_right_argument_of (w,LT,v))} \ the of v is functional trivial finite V42() Element of bool {(the_right_argument_of (w,LT,v))}
bool {(the_right_argument_of (w,LT,v))} is non empty finite V42() set
( the of v \ {(w,LT,v)}) \/ ({(the_right_argument_of (w,LT,v))} \ the of v) is finite set
the of v \/ {(the_right_argument_of (w,LT,v))} is non empty finite set
the of v \/ {(w,LT,v)} is non empty finite set
L is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w,v,(w,LT,v)) is (w) (w)
(w,(w,v,(w,LT,v))) is Element of bool LTL_WFF
the of (w,v,(w,LT,v)) is finite Element of bool (w)
the of (w,v,(w,LT,v)) is finite Element of bool (w)
the of (w,v,(w,LT,v)) \/ the of (w,v,(w,LT,v)) is finite Element of bool (w)
the of (w,v,(w,LT,v)) is finite Element of bool (w)
(w, the of (w,v,(w,LT,v))) is Element of bool LTL_WFF
'X' (w, the of (w,v,(w,LT,v))) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (w,v,(w,LT,v))) & b₁ = 'X' b₂ ) } is set
( the of (w,v,(w,LT,v)) \/ the of (w,v,(w,LT,v))) \/ ('X' (w, the of (w,v,(w,LT,v)))) is set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty finite Element of bool LTL_WFF
BOOL (w) is non empty set
union (BOOL (w)) is non empty set
v is (w) (w)
the of v is finite Element of bool (w)
bool (w) is non empty finite V42() set
LS is Element of Inf_seq AtomicFamily
LT is Relation-like BOOL (w) -defined union (BOOL (w)) -valued Function-like non empty V21( BOOL (w)) V25( BOOL (w), union (BOOL (w))) Choice_Function of BOOL (w)
(w,LT,v) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_right_argument_of (w,LT,v) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(LS,w,LT,v) is (w) (w)
the of (LS,w,LT,v) is finite Element of bool (w)
the of (LS,w,LT,v) is finite Element of bool (w)
the of v is finite Element of bool (w)
(w,v,(w,LT,v)) is (w) (w)
((w,LT,v)) is finite Element of bool ((w,LT,v))
((w,LT,v)) is non empty finite Element of bool LTL_WFF
bool ((w,LT,v)) is non empty finite V42() set
{(the_right_argument_of (w,LT,v))} is functional non empty trivial finite V42() 1 -element set
{(w,LT,v)} is functional non empty trivial finite V42() 1 -element set
the of v \ {(w,LT,v)} is finite Element of bool (w)
{(the_right_argument_of (w,LT,v))} \ the of v is functional trivial finite V42() Element of bool {(the_right_argument_of (w,LT,v))}
bool {(the_right_argument_of (w,LT,v))} is non empty finite V42() set
( the of v \ {(w,LT,v)}) \/ ({(the_right_argument_of (w,LT,v))} \ the of v) is finite set
the of v \/ {(w,LT,v)} is non empty finite set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty finite Element of bool LTL_WFF
BOOL (w) is non empty set
union (BOOL (w)) is non empty set
v is (w) (w)
(w,v) is Element of bool LTL_WFF
the of v is finite Element of bool (w)
bool (w) is non empty finite V42() set
the of v is finite Element of bool (w)
the of v \/ the of v is finite Element of bool (w)
the of v is finite Element of bool (w)
(w, the of v) is Element of bool LTL_WFF
'X' (w, the of v) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of v) & b₁ = 'X' b₂ ) } is set
( the of v \/ the of v) \/ ('X' (w, the of v)) is set
LS is Element of Inf_seq AtomicFamily
LT is Relation-like BOOL (w) -defined union (BOOL (w)) -valued Function-like non empty V21( BOOL (w)) V25( BOOL (w), union (BOOL (w))) Choice_Function of BOOL (w)
(LS,w,LT,v) is (w) (w)
the of (LS,w,LT,v) is finite Element of bool (w)
the of (LS,w,LT,v) is finite Element of bool (w)
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(v) is non empty finite Element of bool LTL_WFF
BOOL (v) is non empty set
union (BOOL (v)) is non empty set
(v) is non empty finite set
[:(v),(v):] is Relation-like non empty finite set
bool [:(v),(v):] is non empty finite V42() set
w is Element of Inf_seq AtomicFamily
LS is Relation-like BOOL (v) -defined union (BOOL (v)) -valued Function-like non empty V21( BOOL (v)) V25( BOOL (v), union (BOOL (v))) Choice_Function of BOOL (v)
LT is set
(LT,v) is (v) (v)
(w,v,LS,(LT,v)) is (v) (v)
LT is Relation-like (v) -defined (v) -valued Function-like non empty V21((v)) V25((v),(v)) finite Element of bool [:(v),(v):]
IS is set
LT . IS is set
(IS,v) is (v) (v)
(w,v,LS,(IS,v)) is (v) (v)
LT is Relation-like (v) -defined (v) -valued Function-like non empty V21((v)) V25((v),(v)) finite Element of bool [:(v),(v):]
IS is Relation-like (v) -defined (v) -valued Function-like non empty V21((v)) V25((v),(v)) finite Element of bool [:(v),(v):]
FS is set
LT . FS is set
IS . FS is set
(FS,v) is (v) (v)
(w,v,LS,(FS,v)) is (v) (v)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w) is non empty finite Element of bool LTL_WFF
BOOL (w) is non empty set
union (BOOL (w)) is non empty set
v is Element of Inf_seq AtomicFamily
LS is Relation-like BOOL (w) -defined union (BOOL (w)) -valued Function-like non empty V21( BOOL (w)) V25( BOOL (w), union (BOOL (w))) Choice_Function of BOOL (w)
(v,w,LS) is Relation-like (w) -defined (w) -valued Function-like non empty V21((w)) V25((w),(w)) finite Element of bool [:(w),(w):]
(w) is non empty finite set
[:(w),(w):] is Relation-like non empty finite set
bool [:(w),(w):] is non empty finite V42() set
IS is set
(IS,w) is (w) (w)
(w,(IS,w)) is Element of bool LTL_WFF
the of (IS,w) is finite Element of bool (w)
bool (w) is non empty finite V42() set
the of (IS,w) is finite Element of bool (w)
the of (IS,w) \/ the of (IS,w) is finite Element of bool (w)
the of (IS,w) is finite Element of bool (w)
(w, the of (IS,w)) is Element of bool LTL_WFF
'X' (w, the of (IS,w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (IS,w)) & b₁ = 'X' b₂ ) } is set
( the of (IS,w) \/ the of (IS,w)) \/ ('X' (w, the of (IS,w))) is set
(v,w,LS) . IS is set
(((v,w,LS) . IS),w) is (w) (w)
(w,(((v,w,LS) . IS),w)) is Element of bool LTL_WFF
the of (((v,w,LS) . IS),w) is finite Element of bool (w)
the of (((v,w,LS) . IS),w) is finite Element of bool (w)
the of (((v,w,LS) . IS),w) \/ the of (((v,w,LS) . IS),w) is finite Element of bool (w)
the of (((v,w,LS) . IS),w) is finite Element of bool (w)
(w, the of (((v,w,LS) . IS),w)) is Element of bool LTL_WFF
'X' (w, the of (((v,w,LS) . IS),w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w, the of (((v,w,LS) . IS),w)) & b₁ = 'X' b₂ ) } is set
( the of (((v,w,LS) . IS),w) \/ the of (((v,w,LS) . IS),w)) \/ ('X' (w, the of (((v,w,LS) . IS),w))) is set
(v,w,LS,(IS,w)) is (w) (w)
((v,w,LS,(IS,w)),w) is (w) (w)
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_argument_of v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LT is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len LT is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LT . 1 is set
LT . LS is set
LS - 1 is real integer ext-real V257() Element of REAL
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
1 + FS is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
FS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LT . FS is set
LT . (FS + 1) is set
chf is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
run is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_argument_of LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
'not' v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*0*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*0*> ^ v is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
'not' v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*0*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*0*> ^ v is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
'not' (the_argument_of w) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*0*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*0*> ^ (the_argument_of w) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
'not' (the_argument_of w) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*0*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*0*> ^ (the_argument_of w) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_argument_of LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_left_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_right_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_argument_of LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LT is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_argument_of LT is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is non empty set
Inf_seq w is non empty set
K86(NAT,w) is functional non empty M4( NAT ,w)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() () FinSequence of NAT
v is (w) (w)
the of v is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ( b₁ is atomic & b₁ in the of v ) } is set
LT is set
IS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ( b₁ is atomic & 'not' b₁ in the of v ) } is set
LT is set
IS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
'not' IS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*0*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*0*> ^ IS is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() () FinSequence of NAT
v is (w) (w)
(w,v) is Element of bool LTL_WFF
the of v is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ( b₁ is atomic & b₁ in the of v ) } is set
(w,v) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ( b₁ is atomic & 'not' b₁ in the of v ) } is set
{ b₁ where b₁ is Element of bool atomic_LTL : ( (w,v) c= b₁ & (w,v) misses b₁ ) } is set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() () FinSequence of NAT
(w) is non empty finite set
(w) is non empty finite set
{ b₁ where b₁ is Element of (w) : b₁ is (w) (w) (w) } is set
[:(w),AtomicFamily,(w):] is non empty set
{ b₁ where b₁ is Element of [:(w),AtomicFamily,(w):] : ex b₂, b₃ being (w) (w) (w) ex b₄ being set st
( b₁ = [[b₂,b₄],b₃] & (w,b₂,b₃) & b₄ in (w,b₃) ) } is set
[:(w),AtomicFamily:] is Relation-like non empty set
[:[:(w),AtomicFamily:],(w):] is Relation-like non empty set
bool [:[:(w),AtomicFamily:],(w):] is non empty set
LS is set
LT is Element of [:(w),AtomicFamily,(w):]
IS is (w) (w) (w)
chf is set
[IS,chf] is set
{IS,chf} is non empty finite set
{IS} is non empty trivial finite 1 -element set
{{IS,chf},{IS}} is non empty finite V42() set
FS is (w) (w) (w)
[[IS,chf],FS] is set
{[IS,chf],FS} is non empty finite set
{[IS,chf]} is Relation-like Function-like constant non empty trivial finite 1 -element set
{{[IS,chf],FS},{[IS,chf]}} is non empty finite V42() set
(w,FS) is set
(w,FS) is Element of bool LTL_WFF
the of FS is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ( b₁ is atomic & b₁ in the of FS ) } is set
(w,FS) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ( b₁ is atomic & 'not' b₁ in the of FS ) } is set
{ b₁ where b₁ is Element of bool atomic_LTL : ( (w,FS) c= b₁ & (w,FS) misses b₁ ) } is set
LS is Relation-like [:(w),AtomicFamily:] -defined (w) -valued Element of bool [:[:(w),AtomicFamily:],(w):]
(w) is (w) (w) (w)
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
(w) is finite Element of bool (w)
{w} is functional non empty trivial finite V42() 1 -element set
(w,(w),(w),(w)) is (w) (w)
{(w)} is non empty trivial finite 1 -element set
bool (w) is non empty finite V42() set
LS is (w) (w) (w)
{LS} is non empty trivial finite 1 -element set
LT is set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() () FinSequence of NAT
(w) is non empty finite set
(w) is non empty finite set
{ b₁ where b₁ is Element of (w) : b₁ is (w) (w) (w) } is set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_right_argument_of v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{ b₁ where b₁ is Element of (w) : ( not v in the of (b₁,w) or the_right_argument_of v in the of (b₁,w) ) } is set
bool (w) is non empty finite V42() set
LT is set
IS is Element of (w)
(IS,w) is (w) (w)
the of (IS,w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() () FinSequence of NAT
(w) is non empty finite set
(w) is non empty finite set
{ b₁ where b₁ is Element of (w) : b₁ is (w) (w) (w) } is set
bool (w) is non empty finite V42() set
{ b₁ where b₁ is finite Element of bool (w) : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ is_subformula_of w & b₂ is Until & b₁ = (w,b₂) ) } is set
bool (bool (w)) is non empty finite V42() set
LS is set
LT is finite Element of bool (w)
IS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w,IS) is finite Element of bool (w)
the_right_argument_of IS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{ b₁ where b₁ is Element of (w) : ( not IS in the of (b₁,w) or the_right_argument_of IS in the of (b₁,w) ) } is set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() () FinSequence of NAT
(w) is non empty finite set
(w) is non empty finite set
{ b₁ where b₁ is Element of (w) : b₁ is (w) (w) (w) } is set
(w) is Relation-like [:(w),AtomicFamily:] -defined (w) -valued Element of bool [:[:(w),AtomicFamily:],(w):]
[:(w),AtomicFamily:] is Relation-like non empty set
[:[:(w),AtomicFamily:],(w):] is Relation-like non empty set
bool [:[:(w),AtomicFamily:],(w):] is non empty set
[:(w),AtomicFamily,(w):] is non empty set
{ b₁ where b₁ is Element of [:(w),AtomicFamily,(w):] : ex b₂, b₃ being (w) (w) (w) ex b₄ being set st
( b₁ = [[b₂,b₄],b₃] & (w,b₂,b₃) & b₄ in (w,b₃) ) } is set
(w) is finite Element of bool (w)
bool (w) is non empty finite V42() set
(w) is (w) (w) (w)
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
(w) is finite Element of bool (w)
{w} is functional non empty trivial finite V42() 1 -element set
(w,(w),(w),(w)) is (w) (w)
{(w)} is non empty trivial finite 1 -element set
(w) is finite V42() Element of bool (bool (w))
bool (bool (w)) is non empty finite V42() set
{ b₁ where b₁ is finite Element of bool (w) : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ is_subformula_of w & b₂ is Until & b₁ = (w,b₂) ) } is set
(AtomicFamily,(w),(w),(w),(w)) is ( AtomicFamily ) ( AtomicFamily )
w is Element of Inf_seq AtomicFamily
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() () FinSequence of NAT
(v) is ( AtomicFamily )
(v) is non empty finite set
(v) is non empty finite set
{ b₁ where b₁ is Element of (v) : b₁ is (v) (v) (v) } is set
(v) is Relation-like [:(v),AtomicFamily:] -defined (v) -valued Element of bool [:[:(v),AtomicFamily:],(v):]
[:(v),AtomicFamily:] is Relation-like non empty set
[:[:(v),AtomicFamily:],(v):] is Relation-like non empty set
bool [:[:(v),AtomicFamily:],(v):] is non empty set
[:(v),AtomicFamily,(v):] is non empty set
{ b₁ where b₁ is Element of [:(v),AtomicFamily,(v):] : ex b₂, b₃ being (v) (v) (v) ex b₄ being set st
( b₁ = [[b₂,b₄],b₃] & (v,b₂,b₃) & b₄ in (v,b₃) ) } is set
(v) is finite Element of bool (v)
bool (v) is non empty finite V42() set
(v) is (v) (v) (v)
(v) is finite Element of bool (v)
(v) is non empty finite Element of bool LTL_WFF
bool (v) is non empty finite V42() set
(v) is finite Element of bool (v)
{v} is functional non empty trivial finite V42() 1 -element set
(v,(v),(v),(v)) is (v) (v)
{(v)} is non empty trivial finite 1 -element set
(v) is finite V42() Element of bool (bool (v))
bool (bool (v)) is non empty finite V42() set
{ b₁ where b₁ is finite Element of bool (v) : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ is_subformula_of v & b₂ is Until & b₁ = (v,b₂) ) } is set
(AtomicFamily,(v),(v),(v),(v)) is ( AtomicFamily ) ( AtomicFamily )
CastSeq (w,AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
[:NAT,AtomicFamily:] is Relation-like non empty non trivial non finite set
bool [:NAT,AtomicFamily:] is non empty non trivial non finite set
[:NAT,(v):] is Relation-like non empty non trivial non finite set
bool [:NAT,(v):] is non empty non trivial non finite set
LS is Relation-like NAT -defined (v) -valued Function-like non empty V21( NAT ) V25( NAT ,(v)) Element of bool [:NAT,(v):]
LS . 0 is Element of (v)
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LS . (0 + 1) is set
((LS . (0 + 1)),v) is (v) (v)
LS . 0 is set
((LS . 0),v) is (v) (v)
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS . FS is set
((LS . FS),v) is (v) (v)
FS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LS . (FS + 1) is set
((LS . (FS + 1)),v) is (v) (v)
(CastSeq (w,AtomicFamily)) . FS is set
(v,H₂(FS + 1)) is set
(v,((LS . (FS + 1)),v)) is Element of bool LTL_WFF
the of ((LS . (FS + 1)),v) is finite Element of bool (v)
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ( b₁ is atomic & b₁ in the of ((LS . (FS + 1)),v) ) } is set
(v,((LS . (FS + 1)),v)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ( b₁ is atomic & 'not' b₁ in the of ((LS . (FS + 1)),v) ) } is set
{ b₁ where b₁ is Element of bool atomic_LTL : ( (v,((LS . (FS + 1)),v)) c= b₁ & (v,((LS . (FS + 1)),v)) misses b₁ ) } is set
[(LS . FS),H₁(FS)] is set
{(LS . FS),((CastSeq (w,AtomicFamily)) . FS)} is non empty finite set
{(LS . FS)} is non empty trivial finite 1 -element set
{{(LS . FS),((CastSeq (w,AtomicFamily)) . FS)},{(LS . FS)}} is non empty finite V42() set
LS . (FS + 1) is Element of (v)
[[(LS . FS),H₁(FS)],(LS . (FS + 1))] is set
{[(LS . FS),H₁(FS)],(LS . (FS + 1))} is non empty finite set
{[(LS . FS),H₁(FS)]} is Relation-like Function-like constant non empty trivial finite 1 -element set
{{[(LS . FS),H₁(FS)],(LS . (FS + 1))},{[(LS . FS),H₁(FS)]}} is non empty finite V42() set
run is Element of [:(v),AtomicFamily,(v):]
FSet is (v) (v) (v)
x is set
[FSet,x] is set
{FSet,x} is non empty finite set
{FSet} is non empty trivial finite 1 -element set
{{FSet,x},{FSet}} is non empty finite V42() set
FK is (v) (v) (v)
[[FSet,x],FK] is set
{[FSet,x],FK} is non empty finite set
{[FSet,x]} is Relation-like Function-like constant non empty trivial finite 1 -element set
{{[FSet,x],FK},{[FSet,x]}} is non empty finite V42() set
(v,FK) is set
(v,FK) is Element of bool LTL_WFF
the of FK is finite Element of bool (v)
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ( b₁ is atomic & b₁ in the of FK ) } is set
(v,FK) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ( b₁ is atomic & 'not' b₁ in the of FK ) } is set
{ b₁ where b₁ is Element of bool atomic_LTL : ( (v,FK) c= b₁ & (v,FK) misses b₁ ) } is set
FSet is (v) (v) (v)
x is set
[FSet,x] is set
{FSet,x} is non empty finite set
{FSet} is non empty trivial finite 1 -element set
{{FSet,x},{FSet}} is non empty finite V42() set
FK is (v) (v) (v)
[[FSet,x],FK] is set
{[FSet,x],FK} is non empty finite set
{[FSet,x]} is Relation-like Function-like constant non empty trivial finite 1 -element set
{{[FSet,x],FK},{[FSet,x]}} is non empty finite V42() set
(v,FK) is set
(v,FK) is Element of bool LTL_WFF
the of FK is finite Element of bool (v)
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ( b₁ is atomic & b₁ in the of FK ) } is set
(v,FK) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ( b₁ is atomic & 'not' b₁ in the of FK ) } is set
{ b₁ where b₁ is Element of bool atomic_LTL : ( (v,FK) c= b₁ & (v,FK) misses b₁ ) } is set
(FK,v) is (v) (v)
(FSet,v) is (v) (v)
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS . FS is set
((LS . FS),v) is (v) (v)
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LS . chf is Element of (v)
run is Element of (v)
FS is set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT : H₂(b₁) in FS } is set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT : LS . b₁ in FS } is set
FSet is set
FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LS . FK is Element of (v)
LS . FK is set
((LS . FK),v) is (v) (v)
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
chf + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LS . (chf + 1) is set
((LS . (chf + 1)),v) is (v) (v)
the of H₂(chf + 1) is finite Element of bool (v)
Shift (w,chf) is Element of Inf_seq AtomicFamily
Shift (w,chf,AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ chf is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ chf) is Element of Inf_seq AtomicFamily
run is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
len run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(CastSeq (w,AtomicFamily)) . chf is set
CastSeq ((Shift (w,chf)),AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
(CastSeq ((Shift (w,chf)),AtomicFamily)) . 0 is Element of AtomicFamily
0 + chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(CastSeq (w,AtomicFamily)) . (0 + chf) is Element of AtomicFamily
(v,H₂(chf + 1)) is set
(v,((LS . (chf + 1)),v)) is Element of bool LTL_WFF
the of ((LS . (chf + 1)),v) is finite Element of bool (v)
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ( b₁ is atomic & b₁ in the of ((LS . (chf + 1)),v) ) } is set
(v,((LS . (chf + 1)),v)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ( b₁ is atomic & 'not' b₁ in the of ((LS . (chf + 1)),v) ) } is set
{ b₁ where b₁ is Element of bool atomic_LTL : ( (v,((LS . (chf + 1)),v)) c= b₁ & (v,((LS . (chf + 1)),v)) misses b₁ ) } is set
(v,H₂(chf + 1)) is Element of bool LTL_WFF
(v,H₂(chf + 1)) is Element of bool LTL_WFF
F is Element of bool atomic_LTL
(v,H₂(chf + 1)) /\ F is Element of bool atomic_LTL
the_argument_of run is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
'not' (the_argument_of run) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*0*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*0*> ^ (the_argument_of run) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
the_argument_of run is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_left_argument_of run is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
len (the_left_argument_of run) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LS . chf is set
((LS . chf),v) is (v) (v)
the_right_argument_of run is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
len (the_right_argument_of run) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
L is (v) (v) (v)
F1 is (v) (v) (v)
the of F1 is finite Element of bool (v)
(the_left_argument_of run) '&' (the_right_argument_of run) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*1*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*1*> ^ (the_left_argument_of run) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(<*1*> ^ (the_left_argument_of run)) ^ (the_right_argument_of run) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(the_left_argument_of run) 'or' (the_right_argument_of run) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*2*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*2*> ^ (the_left_argument_of run) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(<*2*> ^ (the_left_argument_of run)) ^ (the_right_argument_of run) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(chf + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LS . ((chf + 1) + 1) is set
((LS . ((chf + 1) + 1)),v) is (v) (v)
LS . chf is set
((LS . chf),v) is (v) (v)
the_argument_of run is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
len (the_argument_of run) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
w1 is (v) (v) (v)
m is (v) (v) (v)
the of m is finite Element of bool (v)
the of m is finite Element of bool (v)
F2 is (v) (v) (v)
the of F2 is finite Element of bool (v)
Shift (w,(chf + 1)) is Element of Inf_seq AtomicFamily
Shift (w,(chf + 1),AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ (chf + 1) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ (chf + 1)) is Element of Inf_seq AtomicFamily
Shift ((Shift (w,chf)),1) is Element of Inf_seq AtomicFamily
Shift ((Shift (w,chf)),1,AtomicFamily) is Element of Inf_seq AtomicFamily
CastSeq ((Shift (w,chf)),AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
(CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ 1 is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ 1) is Element of Inf_seq AtomicFamily
'X' (the_argument_of run) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*3*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*3*> ^ (the_argument_of run) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(v,run) is finite Element of bool (v)
the_right_argument_of run is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{ b₁ where b₁ is Element of (v) : ( not run in the of (b₁,v) or the_right_argument_of run in the of (b₁,v) ) } is set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT : H₂(b₁) in (v,run) } is set
F is set
CastNat F is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(CastNat F) + chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS . ((CastNat F) + chf) is set
F1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LS . F1 is Element of (v)
F is Relation-like NAT -defined (v) -valued Function-like non empty V21( NAT ) V25( NAT ,(v)) Element of bool [:NAT,(v):]
F2 is Relation-like NAT -defined (v) -valued Function-like non empty V21( NAT ) V25( NAT ,(v)) Element of bool [:NAT,(v):]
F1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
F2 . F1 is set
((F2 . F1),v) is (v) (v)
F1 + chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS . (F1 + chf) is set
((LS . (F1 + chf)),v) is (v) (v)
L is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
F2 . L is set
((F2 . L),v) is (v) (v)
CastNat L is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(CastNat L) + chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS . ((CastNat L) + chf) is set
(H₃(L),v) is (v) (v)
L + chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LS . (L + chf) is set
((LS . (L + chf)),v) is (v) (v)
F1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
F2 . F1 is set
((F2 . F1),v) is (v) (v)
F1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
F2 . (F1 + 1) is set
((F2 . (F1 + 1)),v) is (v) (v)
F1 + chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(F1 + 1) + chf is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LS . ((F1 + 1) + chf) is set
((LS . ((F1 + 1) + chf)),v) is (v) (v)
(F1 + chf) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LS . ((F1 + chf) + 1) is set
((LS . ((F1 + chf) + 1)),v) is (v) (v)
LS . (F1 + chf) is set
((LS . (F1 + chf)),v) is (v) (v)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT : H₄(b₁) in (v,run) } is set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT : ( not b₁ <= chf & b₁ in { b₁ where b₂ is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT : H₂(b₁) in (v,run) } ) } is set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT : ( b₁ <= chf & b₁ in { b₁ where b₂ is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT : H₂(b₁) in (v,run) } ) } is set
Seg chf is finite chf -element Element of bool NAT
{0} is functional non empty trivial finite V42() 1 -element set
(Seg chf) \/ {0} is non empty finite set
w1 is set
m1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
0 + m1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
w1 is Relation-like Function-like set
dom w1 is set
m1 is set
CastNat m1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(CastNat m1) - chf is real integer ext-real V257() set
h is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
h - chf is real integer ext-real V257() Element of REAL
m3 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
F2 . m3 is set
((F2 . m3),v) is (v) (v)
m3 + chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LS . (m3 + chf) is set
((LS . (m3 + chf)),v) is (v) (v)
LS . h is set
((LS . h),v) is (v) (v)
natMAX is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LS . natMAX is set
((LS . natMAX),v) is (v) (v)
m1 is set
h is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
CastNat m1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(CastNat m1) - chf is real integer ext-real V257() set
h - chf is real integer ext-real V257() Element of REAL
natMAX is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
w1 . ((CastNat m1) - chf) is set
CastNat ((CastNat m1) - chf) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(CastNat ((CastNat m1) - chf)) + chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
natMAX + chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
rng w1 is set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT : ( b₁ <= chf & b₁ in { b₁ where b₂ is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT : H₂(b₁) in (v,run) } ) } \/ { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT : ( not b₁ <= chf & b₁ in { b₁ where b₂ is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT : H₂(b₁) in (v,run) } ) } is set
w1 is set
h is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
LS . h is set
((LS . h),v) is (v) (v)
m1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
m1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
m1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
m1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
the_left_argument_of run is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
len (the_left_argument_of run) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
{0} is functional non empty trivial finite V42() 1 -element set
w1 is set
m1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
F2 . m1 is set
((F2 . m1),v) is (v) (v)
0 + m1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
m2 is Element of (v)
(m2,v) is (v) (v)
the of (m2,v) is finite Element of bool (v)
m3 is (v) (v)
(m3,v) is (v) (v)
F2 . 1 is set
((F2 . 1),v) is (v) (v)
the of H₄(1) is finite Element of bool (v)
w1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
F2 . w1 is set
((F2 . w1),v) is (v) (v)
the of ((F2 . w1),v) is finite Element of bool (v)
w1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
F2 . w1 is set
((F2 . w1),v) is (v) (v)
the of H₄(w1) is finite Element of bool (v)
w1 - 1 is real integer ext-real V257() Element of REAL
h is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
h + chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(h + chf) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
w1 + chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
LS . ((h + chf) + 1) is set
((LS . ((h + chf) + 1)),v) is (v) (v)
the of H₂((h + chf) + 1) is finite Element of bool (v)
m3 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Shift ((Shift (w,chf)),m3) is Element of Inf_seq AtomicFamily
Shift ((Shift (w,chf)),m3,AtomicFamily) is Element of Inf_seq AtomicFamily
CastSeq ((Shift (w,chf)),AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
(CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ m3 is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ m3) is Element of Inf_seq AtomicFamily
m3 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
m3 + chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
h + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
F2 . (m3 + 1) is set
((F2 . (m3 + 1)),v) is (v) (v)
the of H₄(m3 + 1) is finite Element of bool (v)
(m3 + 1) + chf is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LS . ((m3 + 1) + chf) is set
((LS . ((m3 + 1) + chf)),v) is (v) (v)
the of H₂((m3 + 1) + chf) is finite Element of bool (v)
(m3 + chf) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LS . ((m3 + chf) + 1) is set
((LS . ((m3 + chf) + 1)),v) is (v) (v)
the of H₂((m3 + chf) + 1) is finite Element of bool (v)
Shift (w,(m3 + chf)) is Element of Inf_seq AtomicFamily
Shift (w,(m3 + chf),AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ (m3 + chf) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ (m3 + chf)) is Element of Inf_seq AtomicFamily
len (the_right_argument_of run) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
Shift (w,(h + chf)) is Element of Inf_seq AtomicFamily
Shift (w,(h + chf),AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ (h + chf) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ (h + chf)) is Element of Inf_seq AtomicFamily
Shift ((Shift (w,chf)),h) is Element of Inf_seq AtomicFamily
Shift ((Shift (w,chf)),h,AtomicFamily) is Element of Inf_seq AtomicFamily
CastSeq ((Shift (w,chf)),AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
(CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ h is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ h) is Element of Inf_seq AtomicFamily
(the_left_argument_of run) 'U' (the_right_argument_of run) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
4 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
<*4*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*4*> ^ (the_left_argument_of run) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(<*4*> ^ (the_left_argument_of run)) ^ (the_right_argument_of run) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
the_right_argument_of run is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_left_argument_of run is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
'not' (the_left_argument_of run) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*0*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*0*> ^ (the_left_argument_of run) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
len (the_left_argument_of run) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
len (the_right_argument_of run) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
F is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Shift ((Shift (w,chf)),F) is Element of Inf_seq AtomicFamily
Shift ((Shift (w,chf)),F,AtomicFamily) is Element of Inf_seq AtomicFamily
CastSeq ((Shift (w,chf)),AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
(CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ F is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ F) is Element of Inf_seq AtomicFamily
(chf + 1) + F is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LS . ((chf + 1) + F) is set
((LS . ((chf + 1) + F)),v) is (v) (v)
the of H₂((chf + 1) + F) is finite Element of bool (v)
F + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
Shift ((Shift (w,chf)),(F + 1)) is Element of Inf_seq AtomicFamily
Shift ((Shift (w,chf)),(F + 1),AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ (F + 1) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ (F + 1)) is Element of Inf_seq AtomicFamily
(chf + 1) + (F + 1) is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LS . ((chf + 1) + (F + 1)) is set
((LS . ((chf + 1) + (F + 1))),v) is (v) (v)
the of H₂((chf + 1) + (F + 1)) is finite Element of bool (v)
chf + F is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(chf + F) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LS . ((chf + F) + 1) is set
((LS . ((chf + F) + 1)),v) is (v) (v)
LS . (chf + F) is set
((LS . (chf + F)),v) is (v) (v)
m is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Shift ((Shift (w,chf)),m) is Element of Inf_seq AtomicFamily
Shift ((Shift (w,chf)),m,AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ m is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ m) is Element of Inf_seq AtomicFamily
((chf + F) + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LS . (((chf + F) + 1) + 1) is set
((LS . (((chf + F) + 1) + 1)),v) is (v) (v)
m2 is (v) (v) (v)
the of m2 is finite Element of bool (v)
Shift (w,(chf + F)) is Element of Inf_seq AtomicFamily
Shift (w,(chf + F),AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ (chf + F) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ (chf + F)) is Element of Inf_seq AtomicFamily
m is (v) (v) (v)
the of m2 is finite Element of bool (v)
h is (v) (v) (v)
the of h is finite Element of bool (v)
m3 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Shift ((Shift (w,chf)),m3) is Element of Inf_seq AtomicFamily
Shift ((Shift (w,chf)),m3,AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ m3 is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ m3) is Element of Inf_seq AtomicFamily
chf + (F + 1) is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
Shift (w,(chf + (F + 1))) is Element of Inf_seq AtomicFamily
Shift (w,(chf + (F + 1)),AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ (chf + (F + 1)) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ (chf + (F + 1))) is Element of Inf_seq AtomicFamily
m3 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Shift ((Shift (w,chf)),m3) is Element of Inf_seq AtomicFamily
Shift ((Shift (w,chf)),m3,AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ m3 is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ m3) is Element of Inf_seq AtomicFamily
F2 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Shift ((Shift (w,chf)),F2) is Element of Inf_seq AtomicFamily
Shift ((Shift (w,chf)),F2,AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ F2 is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ F2) is Element of Inf_seq AtomicFamily
(the_left_argument_of run) 'R' (the_right_argument_of run) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
5 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
<*5*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*5*> ^ (the_left_argument_of run) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(<*5*> ^ (the_left_argument_of run)) ^ (the_right_argument_of run) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
F is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Shift ((Shift (w,chf)),F) is Element of Inf_seq AtomicFamily
Shift ((Shift (w,chf)),F,AtomicFamily) is Element of Inf_seq AtomicFamily
CastSeq ((Shift (w,chf)),AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
(CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ F is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ F) is Element of Inf_seq AtomicFamily
Shift ((Shift (w,chf)),0) is Element of Inf_seq AtomicFamily
Shift ((Shift (w,chf)),0,AtomicFamily) is Element of Inf_seq AtomicFamily
CastSeq ((Shift (w,chf)),AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
(CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ 0 is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ 0) is Element of Inf_seq AtomicFamily
(chf + 1) + 0 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LS . ((chf + 1) + 0) is set
((LS . ((chf + 1) + 0)),v) is (v) (v)
the of H₂((chf + 1) + 0) is finite Element of bool (v)
LS . chf is set
((LS . chf),v) is (v) (v)
L is (v) (v) (v)
F1 is (v) (v) (v)
the of F1 is finite Element of bool (v)
F is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Shift ((Shift (w,chf)),F) is Element of Inf_seq AtomicFamily
Shift ((Shift (w,chf)),F,AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ F is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq ((Shift (w,chf)),AtomicFamily)) ^\ F) is Element of Inf_seq AtomicFamily
(chf + 1) + F is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LS . ((chf + 1) + F) is set
((LS . ((chf + 1) + F)),v) is (v) (v)
the of ((LS . ((chf + 1) + F)),v) is finite Element of bool (v)
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
chf + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LS . (chf + 1) is set
((LS . (chf + 1)),v) is (v) (v)
the of H₂(chf + 1) is finite Element of bool (v)
Shift (w,chf) is Element of Inf_seq AtomicFamily
Shift (w,chf,AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ chf is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ chf) is Element of Inf_seq AtomicFamily
run is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
len run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
len run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
chf + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LS . (chf + 1) is set
((LS . (chf + 1)),v) is (v) (v)
the of ((LS . (chf + 1)),v) is finite Element of bool (v)
Shift (w,chf) is Element of Inf_seq AtomicFamily
Shift (w,chf,AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ chf is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ chf) is Element of Inf_seq AtomicFamily
chf is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
len chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
LS . (FS + 1) is set
((LS . (FS + 1)),v) is (v) (v)
the of ((LS . (FS + 1)),v) is finite Element of bool (v)
Shift (w,FS) is Element of Inf_seq AtomicFamily
Shift (w,FS,AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ FS is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ FS) is Element of Inf_seq AtomicFamily
len v is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
run is (v) (v) (v)
the of run is finite Element of bool (v)
chf is (v) (v) (v)
the of chf is finite Element of bool (v)
((v),v) is (v) (v)
Shift (w,0) is Element of Inf_seq AtomicFamily
Shift (w,0,AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ 0 is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ 0) is Element of Inf_seq AtomicFamily
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() () FinSequence of NAT
(v) is non empty finite Element of bool LTL_WFF
BOOL (v) is non empty set
union (BOOL (v)) is non empty set
LT is (v) (v)
w is Element of Inf_seq AtomicFamily
(v,LT) is Element of bool LTL_WFF
the of LT is finite Element of bool (v)
bool (v) is non empty finite V42() set
the of LT is finite Element of bool (v)
the of LT \/ the of LT is finite Element of bool (v)
the of LT is finite Element of bool (v)
(v, the of LT) is Element of bool LTL_WFF
'X' (v, the of LT) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of LT) & b₁ = 'X' b₂ ) } is set
( the of LT \/ the of LT) \/ ('X' (v, the of LT)) is set
(v) is non empty finite set
LS is Relation-like BOOL (v) -defined union (BOOL (v)) -valued Function-like non empty V21( BOOL (v)) V25( BOOL (v), union (BOOL (v))) Choice_Function of BOOL (v)
(w,v,LS) is Relation-like (v) -defined (v) -valued Function-like non empty V21((v)) V25((v),(v)) finite Element of bool [:(v),(v):]
[:(v),(v):] is Relation-like non empty finite set
bool [:(v),(v):] is non empty finite V42() set
(LT,v) is (v) (v)
(v,(LT,v)) is Element of bool LTL_WFF
the of (LT,v) is finite Element of bool (v)
the of (LT,v) is finite Element of bool (v)
the of (LT,v) \/ the of (LT,v) is finite Element of bool (v)
the of (LT,v) is finite Element of bool (v)
(v, the of (LT,v)) is Element of bool LTL_WFF
'X' (v, the of (LT,v)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (LT,v)) & b₁ = 'X' b₂ ) } is set
( the of (LT,v) \/ the of (LT,v)) \/ ('X' (v, the of (LT,v))) is set
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(w,v,LS) |** FS is Relation-like (v) -defined (v) -valued Function-like non empty V21((v)) V25((v),(v)) finite Element of bool [:(v),(v):]
((w,v,LS) |** FS) . LT is set
((((w,v,LS) |** FS) . LT),v) is (v) (v)
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(w,v,LS) |** chf is Relation-like (v) -defined (v) -valued Function-like non empty V21((v)) V25((v),(v)) finite Element of bool [:(v),(v):]
((w,v,LS) |** chf) . LT is set
((((w,v,LS) |** chf) . LT),v) is (v) (v)
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() () FinSequence of NAT
(v) is non empty finite Element of bool LTL_WFF
BOOL (v) is non empty set
union (BOOL (v)) is non empty set
w is Element of Inf_seq AtomicFamily
LT is (v) (v)
(v,LT) is (v) (v)
(v) is finite Element of bool (v)
bool (v) is non empty finite V42() set
the of LT is finite Element of bool (v)
(v,(v), the of LT,(v)) is (v) (v)
(v,(v,LT)) is Element of bool LTL_WFF
the of (v,LT) is finite Element of bool (v)
the of (v,LT) is finite Element of bool (v)
the of (v,LT) \/ the of (v,LT) is finite Element of bool (v)
the of (v,LT) is finite Element of bool (v)
(v, the of (v,LT)) is Element of bool LTL_WFF
'X' (v, the of (v,LT)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,LT)) & b₁ = 'X' b₂ ) } is set
( the of (v,LT) \/ the of (v,LT)) \/ ('X' (v, the of (v,LT))) is set
(v) is non empty finite set
LS is Relation-like BOOL (v) -defined union (BOOL (v)) -valued Function-like non empty V21( BOOL (v)) V25( BOOL (v), union (BOOL (v))) Choice_Function of BOOL (v)
(w,v,LS) is Relation-like (v) -defined (v) -valued Function-like non empty V21((v)) V25((v),(v)) finite Element of bool [:(v),(v):]
[:(v),(v):] is Relation-like non empty finite set
bool [:(v),(v):] is non empty finite V42() set
(w,v,LS,(v,LT)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(w,v,LS) |** (w,v,LS,(v,LT)) is Relation-like (v) -defined (v) -valued Function-like non empty V21((v)) V25((v),(v)) finite Element of bool [:(v),(v):]
((w,v,LS) |** (w,v,LS,(v,LT))) . (v,LT) is set
((((w,v,LS) |** (w,v,LS,(v,LT))) . (v,LT)),v) is (v) (v)
(v) is (v) (v) (v)
(v,(v),(v),(v)) is (v) (v)
w is Element of Inf_seq AtomicFamily
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() () FinSequence of NAT
(v) is non empty finite Element of bool LTL_WFF
BOOL (v) is non empty set
union (BOOL (v)) is non empty set
LS is Relation-like BOOL (v) -defined union (BOOL (v)) -valued Function-like non empty V21( BOOL (v)) V25( BOOL (v), union (BOOL (v))) Choice_Function of BOOL (v)
LT is (v) (v) (v)
(v,LT) is (v) (v)
(v) is finite Element of bool (v)
bool (v) is non empty finite V42() set
the of LT is finite Element of bool (v)
(v,(v), the of LT,(v)) is (v) (v)
(v,(v,LT)) is Element of bool LTL_WFF
the of (v,LT) is finite Element of bool (v)
the of (v,LT) is finite Element of bool (v)
the of (v,LT) \/ the of (v,LT) is finite Element of bool (v)
the of (v,LT) is finite Element of bool (v)
(v, the of (v,LT)) is Element of bool LTL_WFF
'X' (v, the of (v,LT)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,LT)) & b₁ = 'X' b₂ ) } is set
( the of (v,LT) \/ the of (v,LT)) \/ ('X' (v, the of (v,LT))) is set
(w,v,LS,LT) is (v) (v) (v)
(v,(w,v,LS,LT)) is Element of bool LTL_WFF
the of (w,v,LS,LT) is finite Element of bool (v)
the of (w,v,LS,LT) is finite Element of bool (v)
the of (w,v,LS,LT) \/ the of (w,v,LS,LT) is finite Element of bool (v)
the of (w,v,LS,LT) is finite Element of bool (v)
(v, the of (w,v,LS,LT)) is Element of bool LTL_WFF
'X' (v, the of (w,v,LS,LT)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (w,v,LS,LT)) & b₁ = 'X' b₂ ) } is set
( the of (w,v,LS,LT) \/ the of (w,v,LS,LT)) \/ ('X' (v, the of (w,v,LS,LT))) is set
(v) is non empty finite set
(w,v,LS,(v,LT)) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(w,v,LS) is Relation-like (v) -defined (v) -valued Function-like non empty V21((v)) V25((v),(v)) finite Element of bool [:(v),(v):]
[:(v),(v):] is Relation-like non empty finite set
bool [:(v),(v):] is non empty finite V42() set
(w,v,LS) |** (w,v,LS,(v,LT)) is Relation-like (v) -defined (v) -valued Function-like non empty V21((v)) V25((v),(v)) finite Element of bool [:(v),(v):]
((w,v,LS) |** (w,v,LS,(v,LT))) . (v,LT) is set
((((w,v,LS) |** (w,v,LS,(v,LT))) . (v,LT)),v) is (v) (v)
(w,v,LS,(v,LT)) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len x is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
dom x is finite Element of bool NAT
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len x is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
dom x is finite Element of bool NAT
Seg ((w,v,LS,(v,LT)) + 1) is non empty finite (w,v,LS,(v,LT)) + 1 -element Element of bool NAT
F is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
x . F is set
F - 1 is real integer ext-real V257() Element of REAL
CastNat (F - 1) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(w,v,LS) |** (CastNat (F - 1)) is Relation-like (v) -defined (v) -valued Function-like non empty V21((v)) V25((v),(v)) finite Element of bool [:(v),(v):]
((w,v,LS) |** (CastNat (F - 1))) . (v,LT) is set
((((w,v,LS) |** (CastNat (F - 1))) . (v,LT)),v) is (v) (v)
CastNat F is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(CastNat F) - 1 is real integer ext-real V257() Element of REAL
CastNat ((CastNat F) - 1) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(w,v,LS) |** (CastNat ((CastNat F) - 1)) is Relation-like (v) -defined (v) -valued Function-like non empty V21((v)) V25((v),(v)) finite Element of bool [:(v),(v):]
((w,v,LS) |** (CastNat ((CastNat F) - 1))) . (v,LT) is set
((((w,v,LS) |** (CastNat ((CastNat F) - 1))) . (v,LT)),v) is (v) (v)
F is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
x . F is set
F + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
x . (F + 1) is set
F - 1 is real integer ext-real V257() Element of REAL
F1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
F1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
(w,v,LS) |** (F1 + 1) is Relation-like (v) -defined (v) -valued Function-like non empty V21((v)) V25((v),(v)) finite Element of bool [:(v),(v):]
((w,v,LS) |** (F1 + 1)) . (v,LT) is set
((((w,v,LS) |** (F1 + 1)) . (v,LT)),v) is (v) (v)
(F + 1) - 1 is real integer ext-real V257() Element of REAL
CastNat ((F + 1) - 1) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(w,v,LS) |** (CastNat ((F + 1) - 1)) is Relation-like (v) -defined (v) -valued Function-like non empty V21((v)) V25((v),(v)) finite Element of bool [:(v),(v):]
((w,v,LS) |** (CastNat ((F + 1) - 1))) . (v,LT) is set
((((w,v,LS) |** (CastNat ((F + 1) - 1))) . (v,LT)),v) is (v) (v)
(w,v,LS) |** F1 is Relation-like (v) -defined (v) -valued Function-like non empty V21((v)) V25((v),(v)) finite Element of bool [:(v),(v):]
((w,v,LS) |** F1) . (v,LT) is set
((((w,v,LS) |** F1) . (v,LT)),v) is (v) (v)
((w,v,LS,(v,LT)) + 1) - 1 is real integer ext-real V257() Element of REAL
CastNat F1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(w,v,LS) |** (CastNat F1) is Relation-like (v) -defined (v) -valued Function-like non empty V21((v)) V25((v),(v)) finite Element of bool [:(v),(v):]
((w,v,LS) |** (CastNat F1)) . (v,LT) is set
((((w,v,LS) |** (CastNat F1)) . (v,LT)),v) is (v) (v)
x . (len x) is set
((w,v,LS,(v,LT)) + 1) - 1 is real integer ext-real V257() Element of REAL
CastNat (((w,v,LS,(v,LT)) + 1) - 1) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(w,v,LS) |** (CastNat (((w,v,LS,(v,LT)) + 1) - 1)) is Relation-like (v) -defined (v) -valued Function-like non empty V21((v)) V25((v),(v)) finite Element of bool [:(v),(v):]
((w,v,LS) |** (CastNat (((w,v,LS,(v,LT)) + 1) - 1))) . (v,LT) is set
((((w,v,LS) |** (CastNat (((w,v,LS,(v,LT)) + 1) - 1))) . (v,LT)),v) is (v) (v)
x . 1 is set
1 - 1 is real integer ext-real V257() Element of REAL
CastNat (1 - 1) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(w,v,LS) |** (CastNat (1 - 1)) is Relation-like (v) -defined (v) -valued Function-like non empty V21((v)) V25((v),(v)) finite Element of bool [:(v),(v):]
((w,v,LS) |** (CastNat (1 - 1))) . (v,LT) is set
((((w,v,LS) |** (CastNat (1 - 1))) . (v,LT)),v) is (v) (v)
(w,v,LS) |** 0 is Relation-like (v) -defined (v) -valued Function-like non empty V21((v)) V25((v),(v)) finite Element of bool [:(v),(v):]
((w,v,LS) |** 0) . (v,LT) is set
((((w,v,LS) |** 0) . (v,LT)),v) is (v) (v)
id (v) is Relation-like (v) -defined (v) -valued Function-like one-to-one non empty V21((v)) V25((v),(v)) finite being_quasi-order being_partial-order Element of bool [:(v),(v):]
(id (v)) . (v,LT) is set
(((id (v)) . (v,LT)),v) is (v) (v)
((v,LT),v) is (v) (v)
(v) is (v) (v) (v)
(v,(v),(v),(v)) is (v) (v)
the of (v) is finite Element of bool (v)
<*(v,LT)*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
dom <*(v,LT)*> is non empty trivial finite 1 -element Element of bool NAT
x is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
<*(v,LT)*> . x is set
len <*(v,LT)*> is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
x is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
<*(v,LT)*> . x is set
x + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
<*(v,LT)*> . (x + 1) is set
<*(v,LT)*> . 1 is set
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() () FinSequence of NAT
(v) is non empty finite Element of bool LTL_WFF
BOOL (v) is non empty set
union (BOOL (v)) is non empty set
(v) is non empty finite set
(v) is non empty finite set
{ b₁ where b₁ is Element of (v) : b₁ is (v) (v) (v) } is set
[:NAT,(v):] is Relation-like non empty non trivial non finite set
bool [:NAT,(v):] is non empty non trivial non finite set
(v) is (v) (v) (v)
(v) is finite Element of bool (v)
bool (v) is non empty finite V42() set
(v) is finite Element of bool (v)
{v} is functional non empty trivial finite V42() 1 -element set
(v,(v),(v),(v)) is (v) (v)
w is Element of Inf_seq AtomicFamily
LS is Relation-like BOOL (v) -defined union (BOOL (v)) -valued Function-like non empty V21( BOOL (v)) V25( BOOL (v), union (BOOL (v))) Choice_Function of BOOL (v)
IS is set
FS is Relation-like Function-like set
FS . 0 is set
dom FS is set
IS is Relation-like Function-like set
dom IS is set
IS . 0 is set
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
IS . (FS + 1) is set
IS . FS is set
CastNat FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Shift (w,(CastNat FS)) is Element of Inf_seq AtomicFamily
Shift (w,(CastNat FS),AtomicFamily) is Element of Inf_seq AtomicFamily
CastSeq (w,AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
[:NAT,AtomicFamily:] is Relation-like non empty non trivial non finite set
bool [:NAT,AtomicFamily:] is non empty non trivial non finite set
(CastSeq (w,AtomicFamily)) ^\ (CastNat FS) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ (CastNat FS)) is Element of Inf_seq AtomicFamily
((IS . FS),v) is (v) (v)
((Shift (w,(CastNat FS))),v,LS,((IS . FS),v)) is (v) (v) (v)
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
chf + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
IS . (chf + 1) is set
IS . chf is set
CastNat chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Shift (w,(CastNat chf)) is Element of Inf_seq AtomicFamily
Shift (w,(CastNat chf),AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ (CastNat chf) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ (CastNat chf)) is Element of Inf_seq AtomicFamily
((IS . chf),v) is (v) (v)
((Shift (w,(CastNat chf))),v,LS,((IS . chf),v)) is (v) (v) (v)
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
IS . (FS + 1) is set
Shift (w,FS) is Element of Inf_seq AtomicFamily
Shift (w,FS,AtomicFamily) is Element of Inf_seq AtomicFamily
CastSeq (w,AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
[:NAT,AtomicFamily:] is Relation-like non empty non trivial non finite set
bool [:NAT,AtomicFamily:] is non empty non trivial non finite set
(CastSeq (w,AtomicFamily)) ^\ FS is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ FS) is Element of Inf_seq AtomicFamily
IS . FS is set
((IS . FS),v) is (v) (v)
((Shift (w,FS)),v,LS,((IS . FS),v)) is (v) (v) (v)
CastNat FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Shift (w,(CastNat FS)) is Element of Inf_seq AtomicFamily
Shift (w,(CastNat FS),AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ (CastNat FS) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ (CastNat FS)) is Element of Inf_seq AtomicFamily
((Shift (w,(CastNat FS))),v,LS,((IS . FS),v)) is (v) (v) (v)
FS is set
IS . FS is set
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
0 + chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
IS . chf is set
FSet is Element of (v)
chf - 1 is real integer ext-real V257() Element of REAL
IS . chf is set
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FSet + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
IS . (FSet + 1) is set
IS . FSet is set
CastNat FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Shift (w,(CastNat FSet)) is Element of Inf_seq AtomicFamily
Shift (w,(CastNat FSet),AtomicFamily) is Element of Inf_seq AtomicFamily
CastSeq (w,AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
[:NAT,AtomicFamily:] is Relation-like non empty non trivial non finite set
bool [:NAT,AtomicFamily:] is non empty non trivial non finite set
(CastSeq (w,AtomicFamily)) ^\ (CastNat FSet) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ (CastNat FSet)) is Element of Inf_seq AtomicFamily
((IS . FSet),v) is (v) (v)
((Shift (w,(CastNat FSet))),v,LS,((IS . FSet),v)) is (v) (v) (v)
x is Element of (v)
FS is Relation-like NAT -defined (v) -valued Function-like non empty V21( NAT ) V25( NAT ,(v)) Element of bool [:NAT,(v):]
FS . 0 is Element of (v)
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
chf + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
FS . (chf + 1) is Element of (v)
Shift (w,chf) is Element of Inf_seq AtomicFamily
Shift (w,chf,AtomicFamily) is Element of Inf_seq AtomicFamily
CastSeq (w,AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
[:NAT,AtomicFamily:] is Relation-like non empty non trivial non finite set
bool [:NAT,AtomicFamily:] is non empty non trivial non finite set
(CastSeq (w,AtomicFamily)) ^\ chf is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ chf) is Element of Inf_seq AtomicFamily
FS . chf is set
((FS . chf),v) is (v) (v)
((Shift (w,chf)),v,LS,((FS . chf),v)) is (v) (v) (v)
IS is Relation-like NAT -defined (v) -valued Function-like non empty V21( NAT ) V25( NAT ,(v)) Element of bool [:NAT,(v):]
IS . 0 is Element of (v)
FS is Relation-like NAT -defined (v) -valued Function-like non empty V21( NAT ) V25( NAT ,(v)) Element of bool [:NAT,(v):]
FS . 0 is Element of (v)
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
IS . chf is set
FS . chf is set
chf + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
IS . (chf + 1) is set
FS . (chf + 1) is set
IS . (chf + 1) is Element of (v)
FS . chf is Element of (v)
CastNat chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Shift (w,(CastNat chf)) is Element of Inf_seq AtomicFamily
Shift (w,(CastNat chf),AtomicFamily) is Element of Inf_seq AtomicFamily
CastSeq (w,AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
[:NAT,AtomicFamily:] is Relation-like non empty non trivial non finite set
bool [:NAT,AtomicFamily:] is non empty non trivial non finite set
(CastSeq (w,AtomicFamily)) ^\ (CastNat chf) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ (CastNat chf)) is Element of Inf_seq AtomicFamily
((FS . chf),v) is (v) (v)
((Shift (w,(CastNat chf))),v,LS,((FS . chf),v)) is (v) (v) (v)
FS . (chf + 1) is Element of (v)
IS . 0 is set
FS . 0 is set
dom IS is non empty Element of bool NAT
chf is set
IS . chf is set
FS . chf is set
dom FS is non empty Element of bool NAT
IS is Relation-like NAT -defined (v) -valued Function-like non empty V21( NAT ) V25( NAT ,(v)) Element of bool [:NAT,(v):]
IS . 0 is Element of (v)
FS is Relation-like NAT -defined (v) -valued Function-like non empty V21( NAT ) V25( NAT ,(v)) Element of bool [:NAT,(v):]
FS . 0 is Element of (v)
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
chf + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
FS . (chf + 1) is Element of (v)
FS . chf is set
CastNat chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Shift (w,(CastNat chf)) is Element of Inf_seq AtomicFamily
Shift (w,(CastNat chf),AtomicFamily) is Element of Inf_seq AtomicFamily
CastSeq (w,AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
[:NAT,AtomicFamily:] is Relation-like non empty non trivial non finite set
bool [:NAT,AtomicFamily:] is non empty non trivial non finite set
(CastSeq (w,AtomicFamily)) ^\ (CastNat chf) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ (CastNat chf)) is Element of Inf_seq AtomicFamily
((FS . chf),v) is (v) (v)
((Shift (w,(CastNat chf))),v,LS,((FS . chf),v)) is (v) (v) (v)
Shift (w,chf) is Element of Inf_seq AtomicFamily
Shift (w,chf,AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ chf is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ chf) is Element of Inf_seq AtomicFamily
((Shift (w,chf)),v,LS,((FS . chf),v)) is (v) (v) (v)
chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
chf + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
IS . (chf + 1) is Element of (v)
IS . chf is set
CastNat chf is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Shift (w,(CastNat chf)) is Element of Inf_seq AtomicFamily
Shift (w,(CastNat chf),AtomicFamily) is Element of Inf_seq AtomicFamily
CastSeq (w,AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
[:NAT,AtomicFamily:] is Relation-like non empty non trivial non finite set
bool [:NAT,AtomicFamily:] is non empty non trivial non finite set
(CastSeq (w,AtomicFamily)) ^\ (CastNat chf) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ (CastNat chf)) is Element of Inf_seq AtomicFamily
((IS . chf),v) is (v) (v)
((Shift (w,(CastNat chf))),v,LS,((IS . chf),v)) is (v) (v) (v)
Shift (w,chf) is Element of Inf_seq AtomicFamily
Shift (w,chf,AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ chf is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ chf) is Element of Inf_seq AtomicFamily
((Shift (w,chf)),v,LS,((IS . chf),v)) is (v) (v) (v)
IS is Relation-like NAT -defined (v) -valued Function-like non empty V21( NAT ) V25( NAT ,(v)) Element of bool [:NAT,(v):]
IS . 0 is Element of (v)
FS is Relation-like NAT -defined (v) -valued Function-like non empty V21( NAT ) V25( NAT ,(v)) Element of bool [:NAT,(v):]
FS . 0 is Element of (v)
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() () FinSequence of NAT
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
(w,(w)) is Element of bool LTL_WFF
'X' (w,(w)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (w,(w)) & b₁ = 'X' b₂ ) } is set
v is set
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LT is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
'X' LT is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*3*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*3*> ^ LT is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
w is Element of Inf_seq AtomicFamily
Shift (w,1) is Element of Inf_seq AtomicFamily
Shift (w,1,AtomicFamily) is Element of Inf_seq AtomicFamily
CastSeq (w,AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
[:NAT,AtomicFamily:] is Relation-like non empty non trivial non finite set
bool [:NAT,AtomicFamily:] is non empty non trivial non finite set
(CastSeq (w,AtomicFamily)) ^\ 1 is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ 1) is Element of Inf_seq AtomicFamily
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() () FinSequence of NAT
LS is (v) (v)
(v,LS) is Element of bool LTL_WFF
(v) is non empty finite Element of bool LTL_WFF
the of LS is finite Element of bool (v)
bool (v) is non empty finite V42() set
the of LS is finite Element of bool (v)
the of LS \/ the of LS is finite Element of bool (v)
the of LS is finite Element of bool (v)
(v, the of LS) is Element of bool LTL_WFF
'X' (v, the of LS) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of LS) & b₁ = 'X' b₂ ) } is set
( the of LS \/ the of LS) \/ ('X' (v, the of LS)) is set
(v,LS) is (v) (v)
(v) is finite Element of bool (v)
(v,(v), the of LS,(v)) is (v) (v)
(v,(v,LS)) is Element of bool LTL_WFF
the of (v,LS) is finite Element of bool (v)
the of (v,LS) is finite Element of bool (v)
the of (v,LS) \/ the of (v,LS) is finite Element of bool (v)
the of (v,LS) is finite Element of bool (v)
(v, the of (v,LS)) is Element of bool LTL_WFF
'X' (v, the of (v,LS)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,LS)) & b₁ = 'X' b₂ ) } is set
( the of (v,LS) \/ the of (v,LS)) \/ ('X' (v, the of (v,LS))) is set
IS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Element of Inf_seq AtomicFamily
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() () FinSequence of NAT
'X' v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*3*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*3*> ^ v is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(v) is (v) (v) (v)
(v) is finite Element of bool (v)
(v) is non empty finite Element of bool LTL_WFF
bool (v) is non empty finite V42() set
(v) is finite Element of bool (v)
{v} is functional non empty trivial finite V42() 1 -element set
(v,(v),(v),(v)) is (v) (v)
(v,(v)) is Element of bool LTL_WFF
the of (v) is finite Element of bool (v)
the of (v) is finite Element of bool (v)
the of (v) \/ the of (v) is finite Element of bool (v)
the of (v) is finite Element of bool (v)
(v, the of (v)) is Element of bool LTL_WFF
'X' (v, the of (v)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v)) & b₁ = 'X' b₂ ) } is set
( the of (v) \/ the of (v)) \/ ('X' (v, the of (v))) is set
(v,(v)) is Element of bool LTL_WFF
'X' (v,(v)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v,(v)) & b₁ = 'X' b₂ ) } is set
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
LT is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
IS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
'X' IS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*3*> ^ IS is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
w is Element of Inf_seq AtomicFamily
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() () FinSequence of NAT
(v) is (v) (v) (v)
(v) is finite Element of bool (v)
(v) is non empty finite Element of bool LTL_WFF
bool (v) is non empty finite V42() set
(v) is finite Element of bool (v)
{v} is functional non empty trivial finite V42() 1 -element set
(v,(v),(v),(v)) is (v) (v)
(v,(v)) is (v) (v)
the of (v) is finite Element of bool (v)
(v,(v), the of (v),(v)) is (v) (v)
(v,(v,(v))) is Element of bool LTL_WFF
the of (v,(v)) is finite Element of bool (v)
the of (v,(v)) is finite Element of bool (v)
the of (v,(v)) \/ the of (v,(v)) is finite Element of bool (v)
the of (v,(v)) is finite Element of bool (v)
(v, the of (v,(v))) is Element of bool LTL_WFF
'X' (v, the of (v,(v))) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,(v))) & b₁ = 'X' b₂ ) } is set
( the of (v,(v)) \/ the of (v,(v))) \/ ('X' (v, the of (v,(v)))) is set
IS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
w is Element of Inf_seq AtomicFamily
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() () FinSequence of NAT
(v) is non empty finite Element of bool LTL_WFF
BOOL (v) is non empty set
union (BOOL (v)) is non empty set
(v) is non empty finite set
(v) is non empty finite set
{ b₁ where b₁ is Element of (v) : b₁ is (v) (v) (v) } is set
LS is Relation-like BOOL (v) -defined union (BOOL (v)) -valued Function-like non empty V21( BOOL (v)) V25( BOOL (v), union (BOOL (v))) Choice_Function of BOOL (v)
(w,v,LS) is Relation-like NAT -defined (v) -valued Function-like non empty V21( NAT ) V25( NAT ,(v)) Element of bool [:NAT,(v):]
[:NAT,(v):] is Relation-like non empty non trivial non finite set
bool [:NAT,(v):] is non empty non trivial non finite set
(v) is (v) (v) (v)
(v) is finite Element of bool (v)
bool (v) is non empty finite V42() set
(v) is finite Element of bool (v)
{v} is functional non empty trivial finite V42() 1 -element set
(v,(v),(v),(v)) is (v) (v)
(v,(v)) is (v) (v)
the of (v) is finite Element of bool (v)
(v,(v), the of (v),(v)) is (v) (v)
(v,(v,(v))) is Element of bool LTL_WFF
the of (v,(v)) is finite Element of bool (v)
the of (v,(v)) is finite Element of bool (v)
the of (v,(v)) \/ the of (v,(v)) is finite Element of bool (v)
the of (v,(v)) is finite Element of bool (v)
(v, the of (v,(v))) is Element of bool LTL_WFF
'X' (v, the of (v,(v))) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,(v))) & b₁ = 'X' b₂ ) } is set
( the of (v,(v)) \/ the of (v,(v))) \/ ('X' (v, the of (v,(v)))) is set
(w,v,LS) . 0 is Element of (v)
(((w,v,LS) . 0),v) is (v) (v)
((v),v) is (v) (v)
IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(w,v,LS) . IS is set
(((w,v,LS) . IS),v) is (v) (v)
IS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
(w,v,LS) . (IS + 1) is set
(((w,v,LS) . (IS + 1)),v) is (v) (v)
Shift (w,IS) is Element of Inf_seq AtomicFamily
Shift (w,IS,AtomicFamily) is Element of Inf_seq AtomicFamily
CastSeq (w,AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
[:NAT,AtomicFamily:] is Relation-like non empty non trivial non finite set
bool [:NAT,AtomicFamily:] is non empty non trivial non finite set
(CastSeq (w,AtomicFamily)) ^\ IS is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ IS) is Element of Inf_seq AtomicFamily
(v,H₁(IS)) is (v) (v)
the of (((w,v,LS) . IS),v) is finite Element of bool (v)
(v,(v), the of (((w,v,LS) . IS),v),(v)) is (v) (v)
(v,(v,H₁(IS))) is Element of bool LTL_WFF
the of (v,H₁(IS)) is finite Element of bool (v)
the of (v,H₁(IS)) is finite Element of bool (v)
the of (v,H₁(IS)) \/ the of (v,H₁(IS)) is finite Element of bool (v)
the of (v,H₁(IS)) is finite Element of bool (v)
(v, the of (v,H₁(IS))) is Element of bool LTL_WFF
'X' (v, the of (v,H₁(IS))) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,H₁(IS))) & b₁ = 'X' b₂ ) } is set
( the of (v,H₁(IS)) \/ the of (v,H₁(IS))) \/ ('X' (v, the of (v,H₁(IS)))) is set
(IS + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
(w,v,LS) . ((IS + 1) + 1) is set
(((w,v,LS) . ((IS + 1) + 1)),v) is (v) (v)
Shift (w,(IS + 1)) is Element of Inf_seq AtomicFamily
Shift (w,(IS + 1),AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ (IS + 1) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ (IS + 1)) is Element of Inf_seq AtomicFamily
(v,H₁(IS + 1)) is (v) (v)
the of (((w,v,LS) . (IS + 1)),v) is finite Element of bool (v)
(v,(v), the of (((w,v,LS) . (IS + 1)),v),(v)) is (v) (v)
(v,(v,H₁(IS + 1))) is Element of bool LTL_WFF
the of (v,H₁(IS + 1)) is finite Element of bool (v)
the of (v,H₁(IS + 1)) is finite Element of bool (v)
the of (v,H₁(IS + 1)) \/ the of (v,H₁(IS + 1)) is finite Element of bool (v)
the of (v,H₁(IS + 1)) is finite Element of bool (v)
(v, the of (v,H₁(IS + 1))) is Element of bool LTL_WFF
'X' (v, the of (v,H₁(IS + 1))) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,H₁(IS + 1))) & b₁ = 'X' b₂ ) } is set
( the of (v,H₁(IS + 1)) \/ the of (v,H₁(IS + 1))) \/ ('X' (v, the of (v,H₁(IS + 1)))) is set
IS - 1 is real integer ext-real V257() Element of REAL
run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
Shift (w,run) is Element of Inf_seq AtomicFamily
Shift (w,run,AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ run is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ run) is Element of Inf_seq AtomicFamily
(w,v,LS) . run is set
(((w,v,LS) . run),v) is (v) (v)
((Shift (w,run)),v,LS,(((w,v,LS) . run),v)) is (v) (v) (v)
(((Shift (w,run)),v,LS,(((w,v,LS) . run),v)),v) is (v) (v)
(IS + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
(w,v,LS) . ((IS + 1) + 1) is set
(((w,v,LS) . ((IS + 1) + 1)),v) is (v) (v)
((Shift (w,IS)),v,LS,(((w,v,LS) . IS),v)) is (v) (v) (v)
(((Shift (w,IS)),v,LS,(((w,v,LS) . IS),v)),v) is (v) (v)
chf is (v) (v) (v)
((Shift (w,IS)),v,LS,chf) is (v) (v) (v)
(w,v,LS) . (IS + 1) is Element of (v)
(((w,v,LS) . (IS + 1)),v) is (v) (v)
((Shift (w,(IS + 1))),v,LS,(((w,v,LS) . (IS + 1)),v)) is (v) (v) (v)
(((Shift (w,(IS + 1))),v,LS,(((w,v,LS) . (IS + 1)),v)),v) is (v) (v)
F2 is (v) (v) (v)
((Shift (w,(IS + 1))),v,LS,F2) is (v) (v) (v)
Shift ((Shift (w,IS)),1) is Element of Inf_seq AtomicFamily
Shift ((Shift (w,IS)),1,AtomicFamily) is Element of Inf_seq AtomicFamily
CastSeq ((Shift (w,IS)),AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
(CastSeq ((Shift (w,IS)),AtomicFamily)) ^\ 1 is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq ((Shift (w,IS)),AtomicFamily)) ^\ 1) is Element of Inf_seq AtomicFamily
(v,((Shift (w,IS)),v,LS,chf)) is Element of bool LTL_WFF
the of ((Shift (w,IS)),v,LS,chf) is finite Element of bool (v)
the of ((Shift (w,IS)),v,LS,chf) is finite Element of bool (v)
the of ((Shift (w,IS)),v,LS,chf) \/ the of ((Shift (w,IS)),v,LS,chf) is finite Element of bool (v)
the of ((Shift (w,IS)),v,LS,chf) is finite Element of bool (v)
(v, the of ((Shift (w,IS)),v,LS,chf)) is Element of bool LTL_WFF
'X' (v, the of ((Shift (w,IS)),v,LS,chf)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of ((Shift (w,IS)),v,LS,chf)) & b₁ = 'X' b₂ ) } is set
( the of ((Shift (w,IS)),v,LS,chf) \/ the of ((Shift (w,IS)),v,LS,chf)) \/ ('X' (v, the of ((Shift (w,IS)),v,LS,chf))) is set
(v,F2) is (v) (v)
the of F2 is finite Element of bool (v)
(v,(v), the of F2,(v)) is (v) (v)
(v,(v,F2)) is Element of bool LTL_WFF
the of (v,F2) is finite Element of bool (v)
the of (v,F2) is finite Element of bool (v)
the of (v,F2) \/ the of (v,F2) is finite Element of bool (v)
the of (v,F2) is finite Element of bool (v)
(v, the of (v,F2)) is Element of bool LTL_WFF
'X' (v, the of (v,F2)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,F2)) & b₁ = 'X' b₂ ) } is set
( the of (v,F2) \/ the of (v,F2)) \/ ('X' (v, the of (v,F2))) is set
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
(w,v,LS) . (0 + 1) is set
(((w,v,LS) . (0 + 1)),v) is (v) (v)
Shift (w,0) is Element of Inf_seq AtomicFamily
Shift (w,0,AtomicFamily) is Element of Inf_seq AtomicFamily
CastSeq (w,AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
[:NAT,AtomicFamily:] is Relation-like non empty non trivial non finite set
bool [:NAT,AtomicFamily:] is non empty non trivial non finite set
(CastSeq (w,AtomicFamily)) ^\ 0 is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ 0) is Element of Inf_seq AtomicFamily
((Shift (w,0)),v,LS,(((w,v,LS) . 0),v)) is (v) (v) (v)
(((Shift (w,0)),v,LS,(((w,v,LS) . 0),v)),v) is (v) (v)
(w,v,LS,(v)) is (v) (v) (v)
((w,v,LS,(v)),v) is (v) (v)
(w,v,LS) . 0 is set
(((w,v,LS) . 0),v) is (v) (v)
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
(w,v,LS) . (0 + 1) is set
(((w,v,LS) . (0 + 1)),v) is (v) (v)
(v,H₁( 0 )) is (v) (v)
the of (((w,v,LS) . 0),v) is finite Element of bool (v)
(v,(v), the of (((w,v,LS) . 0),v),(v)) is (v) (v)
(v,(v,H₁( 0 ))) is Element of bool LTL_WFF
the of (v,H₁( 0 )) is finite Element of bool (v)
the of (v,H₁( 0 )) is finite Element of bool (v)
the of (v,H₁( 0 )) \/ the of (v,H₁( 0 )) is finite Element of bool (v)
the of (v,H₁( 0 )) is finite Element of bool (v)
(v, the of (v,H₁( 0 ))) is Element of bool LTL_WFF
'X' (v, the of (v,H₁( 0 ))) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,H₁( 0 ))) & b₁ = 'X' b₂ ) } is set
( the of (v,H₁( 0 )) \/ the of (v,H₁( 0 ))) \/ ('X' (v, the of (v,H₁( 0 )))) is set
IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(w,v,LS) . IS is set
(((w,v,LS) . IS),v) is (v) (v)
IS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
(w,v,LS) . (IS + 1) is Element of (v)
(((w,v,LS) . (IS + 1)),v) is (v) (v)
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Shift (w,FS) is Element of Inf_seq AtomicFamily
Shift (w,FS,AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ FS is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ FS) is Element of Inf_seq AtomicFamily
(w,v,LS) . FS is set
(((w,v,LS) . FS),v) is (v) (v)
(v,(((w,v,LS) . FS),v)) is (v) (v)
the of (((w,v,LS) . FS),v) is finite Element of bool (v)
(v,(v), the of (((w,v,LS) . FS),v),(v)) is (v) (v)
(v,(v,(((w,v,LS) . FS),v))) is Element of bool LTL_WFF
the of (v,(((w,v,LS) . FS),v)) is finite Element of bool (v)
the of (v,(((w,v,LS) . FS),v)) is finite Element of bool (v)
the of (v,(((w,v,LS) . FS),v)) \/ the of (v,(((w,v,LS) . FS),v)) is finite Element of bool (v)
the of (v,(((w,v,LS) . FS),v)) is finite Element of bool (v)
(v, the of (v,(((w,v,LS) . FS),v))) is Element of bool LTL_WFF
'X' (v, the of (v,(((w,v,LS) . FS),v))) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,(((w,v,LS) . FS),v))) & b₁ = 'X' b₂ ) } is set
( the of (v,(((w,v,LS) . FS),v)) \/ the of (v,(((w,v,LS) . FS),v))) \/ ('X' (v, the of (v,(((w,v,LS) . FS),v)))) is set
w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_right_argument_of w is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
v is Element of Inf_seq AtomicFamily
LS is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() () FinSequence of NAT
(LS) is non empty finite Element of bool LTL_WFF
BOOL (LS) is non empty set
union (BOOL (LS)) is non empty set
(LS) is non empty finite set
(LS) is non empty finite set
{ b₁ where b₁ is Element of (LS) : b₁ is (LS) (LS) (LS) } is set
LT is Relation-like BOOL (LS) -defined union (BOOL (LS)) -valued Function-like non empty V21( BOOL (LS)) V25( BOOL (LS), union (BOOL (LS))) Choice_Function of BOOL (LS)
(v,LS,LT) is Relation-like NAT -defined (LS) -valued Function-like non empty V21( NAT ) V25( NAT ,(LS)) Element of bool [:NAT,(LS):]
[:NAT,(LS):] is Relation-like non empty non trivial non finite set
bool [:NAT,(LS):] is non empty non trivial non finite set
FS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
(v,LS,LT) . (FS + 1) is Element of (LS)
(((v,LS,LT) . (FS + 1)),LS) is (LS) (LS)
the of (((v,LS,LT) . (FS + 1)),LS) is finite Element of bool (LS)
bool (LS) is non empty finite V42() set
Shift (v,FS) is Element of Inf_seq AtomicFamily
Shift (v,FS,AtomicFamily) is Element of Inf_seq AtomicFamily
CastSeq (v,AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
[:NAT,AtomicFamily:] is Relation-like non empty non trivial non finite set
bool [:NAT,AtomicFamily:] is non empty non trivial non finite set
(CastSeq (v,AtomicFamily)) ^\ FS is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (v,AtomicFamily)) ^\ FS) is Element of Inf_seq AtomicFamily
(v,LS,LT) . FS is set
(((v,LS,LT) . FS),LS) is (LS) (LS)
(LS,(((v,LS,LT) . FS),LS)) is (LS) (LS)
(LS) is finite Element of bool (LS)
the of (((v,LS,LT) . FS),LS) is finite Element of bool (LS)
(LS,(LS), the of (((v,LS,LT) . FS),LS),(LS)) is (LS) (LS)
((Shift (v,FS)),LS,LT) is Relation-like (LS) -defined (LS) -valued Function-like non empty V21((LS)) V25((LS),(LS)) finite Element of bool [:(LS),(LS):]
[:(LS),(LS):] is Relation-like non empty finite set
bool [:(LS),(LS):] is non empty finite V42() set
((Shift (v,FS)),LS,LT,(LS,(((v,LS,LT) . FS),LS))) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
((Shift (v,FS)),LS,LT) |** ((Shift (v,FS)),LS,LT,(LS,(((v,LS,LT) . FS),LS))) is Relation-like (LS) -defined (LS) -valued Function-like non empty V21((LS)) V25((LS),(LS)) finite Element of bool [:(LS),(LS):]
(((Shift (v,FS)),LS,LT) |** ((Shift (v,FS)),LS,LT,(LS,(((v,LS,LT) . FS),LS)))) . (LS,(((v,LS,LT) . FS),LS)) is set
(((((Shift (v,FS)),LS,LT) |** ((Shift (v,FS)),LS,LT,(LS,(((v,LS,LT) . FS),LS)))) . (LS,(((v,LS,LT) . FS),LS))),LS) is (LS) (LS)
(LS,(LS,(((v,LS,LT) . FS),LS))) is Element of bool LTL_WFF
the of (LS,(((v,LS,LT) . FS),LS)) is finite Element of bool (LS)
the of (LS,(((v,LS,LT) . FS),LS)) is finite Element of bool (LS)
the of (LS,(((v,LS,LT) . FS),LS)) \/ the of (LS,(((v,LS,LT) . FS),LS)) is finite Element of bool (LS)
the of (LS,(((v,LS,LT) . FS),LS)) is finite Element of bool (LS)
(LS, the of (LS,(((v,LS,LT) . FS),LS))) is Element of bool LTL_WFF
'X' (LS, the of (LS,(((v,LS,LT) . FS),LS))) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (LS, the of (LS,(((v,LS,LT) . FS),LS))) & b₁ = 'X' b₂ ) } is set
( the of (LS,(((v,LS,LT) . FS),LS)) \/ the of (LS,(((v,LS,LT) . FS),LS))) \/ ('X' (LS, the of (LS,(((v,LS,LT) . FS),LS)))) is set
((Shift (v,FS)),LS,LT,(LS,(((v,LS,LT) . FS),LS))) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
L is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len L is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
dom L is finite Element of bool NAT
L is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len L is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
dom L is finite Element of bool NAT
Seg (((Shift (v,FS)),LS,LT,(LS,(((v,LS,LT) . FS),LS))) + 1) is non empty finite ((Shift (v,FS)),LS,LT,(LS,(((v,LS,LT) . FS),LS))) + 1 -element Element of bool NAT
m is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
L . m is set
m - 1 is real integer ext-real V257() Element of REAL
CastNat (m - 1) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
((Shift (v,FS)),LS,LT) |** (CastNat (m - 1)) is Relation-like (LS) -defined (LS) -valued Function-like non empty V21((LS)) V25((LS),(LS)) finite Element of bool [:(LS),(LS):]
(((Shift (v,FS)),LS,LT) |** (CastNat (m - 1))) . (LS,(((v,LS,LT) . FS),LS)) is set
(((((Shift (v,FS)),LS,LT) |** (CastNat (m - 1))) . (LS,(((v,LS,LT) . FS),LS))),LS) is (LS) (LS)
CastNat m is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(CastNat m) - 1 is real integer ext-real V257() Element of REAL
CastNat ((CastNat m) - 1) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
((Shift (v,FS)),LS,LT) |** (CastNat ((CastNat m) - 1)) is Relation-like (LS) -defined (LS) -valued Function-like non empty V21((LS)) V25((LS),(LS)) finite Element of bool [:(LS),(LS):]
(((Shift (v,FS)),LS,LT) |** (CastNat ((CastNat m) - 1))) . (LS,(((v,LS,LT) . FS),LS)) is set
(((((Shift (v,FS)),LS,LT) |** (CastNat ((CastNat m) - 1))) . (LS,(((v,LS,LT) . FS),LS))),LS) is (LS) (LS)
m is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
L . m is set
m + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
L . (m + 1) is set
m - 1 is real integer ext-real V257() Element of REAL
m1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
m1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
((Shift (v,FS)),LS,LT) |** (m1 + 1) is Relation-like (LS) -defined (LS) -valued Function-like non empty V21((LS)) V25((LS),(LS)) finite Element of bool [:(LS),(LS):]
(((Shift (v,FS)),LS,LT) |** (m1 + 1)) . (LS,(((v,LS,LT) . FS),LS)) is set
(((((Shift (v,FS)),LS,LT) |** (m1 + 1)) . (LS,(((v,LS,LT) . FS),LS))),LS) is (LS) (LS)
(m + 1) - 1 is real integer ext-real V257() Element of REAL
CastNat ((m + 1) - 1) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
((Shift (v,FS)),LS,LT) |** (CastNat ((m + 1) - 1)) is Relation-like (LS) -defined (LS) -valued Function-like non empty V21((LS)) V25((LS),(LS)) finite Element of bool [:(LS),(LS):]
(((Shift (v,FS)),LS,LT) |** (CastNat ((m + 1) - 1))) . (LS,(((v,LS,LT) . FS),LS)) is set
(((((Shift (v,FS)),LS,LT) |** (CastNat ((m + 1) - 1))) . (LS,(((v,LS,LT) . FS),LS))),LS) is (LS) (LS)
((Shift (v,FS)),LS,LT) |** m1 is Relation-like (LS) -defined (LS) -valued Function-like non empty V21((LS)) V25((LS),(LS)) finite Element of bool [:(LS),(LS):]
(((Shift (v,FS)),LS,LT) |** m1) . (LS,(((v,LS,LT) . FS),LS)) is set
(((((Shift (v,FS)),LS,LT) |** m1) . (LS,(((v,LS,LT) . FS),LS))),LS) is (LS) (LS)
(((Shift (v,FS)),LS,LT,(LS,(((v,LS,LT) . FS),LS))) + 1) - 1 is real integer ext-real V257() Element of REAL
CastNat m1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
((Shift (v,FS)),LS,LT) |** (CastNat m1) is Relation-like (LS) -defined (LS) -valued Function-like non empty V21((LS)) V25((LS),(LS)) finite Element of bool [:(LS),(LS):]
(((Shift (v,FS)),LS,LT) |** (CastNat m1)) . (LS,(((v,LS,LT) . FS),LS)) is set
(((((Shift (v,FS)),LS,LT) |** (CastNat m1)) . (LS,(((v,LS,LT) . FS),LS))),LS) is (LS) (LS)
L . 1 is set
1 - 1 is real integer ext-real V257() Element of REAL
CastNat (1 - 1) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
((Shift (v,FS)),LS,LT) |** (CastNat (1 - 1)) is Relation-like (LS) -defined (LS) -valued Function-like non empty V21((LS)) V25((LS),(LS)) finite Element of bool [:(LS),(LS):]
(((Shift (v,FS)),LS,LT) |** (CastNat (1 - 1))) . (LS,(((v,LS,LT) . FS),LS)) is set
(((((Shift (v,FS)),LS,LT) |** (CastNat (1 - 1))) . (LS,(((v,LS,LT) . FS),LS))),LS) is (LS) (LS)
((Shift (v,FS)),LS,LT) |** 0 is Relation-like (LS) -defined (LS) -valued Function-like non empty V21((LS)) V25((LS),(LS)) finite Element of bool [:(LS),(LS):]
(((Shift (v,FS)),LS,LT) |** 0) . (LS,(((v,LS,LT) . FS),LS)) is set
(((((Shift (v,FS)),LS,LT) |** 0) . (LS,(((v,LS,LT) . FS),LS))),LS) is (LS) (LS)
id (LS) is Relation-like (LS) -defined (LS) -valued Function-like one-to-one non empty V21((LS)) V25((LS),(LS)) finite being_quasi-order being_partial-order Element of bool [:(LS),(LS):]
(id (LS)) . (LS,(((v,LS,LT) . FS),LS)) is set
(((id (LS)) . (LS,(((v,LS,LT) . FS),LS))),LS) is (LS) (LS)
((LS,(((v,LS,LT) . FS),LS)),LS) is (LS) (LS)
L . (len L) is set
(((Shift (v,FS)),LS,LT,(LS,(((v,LS,LT) . FS),LS))) + 1) - 1 is real integer ext-real V257() Element of REAL
CastNat ((((Shift (v,FS)),LS,LT,(LS,(((v,LS,LT) . FS),LS))) + 1) - 1) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
((Shift (v,FS)),LS,LT) |** (CastNat ((((Shift (v,FS)),LS,LT,(LS,(((v,LS,LT) . FS),LS))) + 1) - 1)) is Relation-like (LS) -defined (LS) -valued Function-like non empty V21((LS)) V25((LS),(LS)) finite Element of bool [:(LS),(LS):]
(((Shift (v,FS)),LS,LT) |** (CastNat ((((Shift (v,FS)),LS,LT,(LS,(((v,LS,LT) . FS),LS))) + 1) - 1))) . (LS,(((v,LS,LT) . FS),LS)) is set
(((((Shift (v,FS)),LS,LT) |** (CastNat ((((Shift (v,FS)),LS,LT,(LS,(((v,LS,LT) . FS),LS))) + 1) - 1))) . (LS,(((v,LS,LT) . FS),LS))),LS) is (LS) (LS)
the of (((((Shift (v,FS)),LS,LT) |** ((Shift (v,FS)),LS,LT,(LS,(((v,LS,LT) . FS),LS)))) . (LS,(((v,LS,LT) . FS),LS))),LS) is finite Element of bool (LS)
((L . 1),LS) is (LS) (LS)
the of ((L . 1),LS) is finite Element of bool (LS)
((L . (len L)),LS) is (LS) (LS)
the of ((L . (len L)),LS) is finite Element of bool (LS)
w1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
L . w1 is set
((L . w1),LS) is (LS) (LS)
the of ((L . w1),LS) is finite Element of bool (LS)
w1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
L . (w1 + 1) is set
((L . (w1 + 1)),LS) is (LS) (LS)
the of ((L . (w1 + 1)),LS) is finite Element of bool (LS)
w1 - 1 is real integer ext-real V257() Element of REAL
h is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
((Shift (v,FS)),LS,LT) |** h is Relation-like (LS) -defined (LS) -valued Function-like non empty V21((LS)) V25((LS),(LS)) finite Element of bool [:(LS),(LS):]
(((Shift (v,FS)),LS,LT) |** h) . (LS,(((v,LS,LT) . FS),LS)) is set
natMAX is (LS) (LS)
k is (LS) (LS)
CastNat h is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
((Shift (v,FS)),LS,LT) |** (CastNat h) is Relation-like (LS) -defined (LS) -valued Function-like non empty V21((LS)) V25((LS),(LS)) finite Element of bool [:(LS),(LS):]
(((Shift (v,FS)),LS,LT) |** (CastNat h)) . (LS,(((v,LS,LT) . FS),LS)) is set
(((((Shift (v,FS)),LS,LT) |** (CastNat h)) . (LS,(((v,LS,LT) . FS),LS))),LS) is (LS) (LS)
(((((Shift (v,FS)),LS,LT) |** h) . (LS,(((v,LS,LT) . FS),LS))),LS) is (LS) (LS)
(w1 + 1) - 1 is real integer ext-real V257() Element of REAL
CastNat ((w1 + 1) - 1) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
((Shift (v,FS)),LS,LT) |** (CastNat ((w1 + 1) - 1)) is Relation-like (LS) -defined (LS) -valued Function-like non empty V21((LS)) V25((LS),(LS)) finite Element of bool [:(LS),(LS):]
(((Shift (v,FS)),LS,LT) |** (CastNat ((w1 + 1) - 1))) . (LS,(((v,LS,LT) . FS),LS)) is set
(((((Shift (v,FS)),LS,LT) |** (CastNat ((w1 + 1) - 1))) . (LS,(((v,LS,LT) . FS),LS))),LS) is (LS) (LS)
h + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
((Shift (v,FS)),LS,LT) |** (h + 1) is Relation-like (LS) -defined (LS) -valued Function-like non empty V21((LS)) V25((LS),(LS)) finite Element of bool [:(LS),(LS):]
(((Shift (v,FS)),LS,LT) |** (h + 1)) . (LS,(((v,LS,LT) . FS),LS)) is set
(((((Shift (v,FS)),LS,LT) |** (h + 1)) . (LS,(((v,LS,LT) . FS),LS))),LS) is (LS) (LS)
((Shift (v,FS)),LS,LT) * (((Shift (v,FS)),LS,LT) |** h) is Relation-like (LS) -defined (LS) -valued Function-like non empty V21((LS)) V25((LS),(LS)) finite Element of bool [:(LS),(LS):]
(((Shift (v,FS)),LS,LT) * (((Shift (v,FS)),LS,LT) |** h)) . (LS,(((v,LS,LT) . FS),LS)) is set
(((((Shift (v,FS)),LS,LT) * (((Shift (v,FS)),LS,LT) |** h)) . (LS,(((v,LS,LT) . FS),LS))),LS) is (LS) (LS)
((Shift (v,FS)),LS,LT) . ((((Shift (v,FS)),LS,LT) |** h) . (LS,(((v,LS,LT) . FS),LS))) is set
((((Shift (v,FS)),LS,LT) . ((((Shift (v,FS)),LS,LT) |** h) . (LS,(((v,LS,LT) . FS),LS)))),LS) is (LS) (LS)
((Shift (v,FS)),LS,LT,(((((Shift (v,FS)),LS,LT) |** h) . (LS,(((v,LS,LT) . FS),LS))),LS)) is (LS) (LS)
(((Shift (v,FS)),LS,LT,(((((Shift (v,FS)),LS,LT) |** h) . (LS,(((v,LS,LT) . FS),LS))),LS)),LS) is (LS) (LS)
((Shift (v,FS)),LS,LT,natMAX) is (LS) (LS)
(LS,LT,natMAX) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the of k is finite Element of bool (LS)
the of natMAX is finite Element of bool (LS)
the of natMAX is finite Element of bool (LS)
{(LS,LT,natMAX)} is functional non empty trivial finite V42() 1 -element set
the of natMAX \/ {(LS,LT,natMAX)} is non empty finite set
(LS,natMAX,(LS,LT,natMAX)) is (LS) (LS)
(LS,(LS,natMAX,(LS,LT,natMAX))) is Element of bool LTL_WFF
the of (LS,natMAX,(LS,LT,natMAX)) is finite Element of bool (LS)
the of (LS,natMAX,(LS,LT,natMAX)) is finite Element of bool (LS)
the of (LS,natMAX,(LS,LT,natMAX)) \/ the of (LS,natMAX,(LS,LT,natMAX)) is finite Element of bool (LS)
the of (LS,natMAX,(LS,LT,natMAX)) is finite Element of bool (LS)
(LS, the of (LS,natMAX,(LS,LT,natMAX))) is Element of bool LTL_WFF
'X' (LS, the of (LS,natMAX,(LS,LT,natMAX))) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (LS, the of (LS,natMAX,(LS,LT,natMAX))) & b₁ = 'X' b₂ ) } is set
( the of (LS,natMAX,(LS,LT,natMAX)) \/ the of (LS,natMAX,(LS,LT,natMAX))) \/ ('X' (LS, the of (LS,natMAX,(LS,LT,natMAX)))) is set
the_right_argument_of (LS,LT,natMAX) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(LS,natMAX,(LS,LT,natMAX)) is (LS) (LS)
(LS,(LS,natMAX,(LS,LT,natMAX))) is Element of bool LTL_WFF
the of (LS,natMAX,(LS,LT,natMAX)) is finite Element of bool (LS)
the of (LS,natMAX,(LS,LT,natMAX)) is finite Element of bool (LS)
the of (LS,natMAX,(LS,LT,natMAX)) \/ the of (LS,natMAX,(LS,LT,natMAX)) is finite Element of bool (LS)
the of (LS,natMAX,(LS,LT,natMAX)) is finite Element of bool (LS)
(LS, the of (LS,natMAX,(LS,LT,natMAX))) is Element of bool LTL_WFF
'X' (LS, the of (LS,natMAX,(LS,LT,natMAX))) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (LS, the of (LS,natMAX,(LS,LT,natMAX))) & b₁ = 'X' b₂ ) } is set
( the of (LS,natMAX,(LS,LT,natMAX)) \/ the of (LS,natMAX,(LS,LT,natMAX))) \/ ('X' (LS, the of (LS,natMAX,(LS,LT,natMAX)))) is set
the_right_argument_of (LS,LT,natMAX) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(LS,natMAX,(LS,LT,natMAX)) is (LS) (LS)
(LS,natMAX,(LS,LT,natMAX)) is (LS) (LS)
(LS,(LS,natMAX,(LS,LT,natMAX))) is Element of bool LTL_WFF
the of (LS,natMAX,(LS,LT,natMAX)) is finite Element of bool (LS)
the of (LS,natMAX,(LS,LT,natMAX)) is finite Element of bool (LS)
the of (LS,natMAX,(LS,LT,natMAX)) \/ the of (LS,natMAX,(LS,LT,natMAX)) is finite Element of bool (LS)
the of (LS,natMAX,(LS,LT,natMAX)) is finite Element of bool (LS)
(LS, the of (LS,natMAX,(LS,LT,natMAX))) is Element of bool LTL_WFF
'X' (LS, the of (LS,natMAX,(LS,LT,natMAX))) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (LS, the of (LS,natMAX,(LS,LT,natMAX))) & b₁ = 'X' b₂ ) } is set
( the of (LS,natMAX,(LS,LT,natMAX)) \/ the of (LS,natMAX,(LS,LT,natMAX))) \/ ('X' (LS, the of (LS,natMAX,(LS,LT,natMAX)))) is set
the_right_argument_of (LS,LT,natMAX) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(LS,natMAX,w) is (LS) (LS)
the of natMAX is finite Element of bool (LS)
the of (((((Shift (v,FS)),LS,LT) |** ((Shift (v,FS)),LS,LT,(LS,(((v,LS,LT) . FS),LS)))) . (LS,(((v,LS,LT) . FS),LS))),LS) is finite Element of bool (LS)
the of ((L . (w1 + 1)),LS) is finite Element of bool (LS)
the of k is finite Element of bool (LS)
the of natMAX is finite Element of bool (LS)
(w) is finite Element of bool (w)
(w) is non empty finite Element of bool LTL_WFF
bool (w) is non empty finite V42() set
{(the_right_argument_of w)} is functional non empty trivial finite V42() 1 -element set
{w} is functional non empty trivial finite V42() 1 -element set
the of natMAX \ {w} is finite Element of bool (LS)
{(the_right_argument_of w)} \ the of natMAX is functional trivial finite V42() Element of bool {(the_right_argument_of w)}
bool {(the_right_argument_of w)} is non empty finite V42() set
( the of natMAX \ {w}) \/ ({(the_right_argument_of w)} \ the of natMAX) is finite set
((Shift (v,FS)),LS,LT,(((v,LS,LT) . FS),LS)) is (LS) (LS) (LS)
(LS) is (LS) (LS) (LS)
(LS,(LS),(LS),(LS)) is (LS) (LS)
the of (LS) is finite Element of bool (LS)
((Shift (v,FS)),LS,LT,(((v,LS,LT) . FS),LS)) is (LS) (LS) (LS)
((LS,(((v,LS,LT) . FS),LS)),LS) is (LS) (LS)
IS is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
IS + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
(v,LS,LT) . (IS + 1) is Element of (LS)
(((v,LS,LT) . (IS + 1)),LS) is (LS) (LS)
the of (((v,LS,LT) . (IS + 1)),LS) is finite Element of bool (LS)
bool (LS) is non empty finite V42() set
Shift (v,IS) is Element of Inf_seq AtomicFamily
Shift (v,IS,AtomicFamily) is Element of Inf_seq AtomicFamily
CastSeq (v,AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
[:NAT,AtomicFamily:] is Relation-like non empty non trivial non finite set
bool [:NAT,AtomicFamily:] is non empty non trivial non finite set
(CastSeq (v,AtomicFamily)) ^\ IS is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (v,AtomicFamily)) ^\ IS) is Element of Inf_seq AtomicFamily
w is Element of Inf_seq AtomicFamily
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() () FinSequence of NAT
(v) is ( AtomicFamily )
(v) is non empty finite set
(v) is non empty finite set
{ b₁ where b₁ is Element of (v) : b₁ is (v) (v) (v) } is set
(v) is Relation-like [:(v),AtomicFamily:] -defined (v) -valued Element of bool [:[:(v),AtomicFamily:],(v):]
[:(v),AtomicFamily:] is Relation-like non empty set
[:[:(v),AtomicFamily:],(v):] is Relation-like non empty set
bool [:[:(v),AtomicFamily:],(v):] is non empty set
[:(v),AtomicFamily,(v):] is non empty set
{ b₁ where b₁ is Element of [:(v),AtomicFamily,(v):] : ex b₂, b₃ being (v) (v) (v) ex b₄ being set st
( b₁ = [[b₂,b₄],b₃] & (v,b₂,b₃) & b₄ in (v,b₃) ) } is set
(v) is finite Element of bool (v)
bool (v) is non empty finite V42() set
(v) is (v) (v) (v)
(v) is finite Element of bool (v)
(v) is non empty finite Element of bool LTL_WFF
bool (v) is non empty finite V42() set
(v) is finite Element of bool (v)
{v} is functional non empty trivial finite V42() 1 -element set
(v,(v),(v),(v)) is (v) (v)
{(v)} is non empty trivial finite 1 -element set
(v) is finite V42() Element of bool (bool (v))
bool (bool (v)) is non empty finite V42() set
{ b₁ where b₁ is finite Element of bool (v) : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ is_subformula_of v & b₂ is Until & b₁ = (v,b₂) ) } is set
(AtomicFamily,(v),(v),(v),(v)) is ( AtomicFamily ) ( AtomicFamily )
[:NAT,(v):] is Relation-like non empty non trivial non finite set
bool [:NAT,(v):] is non empty non trivial non finite set
CastSeq (w,AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
[:NAT,AtomicFamily:] is Relation-like non empty non trivial non finite set
bool [:NAT,AtomicFamily:] is non empty non trivial non finite set
BOOL (v) is non empty set
union (BOOL (v)) is non empty set
the Relation-like BOOL (v) -defined union (BOOL (v)) -valued Function-like non empty V21( BOOL (v)) V25( BOOL (v), union (BOOL (v))) Choice_Function of BOOL (v) is Relation-like BOOL (v) -defined union (BOOL (v)) -valued Function-like non empty V21( BOOL (v)) V25( BOOL (v), union (BOOL (v))) Choice_Function of BOOL (v)
(w,v, the Relation-like BOOL (v) -defined union (BOOL (v)) -valued Function-like non empty V21( BOOL (v)) V25( BOOL (v), union (BOOL (v))) Choice_Function of BOOL (v)) is Relation-like NAT -defined (v) -valued Function-like non empty V21( NAT ) V25( NAT ,(v)) Element of bool [:NAT,(v):]
run is set
k_nat run is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(w,v, the Relation-like BOOL (v) -defined union (BOOL (v)) -valued Function-like non empty V21( BOOL (v)) V25( BOOL (v), union (BOOL (v))) Choice_Function of BOOL (v)) . (k_nat run) is Element of (v)
run is Relation-like NAT -defined (v) -valued Function-like non empty V21( NAT ) V25( NAT ,(v)) Element of bool [:NAT,(v):]
run is Relation-like NAT -defined (v) -valued Function-like non empty V21( NAT ) V25( NAT ,(v)) Element of bool [:NAT,(v):]
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . FSet is set
((run . FSet),v) is (v) (v)
FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
run . FK is set
((run . FK),v) is (v) (v)
run . FK is Element of (v)
F is Element of (v)
the of H₂(FK) is finite Element of bool (v)
F2 is (v) (v) (v)
the of F2 is finite Element of bool (v)
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . FSet is set
(w,v, the Relation-like BOOL (v) -defined union (BOOL (v)) -valued Function-like non empty V21( BOOL (v)) V25( BOOL (v), union (BOOL (v))) Choice_Function of BOOL (v)) . FSet is set
FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
run . FK is Element of (v)
k_nat FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(w,v, the Relation-like BOOL (v) -defined union (BOOL (v)) -valued Function-like non empty V21( BOOL (v)) V25( BOOL (v), union (BOOL (v))) Choice_Function of BOOL (v)) . (k_nat FK) is Element of (v)
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . FSet is set
((run . FSet),v) is (v) (v)
FSet + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run . (FSet + 1) is set
((run . (FSet + 1)),v) is (v) (v)
Shift (w,FSet) is Element of Inf_seq AtomicFamily
Shift (w,FSet,AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ FSet is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ FSet) is Element of Inf_seq AtomicFamily
(v,H₂(FSet + 1)) is Element of bool LTL_WFF
the of ((run . (FSet + 1)),v) is finite Element of bool (v)
the of ((run . (FSet + 1)),v) is finite Element of bool (v)
the of ((run . (FSet + 1)),v) \/ the of ((run . (FSet + 1)),v) is finite Element of bool (v)
the of ((run . (FSet + 1)),v) is finite Element of bool (v)
(v, the of ((run . (FSet + 1)),v)) is Element of bool LTL_WFF
'X' (v, the of ((run . (FSet + 1)),v)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of ((run . (FSet + 1)),v)) & b₁ = 'X' b₂ ) } is set
( the of ((run . (FSet + 1)),v) \/ the of ((run . (FSet + 1)),v)) \/ ('X' (v, the of ((run . (FSet + 1)),v))) is set
(w,v, the Relation-like BOOL (v) -defined union (BOOL (v)) -valued Function-like non empty V21( BOOL (v)) V25( BOOL (v), union (BOOL (v))) Choice_Function of BOOL (v)) . FSet is set
(((w,v, the Relation-like BOOL (v) -defined union (BOOL (v)) -valued Function-like non empty V21( BOOL (v)) V25( BOOL (v), union (BOOL (v))) Choice_Function of BOOL (v)) . FSet),v) is (v) (v)
x is (v) (v) (v)
(v,x) is (v) (v)
the of x is finite Element of bool (v)
(v,(v), the of x,(v)) is (v) (v)
(v,(v,x)) is Element of bool LTL_WFF
the of (v,x) is finite Element of bool (v)
the of (v,x) is finite Element of bool (v)
the of (v,x) \/ the of (v,x) is finite Element of bool (v)
the of (v,x) is finite Element of bool (v)
(v, the of (v,x)) is Element of bool LTL_WFF
'X' (v, the of (v,x)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of (v,x)) & b₁ = 'X' b₂ ) } is set
( the of (v,x) \/ the of (v,x)) \/ ('X' (v, the of (v,x))) is set
run . (FSet + 1) is Element of (v)
(w,v, the Relation-like BOOL (v) -defined union (BOOL (v)) -valued Function-like non empty V21( BOOL (v)) V25( BOOL (v), union (BOOL (v))) Choice_Function of BOOL (v)) . (FSet + 1) is Element of (v)
((Shift (w,FSet)),v, the Relation-like BOOL (v) -defined union (BOOL (v)) -valued Function-like non empty V21( BOOL (v)) V25( BOOL (v), union (BOOL (v))) Choice_Function of BOOL (v),x) is (v) (v) (v)
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(CastSeq (w,AtomicFamily)) . FSet is set
FSet + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run . (FSet + 1) is set
((run . (FSet + 1)),v) is (v) (v)
(v,H₂(FSet + 1)) is set
(v,((run . (FSet + 1)),v)) is Element of bool LTL_WFF
the of ((run . (FSet + 1)),v) is finite Element of bool (v)
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ( b₁ is atomic & b₁ in the of ((run . (FSet + 1)),v) ) } is set
(v,((run . (FSet + 1)),v)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ( b₁ is atomic & 'not' b₁ in the of ((run . (FSet + 1)),v) ) } is set
{ b₁ where b₁ is Element of bool atomic_LTL : ( (v,((run . (FSet + 1)),v)) c= b₁ & (v,((run . (FSet + 1)),v)) misses b₁ ) } is set
FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
FK + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run . (FK + 1) is set
((run . (FK + 1)),v) is (v) (v)
Shift (w,FK) is Element of Inf_seq AtomicFamily
Shift (w,FK,AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ FK is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ FK) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) . FK is Element of AtomicFamily
CastSeq ((Shift (w,FK)),AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
(CastSeq ((Shift (w,FK)),AtomicFamily)) . 0 is Element of AtomicFamily
0 + FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
(CastSeq (w,AtomicFamily)) . (0 + FK) is Element of AtomicFamily
(v,H₂(FK + 1)) is Element of bool LTL_WFF
the of ((run . (FK + 1)),v) is finite Element of bool (v)
the of ((run . (FK + 1)),v) is finite Element of bool (v)
the of ((run . (FK + 1)),v) \/ the of ((run . (FK + 1)),v) is finite Element of bool (v)
the of ((run . (FK + 1)),v) is finite Element of bool (v)
(v, the of ((run . (FK + 1)),v)) is Element of bool LTL_WFF
'X' (v, the of ((run . (FK + 1)),v)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of ((run . (FK + 1)),v)) & b₁ = 'X' b₂ ) } is set
( the of ((run . (FK + 1)),v) \/ the of ((run . (FK + 1)),v)) \/ ('X' (v, the of ((run . (FK + 1)),v))) is set
(v,H₂(FK + 1)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ( b₁ is atomic & 'not' b₁ in the of ((run . (FK + 1)),v) ) } is set
F1 is Element of bool atomic_LTL
(v,H₂(FK + 1)) /\ F1 is Element of bool atomic_LTL
L is set
the of H₂(FK + 1) is finite Element of bool (v)
m is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
'not' m is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
<*0*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*0*> ^ m is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(v,H₂(FK + 1)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ( b₁ is atomic & b₁ in the of ((run . (FK + 1)),v) ) } is set
L is set
m is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . FSet is set
(CastSeq (w,AtomicFamily)) . FSet is set
[(run . FSet),((CastSeq (w,AtomicFamily)) . FSet)] is set
{(run . FSet),((CastSeq (w,AtomicFamily)) . FSet)} is non empty finite set
{(run . FSet)} is non empty trivial finite 1 -element set
{{(run . FSet),((CastSeq (w,AtomicFamily)) . FSet)},{(run . FSet)}} is non empty finite V42() set
FSet + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run . (FSet + 1) is Element of (v)
[[(run . FSet),((CastSeq (w,AtomicFamily)) . FSet)],(run . (FSet + 1))] is set
{[(run . FSet),((CastSeq (w,AtomicFamily)) . FSet)],(run . (FSet + 1))} is non empty finite set
{[(run . FSet),((CastSeq (w,AtomicFamily)) . FSet)]} is Relation-like Function-like constant non empty trivial finite 1 -element set
{{[(run . FSet),((CastSeq (w,AtomicFamily)) . FSet)],(run . (FSet + 1))},{[(run . FSet),((CastSeq (w,AtomicFamily)) . FSet)]}} is non empty finite V42() set
FK is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
run . FK is set
((run . FK),v) is (v) (v)
FK + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run . FK is Element of (v)
run . (FK + 1) is Element of (v)
run . (FK + 1) is set
((run . (FK + 1)),v) is (v) (v)
(CastSeq (w,AtomicFamily)) . FK is Element of AtomicFamily
[(run . FK),((CastSeq (w,AtomicFamily)) . FK)] is set
{(run . FK),((CastSeq (w,AtomicFamily)) . FK)} is non empty finite set
{(run . FK)} is non empty trivial finite 1 -element set
{{(run . FK),((CastSeq (w,AtomicFamily)) . FK)},{(run . FK)}} is non empty finite V42() set
[[(run . FK),((CastSeq (w,AtomicFamily)) . FK)],(run . (FK + 1))] is set
{[(run . FK),((CastSeq (w,AtomicFamily)) . FK)],(run . (FK + 1))} is non empty finite set
{[(run . FK),((CastSeq (w,AtomicFamily)) . FK)]} is Relation-like Function-like constant non empty trivial finite 1 -element set
{{[(run . FK),((CastSeq (w,AtomicFamily)) . FK)],(run . (FK + 1))},{[(run . FK),((CastSeq (w,AtomicFamily)) . FK)]}} is non empty finite V42() set
F is (v) (v) (v)
h is (v) (v) (v)
(v,h) is set
(v,h) is Element of bool LTL_WFF
the of h is finite Element of bool (v)
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ( b₁ is atomic & b₁ in the of h ) } is set
(v,h) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ( b₁ is atomic & 'not' b₁ in the of h ) } is set
{ b₁ where b₁ is Element of bool atomic_LTL : ( (v,h) c= b₁ & (v,h) misses b₁ ) } is set
m3 is (v) (v) (v)
m2 is (v) (v) (v)
FSet is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
FSet + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run . (FSet + 1) is set
((run . (FSet + 1)),v) is (v) (v)
the of H₂(FSet + 1) is finite Element of bool (v)
Shift (w,FSet) is Element of Inf_seq AtomicFamily
Shift (w,FSet,AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ FSet is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ FSet) is Element of Inf_seq AtomicFamily
FK is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
the_right_argument_of FK is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(w,v, the Relation-like BOOL (v) -defined union (BOOL (v)) -valued Function-like non empty V21( BOOL (v)) V25( BOOL (v), union (BOOL (v))) Choice_Function of BOOL (v)) . (FSet + 1) is Element of (v)
(((w,v, the Relation-like BOOL (v) -defined union (BOOL (v)) -valued Function-like non empty V21( BOOL (v)) V25( BOOL (v), union (BOOL (v))) Choice_Function of BOOL (v)) . (FSet + 1)),v) is (v) (v)
FSet is set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT : run . b₁ in FSet } is set
x is finite Element of bool (v)
F is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(v,F) is finite Element of bool (v)
the_right_argument_of F is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{ b₁ where b₁ is Element of (v) : ( not F in the of (b₁,v) or the_right_argument_of F in the of (b₁,v) ) } is set
F is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(v,F) is finite Element of bool (v)
the_right_argument_of F is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
{ b₁ where b₁ is Element of (v) : ( not F in the of (b₁,v) or the_right_argument_of F in the of (b₁,v) ) } is set
the_left_argument_of F is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
(the_left_argument_of F) 'U' (the_right_argument_of F) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT
4 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
<*4*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V258() V259() V260() V261() V262() V263() V264() V265() FinSequence of NAT
<*4*> ^ (the_left_argument_of F) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
(<*4*> ^ (the_left_argument_of F)) ^ (the_right_argument_of F) is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like V258() V259() V260() V261() FinSequence of NAT
L is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng L is finite set
len L is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
0 + (len L) is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
w1 is set
m1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
run . m1 is Element of (v)
w1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V258() V259() V260() FinSequence of REAL
max w1 is real ext-real V257() Element of REAL
[/(max w1)\] is real integer ext-real V257() set
[/(max w1)\] + 1 is real integer ext-real V257() Element of REAL
w1 . (len L) is real ext-real V257() Element of REAL
len w1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
Seg (len w1) is finite len w1 -element Element of bool NAT
dom w1 is finite Element of bool NAT
rng w1 is finite V269() V270() V271() Element of bool REAL
natMAX is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
run . natMAX is Element of (v)
m3 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
m3 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
natMAX is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
k is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
dom w1 is finite Element of bool NAT
i1 is set
w1 . i1 is real ext-real V257() Element of REAL
i1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
Seg (len L) is finite len L -element Element of bool NAT
m is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
m is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
m is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
m is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
w1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
run . w1 is set
((run . w1),v) is (v) (v)
the of H₂(w1) is finite Element of bool (v)
m1 is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() Element of NAT
run . m1 is Element of (v)
m2 is (v) (v) (v)
(m2,v) is (v) (v)
the of (m2,v) is finite Element of bool (v)
Shift (w,m) is Element of Inf_seq AtomicFamily
Shift (w,m,AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ m is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ m) is Element of Inf_seq AtomicFamily
m + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run . (m + 1) is set
((run . (m + 1)),v) is (v) (v)
(v,H₂(m + 1)) is Element of bool LTL_WFF
the of ((run . (m + 1)),v) is finite Element of bool (v)
the of ((run . (m + 1)),v) is finite Element of bool (v)
the of ((run . (m + 1)),v) \/ the of ((run . (m + 1)),v) is finite Element of bool (v)
the of ((run . (m + 1)),v) is finite Element of bool (v)
(v, the of ((run . (m + 1)),v)) is Element of bool LTL_WFF
'X' (v, the of ((run . (m + 1)),v)) is Element of bool LTL_WFF
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ in (v, the of ((run . (m + 1)),v)) & b₁ = 'X' b₂ ) } is set
( the of ((run . (m + 1)),v) \/ the of ((run . (m + 1)),v)) \/ ('X' (v, the of ((run . (m + 1)),v))) is set
the of H₂(m + 1) is finite Element of bool (v)
h is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
Shift ((Shift (w,m)),h) is Element of Inf_seq AtomicFamily
Shift ((Shift (w,m)),h,AtomicFamily) is Element of Inf_seq AtomicFamily
CastSeq ((Shift (w,m)),AtomicFamily) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
(CastSeq ((Shift (w,m)),AtomicFamily)) ^\ h is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq ((Shift (w,m)),AtomicFamily)) ^\ h) is Element of Inf_seq AtomicFamily
m + h is epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative V257() set
(m + h) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
h + 1 is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
m + (h + 1) is epsilon-transitive epsilon-connected ordinal natural non empty real integer finite cardinal ext-real positive non negative V257() Element of NAT
run . ((m + h) + 1) is set
((run . ((m + h) + 1)),v) is (v) (v)
the of H₂((m + h) + 1) is finite Element of bool (v)
Shift (w,(m + h)) is Element of Inf_seq AtomicFamily
Shift (w,(m + h),AtomicFamily) is Element of Inf_seq AtomicFamily
(CastSeq (w,AtomicFamily)) ^\ (m + h) is Relation-like NAT -defined AtomicFamily -valued Function-like non empty V21( NAT ) V25( NAT , AtomicFamily ) Element of bool [:NAT,AtomicFamily:]
CastSeq ((CastSeq (w,AtomicFamily)) ^\ (m + h)) is Element of Inf_seq AtomicFamily
run . 0 is Element of (v)
(w,v, the Relation-like BOOL (v) -defined union (BOOL (v)) -valued Function-like non empty V21( BOOL (v)) V25( BOOL (v), union (BOOL (v))) Choice_Function of BOOL (v)) . 0 is Element of (v)
chf is Relation-like NAT -defined (v) -valued Function-like non empty V21( NAT ) V25( NAT ,(v)) Element of bool [:NAT,(v):]
chf . 0 is Element of (v)
v is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() () FinSequence of NAT
(v) is ( AtomicFamily )
(v) is non empty finite set
(v) is non empty finite set
{ b₁ where b₁ is Element of (v) : b₁ is (v) (v) (v) } is set
(v) is Relation-like [:(v),AtomicFamily:] -defined (v) -valued Element of bool [:[:(v),AtomicFamily:],(v):]
[:(v),AtomicFamily:] is Relation-like non empty set
[:[:(v),AtomicFamily:],(v):] is Relation-like non empty set
bool [:[:(v),AtomicFamily:],(v):] is non empty set
[:(v),AtomicFamily,(v):] is non empty set
{ b₁ where b₁ is Element of [:(v),AtomicFamily,(v):] : ex b₂, b₃ being (v) (v) (v) ex b₄ being set st
( b₁ = [[b₂,b₄],b₃] & (v,b₂,b₃) & b₄ in (v,b₃) ) } is set
(v) is finite Element of bool (v)
bool (v) is non empty finite V42() set
(v) is (v) (v) (v)
(v) is finite Element of bool (v)
(v) is non empty finite Element of bool LTL_WFF
bool (v) is non empty finite V42() set
(v) is finite Element of bool (v)
{v} is functional non empty trivial finite V42() 1 -element set
(v,(v),(v),(v)) is (v) (v)
{(v)} is non empty trivial finite 1 -element set
(v) is finite V42() Element of bool (bool (v))
bool (bool (v)) is non empty finite V42() set
{ b₁ where b₁ is finite Element of bool (v) : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ is_subformula_of v & b₂ is Until & b₁ = (v,b₂) ) } is set
(AtomicFamily,(v),(v),(v),(v)) is ( AtomicFamily ) ( AtomicFamily )
w is Element of Inf_seq AtomicFamily
LS is Element of Inf_seq AtomicFamily
LT is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() () FinSequence of NAT
(LT) is ( AtomicFamily )
(LT) is non empty finite set
(LT) is non empty finite set
{ b₁ where b₁ is Element of (LT) : b₁ is (LT) (LT) (LT) } is set
(LT) is Relation-like [:(LT),AtomicFamily:] -defined (LT) -valued Element of bool [:[:(LT),AtomicFamily:],(LT):]
[:(LT),AtomicFamily:] is Relation-like non empty set
[:[:(LT),AtomicFamily:],(LT):] is Relation-like non empty set
bool [:[:(LT),AtomicFamily:],(LT):] is non empty set
[:(LT),AtomicFamily,(LT):] is non empty set
{ b₁ where b₁ is Element of [:(LT),AtomicFamily,(LT):] : ex b₂, b₃ being (LT) (LT) (LT) ex b₄ being set st
( b₁ = [[b₂,b₄],b₃] & (LT,b₂,b₃) & b₄ in (LT,b₃) ) } is set
(LT) is finite Element of bool (LT)
bool (LT) is non empty finite V42() set
(LT) is (LT) (LT) (LT)
(LT) is finite Element of bool (LT)
(LT) is non empty finite Element of bool LTL_WFF
bool (LT) is non empty finite V42() set
(LT) is finite Element of bool (LT)
{LT} is functional non empty trivial finite V42() 1 -element set
(LT,(LT),(LT),(LT)) is (LT) (LT)
{(LT)} is non empty trivial finite 1 -element set
(LT) is finite V42() Element of bool (bool (LT))
bool (bool (LT)) is non empty finite V42() set
{ b₁ where b₁ is finite Element of bool (LT) : ex b₂ being Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like LTL-formula-like V258() V259() V260() V261() FinSequence of NAT st
( b₂ is_subformula_of LT & b₂ is Until & b₁ = (LT,b₂) ) } is set
(AtomicFamily,(LT),(LT),(LT),(LT)) is ( AtomicFamily ) ( AtomicFamily )