:: POLYNOM3 semantic presentation

REAL is non empty non trivial non finite V75() V76() V77() V81() set
NAT is non empty non trivial V26() V27() V28() non finite cardinal limit_cardinal V75() V76() V77() V78() V79() V80() V81() Element of bool REAL
bool REAL is non trivial non finite set
NAT is non empty non trivial V26() V27() V28() non finite cardinal limit_cardinal V75() V76() V77() V78() V79() V80() V81() set
bool NAT is non trivial non finite set
bool NAT is non trivial non finite set
COMPLEX is non empty non trivial non finite V75() V81() set
RAT is non empty non trivial non finite V75() V76() V77() V78() V81() set
INT is non empty non trivial non finite V75() V76() V77() V78() V79() V81() set
[:REAL,REAL:] is non trivial non finite V65() V66() V67() set
bool [:REAL,REAL:] is non trivial non finite set
{} is set
the Function-like functional empty V26() V27() V28() V30() V31() V32() finite V37() cardinal {} -element FinSequence-membered V45() V46() V47() ext-real non positive non negative V75() V76() V77() V78() V79() V80() V81() set is Function-like functional empty V26() V27() V28() V30() V31() V32() finite V37() cardinal {} -element FinSequence-membered V45() V46() V47() ext-real non positive non negative V75() V76() V77() V78() V79() V80() V81() set
1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
{{},1} is finite set
K406() is set
bool K406() is set
K407() is Element of bool K406()
2 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
[:COMPLEX,COMPLEX:] is non trivial non finite V65() set
bool [:COMPLEX,COMPLEX:] is non trivial non finite set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is non trivial non finite V65() set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is non trivial non finite set
[:[:REAL,REAL:],REAL:] is non trivial non finite V65() V66() V67() set
bool [:[:REAL,REAL:],REAL:] is non trivial non finite set
[:RAT,RAT:] is RAT -valued non trivial non finite V65() V66() V67() set
bool [:RAT,RAT:] is non trivial non finite set
[:[:RAT,RAT:],RAT:] is RAT -valued non trivial non finite V65() V66() V67() set
bool [:[:RAT,RAT:],RAT:] is non trivial non finite set
[:INT,INT:] is RAT -valued INT -valued non trivial non finite V65() V66() V67() set
bool [:INT,INT:] is non trivial non finite set
[:[:INT,INT:],INT:] is RAT -valued INT -valued non trivial non finite V65() V66() V67() set
bool [:[:INT,INT:],INT:] is non trivial non finite set
[:NAT,NAT:] is RAT -valued INT -valued non trivial non finite V65() V66() V67() V68() set
[:[:NAT,NAT:],NAT:] is RAT -valued INT -valued non trivial non finite V65() V66() V67() V68() set
bool [:[:NAT,NAT:],NAT:] is non trivial non finite set
K612() is set
[:NAT,REAL:] is non trivial non finite V65() V66() V67() set
bool [:NAT,REAL:] is non trivial non finite set
K467() is Relation-like NAT -defined Function-like total set
3 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
0 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg 1 is non empty trivial finite 1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
{1} is non empty trivial finite V37() 1 -element V75() V76() V77() V78() V79() V80() set
Seg 2 is non empty finite 2 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
{1,2} is finite V37() V75() V76() V77() V78() V79() V80() set
Seg 3 is non empty finite 3 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
K150(1,2,3) is finite V75() V76() V77() V78() V79() V80() set
L is non empty right_complementable add-associative right_zeroed addLoopStr
the carrier of L is non empty set
0. L is V105(L) Element of the carrier of L
the ZeroF of L is Element of the carrier of L
p is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
dom p is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Sum p is Element of the carrier of L
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
p /. q is Element of the carrier of L
p . q is set
L is non empty Abelian add-associative right_zeroed addLoopStr
the carrier of L is non empty set
p is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
Sum p is Element of the carrier of L
Rev p is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
Sum (Rev p) is Element of the carrier of L
q is Element of the carrier of L
<*q*> is Relation-like NAT -defined the carrier of L -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of the carrier of L *
the carrier of L * is functional non empty FinSequence-membered FinSequenceSet of the carrier of L
p ^ <*q*> is Relation-like NAT -defined the carrier of L -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
Sum (p ^ <*q*>) is Element of the carrier of L
Rev (p ^ <*q*>) is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
Sum (Rev (p ^ <*q*>)) is Element of the carrier of L
Sum <*q*> is Element of the carrier of L
(Sum p) + (Sum <*q*>) is Element of the carrier of L
the addF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is set
the addF of L . ((Sum p),(Sum <*q*>)) is Element of the carrier of L
<*q*> ^ (Rev p) is Relation-like NAT -defined the carrier of L -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
Sum (<*q*> ^ (Rev p)) is Element of the carrier of L
<*> the carrier of L is Relation-like NAT -defined the carrier of L -valued Function-like one-to-one constant functional empty Function-yielding V26() V27() V28() V30() V31() V32() finite finite-yielding V37() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V45() V46() V47() ext-real non positive non negative V65() V66() V67() V68() V75() V76() V77() V78() V79() V80() V81() FinSequence-yielding finite-support Element of the carrier of L *
the carrier of L * is functional non empty FinSequence-membered FinSequenceSet of the carrier of L
Sum (<*> the carrier of L) is Element of the carrier of L
Rev (<*> the carrier of L) is Relation-like NAT -defined RAT -valued the carrier of L -valued Function-like one-to-one constant functional empty Function-yielding V26() V27() V28() V30() V31() V32() finite finite-yielding V37() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V45() V46() V47() ext-real non positive non negative V65() V66() V67() V68() V75() V76() V77() V78() V79() V80() V81() FinSequence-yielding finite-support FinSequence of the carrier of L
Sum (Rev (<*> the carrier of L)) is Element of the carrier of L
L is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() finite-support FinSequence of REAL
Sum L is V45() V46() ext-real Element of REAL
Rev L is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() finite-support FinSequence of REAL
Sum (Rev L) is V45() V46() ext-real Element of REAL
p is V45() V46() ext-real Element of REAL
<*p*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V69() V70() V71() V72() finite-support Element of REAL *
REAL * is functional non empty FinSequence-membered FinSequenceSet of REAL
L ^ <*p*> is Relation-like NAT -defined REAL -valued Function-like non empty finite FinSequence-like FinSubsequence-like V65() V66() V67() finite-support FinSequence of REAL
Sum (L ^ <*p*>) is V45() V46() ext-real Element of REAL
Rev (L ^ <*p*>) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() finite-support FinSequence of REAL
Sum (Rev (L ^ <*p*>)) is V45() V46() ext-real Element of REAL
Sum <*p*> is V45() V46() ext-real Element of REAL
(Sum L) + (Sum <*p*>) is V45() V46() ext-real set
<*p*> ^ (Rev L) is Relation-like NAT -defined REAL -valued Function-like non empty finite FinSequence-like FinSubsequence-like V65() V66() V67() finite-support FinSequence of REAL
Sum (<*p*> ^ (Rev L)) is V45() V46() ext-real Element of REAL
<*> REAL is Relation-like NAT -defined REAL -valued Function-like one-to-one constant functional empty Function-yielding V26() V27() V28() V30() V31() V32() finite finite-yielding V37() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V45() V46() V47() ext-real non positive non negative V65() V66() V67() V68() V75() V76() V77() V78() V79() V80() V81() FinSequence-yielding finite-support Element of REAL *
REAL * is functional non empty FinSequence-membered FinSequenceSet of REAL
Sum (<*> REAL) is V45() V46() ext-real Element of REAL
Rev (<*> REAL) is Relation-like NAT -defined REAL -valued RAT -valued Function-like one-to-one constant functional empty Function-yielding V26() V27() V28() V30() V31() V32() finite finite-yielding V37() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V45() V46() V47() ext-real non positive non negative V65() V66() V67() V68() V75() V76() V77() V78() V79() V80() V81() FinSequence-yielding finite-support FinSequence of REAL
Sum (Rev (<*> REAL)) is V45() V46() ext-real Element of REAL
L is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
dom L is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Sum L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
<*p*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V69() V70() V71() V72() V195() finite-support Element of NAT *
NAT * is functional non empty FinSequence-membered FinSequenceSet of NAT
L ^ <*p*> is Relation-like NAT -defined REAL -valued Function-like non empty finite FinSequence-like FinSubsequence-like V65() V66() V67() V195() finite-support FinSequence of NAT
dom (L ^ <*p*>) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Sum (L ^ <*p*>) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L ^ <*p*>) . q is V45() V46() ext-real set
L . q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L . q) + p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len (L ^ <*p*>) is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(len L) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg ((len L) + 1) is non empty finite (len L) + 1 -element (len L) + 1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(len L) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len L) is finite len L -element V75() V76() V77() V78() V79() V80() Element of bool NAT
{((len L) + 1)} is non empty trivial finite V37() 1 -element V75() V76() V77() V78() V79() V80() set
(Seg (len L)) \/ {((len L) + 1)} is finite V75() V76() V77() V78() V79() V80() set
(dom L) \/ {((len L) + 1)} is finite V75() V76() V77() V78() V79() V80() set
(Sum L) + p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum L) + p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
<*> NAT is Relation-like NAT -defined NAT -valued Function-like one-to-one constant functional empty Function-yielding V26() V27() V28() V30() V31() V32() finite finite-yielding V37() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V45() V46() V47() ext-real non positive non negative V65() V66() V67() V68() V75() V76() V77() V78() V79() V80() V81() V195() FinSequence-yielding finite-support Element of NAT *
NAT * is functional non empty FinSequence-membered FinSequenceSet of NAT
dom (<*> NAT) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V75() V76() V77() V78() V79() V80() Element of bool NAT
Sum (<*> NAT) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(<*> NAT) . L is V26() V27() V28() V32() finite cardinal FinSequence-like V45() V46() V47() ext-real non negative set
L is non empty set
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q is Relation-like NAT -defined L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of L
Del (q,p) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
L is non empty set
p is Element of L
q is Element of L
<*p,q*> is Relation-like NAT -defined Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like finite-support set
2 -tuples_on L is functional non empty FinSequence-membered V196() V197() FinSequenceSet of L
L * is functional non empty FinSequence-membered FinSequenceSet of L
{ b₁ where b₁ is Relation-like NAT -defined L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of L * : len b₁ = 2 } is set
L is non empty set
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p -tuples_on L is functional non empty FinSequence-membered V196() V197() FinSequenceSet of L
L * is functional non empty FinSequence-membered FinSequenceSet of L
{ b₁ where b₁ is Relation-like NAT -defined L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of L * : len b₁ = p } is set
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q -tuples_on L is functional non empty FinSequence-membered V196() V197() FinSequenceSet of L
{ b₁ where b₁ is Relation-like NAT -defined L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of L * : len b₁ = q } is set
r is Relation-like NAT -defined L -valued Function-like finite p -element FinSequence-like FinSubsequence-like finite-support Element of p -tuples_on L
p1 is Relation-like NAT -defined L -valued Function-like finite q -element FinSequence-like FinSubsequence-like finite-support Element of q -tuples_on L
r ^ p1 is Relation-like NAT -defined Function-like finite p + q -element FinSequence-like FinSubsequence-like finite-support set
p + q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p + q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p + q) -tuples_on L is functional non empty FinSequence-membered V196() V197() FinSequenceSet of L
{ b₁ where b₁ is Relation-like NAT -defined L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of L * : len b₁ = p + q } is set
r ^ p1 is Relation-like NAT -defined L -valued Function-like finite p + q -element FinSequence-like FinSubsequence-like finite-support FinSequence of L
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L is non empty set
p -tuples_on L is functional non empty FinSequence-membered V196() V197() FinSequenceSet of L
L * is functional non empty FinSequence-membered FinSequenceSet of L
{ b₁ where b₁ is Relation-like NAT -defined L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of L * : len b₁ = p } is set
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q -tuples_on L is functional non empty FinSequence-membered V196() V197() FinSequenceSet of L
{ b₁ where b₁ is Relation-like NAT -defined L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of L * : len b₁ = q } is set
r is Relation-like NAT -defined p -tuples_on L -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of p -tuples_on L
p1 is Relation-like NAT -defined q -tuples_on L -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of q -tuples_on L
r ^^ p1 is Relation-like NAT -defined Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support set
p + q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p + q) -tuples_on L is functional non empty FinSequence-membered V196() V197() FinSequenceSet of L
{ b₁ where b₁ is Relation-like NAT -defined L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of L * : len b₁ = p + q } is set
((p + q) -tuples_on L) * is functional non empty FinSequence-membered FinSequenceSet of (p + q) -tuples_on L
rng (r ^^ p1) is finite set
q1 is set
dom (r ^^ p1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
r1 is set
(r ^^ p1) . r1 is FinSequence-like set
dom r is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
dom p1 is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(dom r) /\ (dom p1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
r . r1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
p1 . r1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(r . r1) ^ (p1 . r1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
r /. r1 is Relation-like NAT -defined L -valued Function-like finite p -element FinSequence-like FinSubsequence-like finite-support Element of p -tuples_on L
(r /. r1) ^ (p1 . r1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
p1 /. r1 is Relation-like NAT -defined L -valued Function-like finite q -element FinSequence-like FinSubsequence-like finite-support Element of q -tuples_on L
(L,p,q,(r /. r1),(p1 /. r1)) is Relation-like NAT -defined L -valued Function-like finite p + q -element p + q -element FinSequence-like FinSubsequence-like finite-support Element of (p + q) -tuples_on L
p + q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
F₁() is non empty set
F₁() * is functional non empty FinSequence-membered FinSequenceSet of F₁()
F₂() is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg F₂() is finite F₂() -element V75() V76() V77() V78() V79() V80() Element of bool NAT
L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
F₃(L) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p is Relation-like NAT -defined F₁() -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of F₁()
len p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom p is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
q is Relation-like NAT -defined F₁() -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of F₁() *
len q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom q is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . r is set
F₄(L,r) is Element of F₁()
L is Relation-like NAT -defined F₁() * -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of F₁() *
dom L is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
len L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L /. p is Relation-like NAT -defined F₁() -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of F₁() *
len (L /. p) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
F₃(p) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (L /. p) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L /. p) . q is set
F₄(p,q) is Element of F₁()
L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
NAT * is functional non empty FinSequence-membered FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = L } is set
Seg L is finite L -element V75() V76() V77() V78() V79() V80() Element of bool NAT
p1 is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
r is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 . q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r . q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r . r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 . r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = L } is set
L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = L } is set
r is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = L } is set
L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = L } is set
p is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
q is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
r is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
Seg L is finite L -element V75() V76() V77() V78() V79() V80() Element of bool NAT
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r . q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
min (p1,q1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r . r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r . p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = L } is set
Seg L is finite L -element V75() V76() V77() V78() V79() V80() Element of bool NAT
L + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L + 1) -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = L + 1 } is set
Seg (L + 1) is non empty finite L + 1 -element L + 1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
L + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p is Relation-like NAT -defined NAT -valued Function-like finite L + 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of (L + 1) -tuples_on NAT
q is Relation-like NAT -defined NAT -valued Function-like finite L + 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of (L + 1) -tuples_on NAT
r is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
<*p1*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V69() V70() V71() V72() V195() finite-support Element of NAT *
r ^ <*p1*> is Relation-like NAT -defined REAL -valued Function-like non empty finite L + 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V195() finite-support FinSequence of NAT
q1 is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
<*r1*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V69() V70() V71() V72() V195() finite-support Element of NAT *
q1 ^ <*r1*> is Relation-like NAT -defined REAL -valued Function-like non empty finite L + 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V195() finite-support FinSequence of NAT
len r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r . p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q1 . p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom r is finite L -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom q1 is finite L -element V75() V76() V77() V78() V79() V80() Element of bool NAT
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r . q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q1 . q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom q1 is finite L -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom r is finite L -element V75() V76() V77() V78() V79() V80() Element of bool NAT
q1 . q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
0 -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = 0 } is set
Seg 0 is Function-like functional empty V26() V27() V28() V30() V31() V32() finite V37() cardinal 0 -element FinSequence-membered V45() V46() V47() ext-real non positive non negative V75() V76() V77() V78() V79() V80() V81() Element of bool NAT
L is Relation-like NAT -defined NAT -valued Function-like one-to-one constant functional empty Function-yielding V26() V27() V28() V30() V31() V32() finite finite-yielding V37() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered V45() V46() V47() ext-real non positive non negative V65() V66() V67() V68() V75() V76() V77() V78() V79() V80() V81() V195() FinSequence-yielding finite-support Element of 0 -tuples_on NAT
p is Relation-like NAT -defined NAT -valued Function-like one-to-one constant functional empty Function-yielding V26() V27() V28() V30() V31() V32() finite finite-yielding V37() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered V45() V46() V47() ext-real non positive non negative V65() V66() V67() V68() V75() V76() V77() V78() V79() V80() V81() V195() FinSequence-yielding finite-support Element of 0 -tuples_on NAT
L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = L } is set
p is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
q is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
Seg L is finite L -element V75() V76() V77() V78() V79() V80() Element of bool NAT
r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = L } is set
[:(L -tuples_on NAT),(L -tuples_on NAT):] is set
bool [:(L -tuples_on NAT),(L -tuples_on NAT):] is set
p is Relation-like L -tuples_on NAT -defined L -tuples_on NAT -valued Element of bool [:(L -tuples_on NAT),(L -tuples_on NAT):]
q is set
r is set
p1 is set
[q,r] is set
{q,r} is finite set
{q} is non empty trivial finite 1 -element set
{{q,r},{q}} is finite V37() set
[r,p1] is set
{r,p1} is finite set
{r} is non empty trivial finite 1 -element set
{{r,p1},{r}} is finite V37() set
[q,p1] is set
{q,p1} is finite set
{{q,p1},{q}} is finite V37() set
q1 is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
r1 is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
p is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
q is set
[q,q] is set
{q,q} is finite set
{q} is non empty trivial finite 1 -element set
{{q,q},{q}} is finite V37() set
r is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
dom p is functional FinSequence-membered Element of bool (L -tuples_on NAT)
bool (L -tuples_on NAT) is set
field p is set
dom p is set
rng p is set
(dom p) \/ (rng p) is set
q is set
r is set
[q,r] is set
{q,r} is finite set
{q} is non empty trivial finite 1 -element set
{{q,r},{q}} is finite V37() set
[r,q] is set
{r,q} is finite set
{r} is non empty trivial finite 1 -element set
{{r,q},{r}} is finite V37() set
p1 is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
q1 is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
q is Relation-like L -tuples_on NAT -defined L -tuples_on NAT -valued total quasi_total reflexive antisymmetric transitive Element of bool [:(L -tuples_on NAT),(L -tuples_on NAT):]
r is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
p1 is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
[r,p1] is set
{r,p1} is functional finite V37() set
{r} is functional non empty trivial finite V37() 1 -element set
{{r,p1},{r}} is finite V37() set
q1 is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
r1 is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
[q1,r1] is set
{q1,r1} is functional finite V37() set
{q1} is functional non empty trivial finite V37() 1 -element set
{{q1,r1},{q1}} is finite V37() set
p is Relation-like L -tuples_on NAT -defined L -tuples_on NAT -valued total quasi_total reflexive antisymmetric transitive Element of bool [:(L -tuples_on NAT),(L -tuples_on NAT):]
q is Relation-like L -tuples_on NAT -defined L -tuples_on NAT -valued total quasi_total reflexive antisymmetric transitive Element of bool [:(L -tuples_on NAT),(L -tuples_on NAT):]
r is set
p1 is set
[r,p1] is set
{r,p1} is finite set
{r} is non empty trivial finite 1 -element set
{{r,p1},{r}} is finite V37() set
q1 is set
r1 is set
[q1,r1] is set
{q1,r1} is finite set
{q1} is non empty trivial finite 1 -element set
{{q1,r1},{q1}} is finite V37() set
p is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
q is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
q1 is set
r1 is set
[q1,r1] is set
{q1,r1} is finite set
{q1} is non empty trivial finite 1 -element set
{{q1,r1},{q1}} is finite V37() set
p is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
q is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L) is Relation-like L -tuples_on NAT -defined L -tuples_on NAT -valued total quasi_total reflexive antisymmetric transitive Element of bool [:(L -tuples_on NAT),(L -tuples_on NAT):]
L -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = L } is set
[:(L -tuples_on NAT),(L -tuples_on NAT):] is set
bool [:(L -tuples_on NAT),(L -tuples_on NAT):] is set
p is set
q is set
[p,q] is set
{p,q} is finite set
{p} is non empty trivial finite 1 -element set
{{p,q},{p}} is finite V37() set
r is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
p1 is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
[q,p] is set
{q,p} is finite set
{q} is non empty trivial finite 1 -element set
{{q,p},{q}} is finite V37() set
field (L) is set
dom (L) is set
rng (L) is set
(dom (L)) \/ (rng (L)) is set
L is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = L } is set
bool (L -tuples_on NAT) is set
(L) is Relation-like L -tuples_on NAT -defined L -tuples_on NAT -valued total quasi_total reflexive antisymmetric transitive being_linear-order Element of bool [:(L -tuples_on NAT),(L -tuples_on NAT):]
[:(L -tuples_on NAT),(L -tuples_on NAT):] is set
bool [:(L -tuples_on NAT),(L -tuples_on NAT):] is set
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r is functional FinSequence-membered Element of bool (L -tuples_on NAT)
L -tuples_on (p + 1) is functional non empty finite FinSequence-membered V196() V197() FinSequenceSet of p + 1
(p + 1) * is functional non empty FinSequence-membered FinSequenceSet of p + 1
{ b₁ where b₁ is Relation-like NAT -defined p + 1 -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (p + 1) * : len b₁ = L } is set
p1 is set
q1 is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
Sum q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
rng q1 is finite V75() V76() V77() V78() V79() V80() Element of bool REAL
r1 is set
{ b₁ where b₁ is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT : not p + 1 <= b₁ } is set
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom q1 is finite L -element V75() V76() V77() V78() V79() V80() Element of bool NAT
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
q1 . q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q is non empty set
L -tuples_on q is functional non empty FinSequence-membered V196() V197() FinSequenceSet of q
q * is functional non empty FinSequence-membered FinSequenceSet of q
{ b₁ where b₁ is Relation-like NAT -defined q -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of q * : len b₁ = L } is set
p1 is functional finite FinSequence-membered Element of bool (L -tuples_on NAT)
SgmX ((L),p1) is Relation-like NAT -defined L -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of L -tuples_on NAT
q is Relation-like NAT -defined L -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of L -tuples_on NAT
r is Relation-like NAT -defined L -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of L -tuples_on NAT
p1 is functional finite FinSequence-membered Element of bool (L -tuples_on NAT)
SgmX ((L),p1) is Relation-like NAT -defined L -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of L -tuples_on NAT
q1 is functional finite FinSequence-membered Element of bool (L -tuples_on NAT)
SgmX ((L),q1) is Relation-like NAT -defined L -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of L -tuples_on NAT
r1 is set
p is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
Sum p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
Sum p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L,p) is Relation-like NAT -defined L -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of L -tuples_on NAT
L -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = L } is set
L -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L -' 1) |-> 0 is Relation-like empty-yielding NAT -defined NAT -valued Function-like finite L -' 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of (L -' 1) -tuples_on NAT
(L -' 1) -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = L -' 1 } is set
Seg (L -' 1) is finite L -' 1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(Seg (L -' 1)) --> 0 is Relation-like Seg (L -' 1) -defined RAT -valued INT -valued {0} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() finite-support Element of bool [:(Seg (L -' 1)),{0}:]
{0} is non empty trivial finite V37() 1 -element V75() V76() V77() V78() V79() V80() set
[:(Seg (L -' 1)),{0}:] is RAT -valued INT -valued finite V65() V66() V67() V68() set
bool [:(Seg (L -' 1)),{0}:] is finite V37() set
(L -' 1) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
<*p*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V69() V70() V71() V72() V195() finite-support Element of NAT *
((L -' 1) |-> 0) ^ <*p*> is Relation-like NAT -defined REAL -valued Function-like non empty finite (L -' 1) + 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V195() finite-support FinSequence of NAT
(L -' 1) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
bool (L -tuples_on NAT) is set
(L) is Relation-like L -tuples_on NAT -defined L -tuples_on NAT -valued total quasi_total reflexive antisymmetric transitive being_linear-order Element of bool [:(L -tuples_on NAT),(L -tuples_on NAT):]
[:(L -tuples_on NAT),(L -tuples_on NAT):] is set
bool [:(L -tuples_on NAT),(L -tuples_on NAT):] is set
p1 is functional finite FinSequence-membered Element of bool (L -tuples_on NAT)
SgmX ((L),p1) is Relation-like NAT -defined L -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of L -tuples_on NAT
r is Relation-like NAT -defined NAT -valued Function-like finite L -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of L -tuples_on NAT
Sum r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V195() finite-support FinSequence of NAT
Sum q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum q) + p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
0 + p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q1 is functional non empty finite FinSequence-membered Element of bool (L -tuples_on NAT)
SgmX ((L),q1) is Relation-like NAT -defined L -tuples_on NAT -valued Function-like one-to-one non empty Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of L -tuples_on NAT
L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(1,L) is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like one-to-one non empty Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 1 -tuples_on NAT
1 -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = 1 } is set
len (1,L) is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
bool (1 -tuples_on NAT) is set
(1) is Relation-like 1 -tuples_on NAT -defined 1 -tuples_on NAT -valued total quasi_total reflexive antisymmetric transitive being_linear-order Element of bool [:(1 -tuples_on NAT),(1 -tuples_on NAT):]
[:(1 -tuples_on NAT),(1 -tuples_on NAT):] is set
bool [:(1 -tuples_on NAT),(1 -tuples_on NAT):] is set
p is functional finite FinSequence-membered Element of bool (1 -tuples_on NAT)
SgmX ((1),p) is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 1 -tuples_on NAT
<*L*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V69() V70() V71() V72() V195() finite-support Element of NAT *
{<*L*>} is functional non empty trivial finite V37() 1 -element set
q is set
r is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V69() V70() V71() V72() V195() finite-support Element of 1 -tuples_on NAT
Sum r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
<*p1*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V69() V70() V71() V72() V195() finite-support Element of NAT *
q is set
Sum <*L*> is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
field (1) is set
dom (1) is set
rng (1) is set
(dom (1)) \/ (rng (1)) is set
card p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(2,L) is Relation-like NAT -defined 2 -tuples_on NAT -valued Function-like one-to-one non empty Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 2 -tuples_on NAT
2 -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = 2 } is set
len (2,L) is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
len p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom p is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Seg L is finite L -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(NAT,0,L) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
<*(NAT,0,L)*> is Relation-like NAT -defined NAT * -valued Function-like constant non empty trivial Function-yielding finite 1 -element FinSequence-like FinSubsequence-like FinSequence-yielding finite-support V214() M42( NAT ,1, len (NAT,0,L))
len (NAT,0,L) is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p ^ <*(NAT,0,L)*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
len (p ^ <*(NAT,0,L)*>) is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (p ^ <*(NAT,0,L)*>) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Seg (L + 1) is non empty finite L + 1 -element L + 1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
L + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r is set
p1 is set
(p ^ <*(NAT,0,L)*>) . r is set
(p ^ <*(NAT,0,L)*>) . p1 is set
{(L + 1)} is non empty trivial finite V37() 1 -element V75() V76() V77() V78() V79() V80() set
(Seg L) \/ {(L + 1)} is finite V75() V76() V77() V78() V79() V80() set
q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p ^ <*(NAT,0,L)*>) . q1 is set
p . q1 is set
r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p ^ <*(NAT,0,L)*>) . r1 is set
p . r1 is set
L -' q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,q1,(L -' q1)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
L -' r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,r1,(L -' r1)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p ^ <*(NAT,0,L)*>) . r1 is set
q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p ^ <*(NAT,0,L)*>) . q1 is set
p . q1 is set
L -' q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,q1,(L -' q1)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p ^ <*(NAT,0,L)*>) . q1 is set
r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p ^ <*(NAT,0,L)*>) . r1 is set
p . r1 is set
L -' r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,r1,(L -' r1)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
rng (p ^ <*(NAT,0,L)*>) is finite set
card (rng (p ^ <*(NAT,0,L)*>)) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
rng p is finite set
{ (NAT,b₁,(L -' b₁)) where b₁ is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT : b₁ <= L } is set
r is set
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
(p ^ <*(NAT,0,L)*>) . p1 is set
q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p ^ <*(NAT,0,L)*>) . q1 is set
p . q1 is set
L -' q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,q1,(L -' q1)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
(p ^ <*(NAT,0,L)*>) . q1 is set
L -' 0 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,0,(L -' 0)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
r is set
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L -' p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,p1,(L -' p1)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
0 + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p ^ <*(NAT,0,L)*>) . (L + 1) is set
p . p1 is set
bool (2 -tuples_on NAT) is set
(2) is Relation-like 2 -tuples_on NAT -defined 2 -tuples_on NAT -valued total quasi_total reflexive antisymmetric transitive being_linear-order Element of bool [:(2 -tuples_on NAT),(2 -tuples_on NAT):]
[:(2 -tuples_on NAT),(2 -tuples_on NAT):] is set
bool [:(2 -tuples_on NAT),(2 -tuples_on NAT):] is set
r is functional finite FinSequence-membered Element of bool (2 -tuples_on NAT)
SgmX ((2),r) is Relation-like NAT -defined 2 -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 2 -tuples_on NAT
p1 is set
q1 is Relation-like NAT -defined NAT -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,r1,p) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
r1 + p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Sum q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L - r1 is V45() V46() V47() ext-real set
L -' r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 is set
q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L -' q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,q1,(L -' q1)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
L - q1 is V45() V46() V47() ext-real set
Sum (NAT,q1,(L -' q1)) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q1 + (L -' q1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q1 + (L - q1) is V45() V46() V47() ext-real set
field (2) is set
dom (2) is set
rng (2) is set
(dom (2)) \/ (rng (2)) is set
L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(1,L) is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like one-to-one non empty Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 1 -tuples_on NAT
1 -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = 1 } is set
<*L*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V69() V70() V71() V72() V195() finite-support Element of NAT *
<*<*L*>*> is Relation-like NAT -defined NAT * -valued Function-like constant non empty trivial Function-yielding finite 1 -element FinSequence-like FinSubsequence-like FinSequence-yielding finite-support V214() M42( NAT ,1, len <*L*>)
len <*L*> is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
bool (1 -tuples_on NAT) is set
(1) is Relation-like 1 -tuples_on NAT -defined 1 -tuples_on NAT -valued total quasi_total reflexive antisymmetric transitive being_linear-order Element of bool [:(1 -tuples_on NAT),(1 -tuples_on NAT):]
[:(1 -tuples_on NAT),(1 -tuples_on NAT):] is set
bool [:(1 -tuples_on NAT),(1 -tuples_on NAT):] is set
p is functional finite FinSequence-membered Element of bool (1 -tuples_on NAT)
SgmX ((1),p) is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 1 -tuples_on NAT
{<*L*>} is functional non empty trivial finite V37() 1 -element set
q is set
r is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V69() V70() V71() V72() V195() finite-support Element of 1 -tuples_on NAT
Sum r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
<*p1*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V69() V70() V71() V72() V195() finite-support Element of NAT *
q is set
Sum <*L*> is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len (1,L) is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (1,L) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
dom <*<*L*>*> is non empty trivial finite 1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
field (1) is set
dom (1) is set
rng (1) is set
(dom (1)) \/ (rng (1)) is set
rng <*<*L*>*> is functional trivial finite FinSequence-membered Element of bool (NAT *)
bool (NAT *) is set
rng (1,L) is functional finite FinSequence-membered Element of bool (1 -tuples_on NAT)
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(2,q) is Relation-like NAT -defined 2 -tuples_on NAT -valued Function-like one-to-one non empty Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 2 -tuples_on NAT
2 -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = 2 } is set
L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(2,q) . L is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q -' r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,r,(q -' r)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(2,q) . p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q -' p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,p1,(q -' p1)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
dom (2,q) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(2,q) /. p is Relation-like NAT -defined NAT -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
bool (2 -tuples_on NAT) is set
(2) is Relation-like 2 -tuples_on NAT -defined 2 -tuples_on NAT -valued total quasi_total reflexive antisymmetric transitive being_linear-order Element of bool [:(2 -tuples_on NAT),(2 -tuples_on NAT):]
[:(2 -tuples_on NAT),(2 -tuples_on NAT):] is set
bool [:(2 -tuples_on NAT),(2 -tuples_on NAT):] is set
q1 is functional finite FinSequence-membered Element of bool (2 -tuples_on NAT)
SgmX ((2),q1) is Relation-like NAT -defined 2 -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 2 -tuples_on NAT
field (2) is set
dom (2) is set
rng (2) is set
(dom (2)) \/ (rng (2)) is set
(2,q) /. L is Relation-like NAT -defined NAT -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
[(NAT,r,(q -' r)),(NAT,p1,(q -' p1))] is set
{(NAT,r,(q -' r)),(NAT,p1,(q -' p1))} is functional finite V37() set
{(NAT,r,(q -' r))} is functional non empty trivial finite V37() 1 -element set
{{(NAT,r,(q -' r)),(NAT,p1,(q -' p1))},{(NAT,r,(q -' r))}} is finite V37() set
r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,p1,(q -' p1)) . r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,r,(q -' r)) . r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,r,(q -' r)) . 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,p1,(q -' p1)) . 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,r,(q -' r)) . r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,p1,(q -' p1)) . r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,r,(q -' r)) . 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,p1,(q -' p1)) . 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
[(NAT,p1,(q -' p1)),(NAT,r,(q -' r))] is set
{(NAT,p1,(q -' p1)),(NAT,r,(q -' r))} is functional finite V37() set
{(NAT,p1,(q -' p1))} is functional non empty trivial finite V37() 1 -element set
{{(NAT,p1,(q -' p1)),(NAT,r,(q -' r))},{(NAT,p1,(q -' p1))}} is finite V37() set
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(2,p) is Relation-like NAT -defined 2 -tuples_on NAT -valued Function-like one-to-one non empty Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 2 -tuples_on NAT
2 -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = 2 } is set
L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(2,p) . L is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p -' q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,q,(p -' q)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
L + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(2,p) . (L + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p -' r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,r,(p -' r)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
q + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L + 0 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
bool (2 -tuples_on NAT) is set
(2) is Relation-like 2 -tuples_on NAT -defined 2 -tuples_on NAT -valued total quasi_total reflexive antisymmetric transitive being_linear-order Element of bool [:(2 -tuples_on NAT),(2 -tuples_on NAT):]
[:(2 -tuples_on NAT),(2 -tuples_on NAT):] is set
bool [:(2 -tuples_on NAT),(2 -tuples_on NAT):] is set
p1 is functional finite FinSequence-membered Element of bool (2 -tuples_on NAT)
SgmX ((2),p1) is Relation-like NAT -defined 2 -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 2 -tuples_on NAT
field (2) is set
dom (2) is set
rng (2) is set
(dom (2)) \/ (rng (2)) is set
rng (2,p) is functional finite FinSequence-membered Element of bool (2 -tuples_on NAT)
Sum (NAT,r,(p -' r)) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r + (p -' r) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (2,p) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
p -' (q + 1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,(q + 1),(p -' (q + 1))) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
Sum (NAT,(q + 1),(p -' (q + 1))) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(q + 1) + (p -' (q + 1)) is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (2,p) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
(2,p) . q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
q + 0 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(2,L) is Relation-like NAT -defined 2 -tuples_on NAT -valued Function-like one-to-one non empty Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 2 -tuples_on NAT
2 -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = 2 } is set
(2,L) . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(NAT,0,L) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
bool (2 -tuples_on NAT) is set
(2) is Relation-like 2 -tuples_on NAT -defined 2 -tuples_on NAT -valued total quasi_total reflexive antisymmetric transitive being_linear-order Element of bool [:(2 -tuples_on NAT),(2 -tuples_on NAT):]
[:(2 -tuples_on NAT),(2 -tuples_on NAT):] is set
bool [:(2 -tuples_on NAT),(2 -tuples_on NAT):] is set
p is functional finite FinSequence-membered Element of bool (2 -tuples_on NAT)
SgmX ((2),p) is Relation-like NAT -defined 2 -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 2 -tuples_on NAT
q is Relation-like NAT -defined NAT -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,r,p1) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
Sum (NAT,r,p1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r + p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,0,L) . 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,r,p1) . 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,0,L) . q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,r,p1) . q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
[(NAT,0,L),q] is set
{(NAT,0,L),q} is functional finite V37() set
{(NAT,0,L)} is functional non empty trivial finite V37() 1 -element set
{{(NAT,0,L),q},{(NAT,0,L)}} is finite V37() set
L + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (L + 1) is non empty finite L + 1 -element L + 1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
L + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len (2,L) is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len (2,L)) is non empty finite len (2,L) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom (2,L) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
field (2) is set
dom (2) is set
rng (2) is set
(dom (2)) \/ (rng (2)) is set
Sum (NAT,0,L) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
0 + L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(SgmX ((2),p)) /. 1 is Relation-like NAT -defined NAT -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (L + 1) is non empty finite L + 1 -element L + 1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
L + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(2,L) is Relation-like NAT -defined 2 -tuples_on NAT -valued Function-like one-to-one non empty Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 2 -tuples_on NAT
2 -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = 2 } is set
(2,L) . p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
p -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L + 1) -' p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,(p -' 1),((L + 1) -' p)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
bool (2 -tuples_on NAT) is set
(2) is Relation-like 2 -tuples_on NAT -defined 2 -tuples_on NAT -valued total quasi_total reflexive antisymmetric transitive being_linear-order Element of bool [:(2 -tuples_on NAT),(2 -tuples_on NAT):]
[:(2 -tuples_on NAT),(2 -tuples_on NAT):] is set
bool [:(2 -tuples_on NAT),(2 -tuples_on NAT):] is set
q is functional finite FinSequence-membered Element of bool (2 -tuples_on NAT)
SgmX ((2),q) is Relation-like NAT -defined 2 -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 2 -tuples_on NAT
field (2) is set
dom (2) is set
rng (2) is set
(dom (2)) \/ (rng (2)) is set
r is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative set
(2,L) . r is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
r -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L + 1) -' r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,(r -' 1),((L + 1) -' r)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
r + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(2,L) . (r + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(r + 1) -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L + 1) -' (r + 1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,((r + 1) -' 1),((L + 1) -' (r + 1))) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
L - r is V45() V46() V47() ext-real set
(L + 1) - (r + 1) is V45() V46() V47() ext-real set
L -' r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
1 - 1 is V45() V46() V47() ext-real set
r - 1 is V45() V46() V47() ext-real set
len (2,L) is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len (2,L)) is non empty finite len (2,L) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom (2,L) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(2,L) /. (r + 1) is Relation-like NAT -defined NAT -valued Function-like finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,q1,r1) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
rng (2,L) is functional finite FinSequence-membered Element of bool (2 -tuples_on NAT)
Sum (NAT,q1,r1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q1 + r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L - q1 is V45() V46() V47() ext-real set
L -' q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L + 1) - r is V45() V46() V47() ext-real set
L - (r - 1) is V45() V46() V47() ext-real set
L - (r -' 1) is V45() V46() V47() ext-real set
L -' (r -' 1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p1 -' 1) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(2,L) . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
1 -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L + 1) -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,(1 -' 1),((L + 1) -' 1)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
(NAT,0,L) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
(NAT,(1 -' 1),L) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
L is non empty multMagma
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
3 -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = 3 } is set
the carrier of L * is functional non empty FinSequence-membered FinSequenceSet of the carrier of L
p1 is Relation-like NAT -defined 3 -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 3 -tuples_on NAT
len p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom p1 is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
r is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q1 is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
len q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom q1 is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Seg (len p1) is finite len p1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
r1 is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of the carrier of L *
len r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 . p is set
p1 /. p is Relation-like NAT -defined NAT -valued Function-like finite 3 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 3 -tuples_on NAT
(p1 /. p) /. 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . ((p1 /. p) /. 1) is Element of the carrier of L
(p1 /. p) /. 2 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . ((p1 /. p) /. 2) is Element of the carrier of L
(p . ((p1 /. p) /. 1)) * (q . ((p1 /. p) /. 2)) is Element of the carrier of L
the multF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is set
the multF of L . ((p . ((p1 /. p) /. 1)),(q . ((p1 /. p) /. 2))) is Element of the carrier of L
(p1 /. p) /. 3 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r . ((p1 /. p) /. 3) is Element of the carrier of L
((p . ((p1 /. p) /. 1)) * (q . ((p1 /. p) /. 2))) * (r . ((p1 /. p) /. 3)) is Element of the carrier of L
the multF of L . (((p . ((p1 /. p) /. 1)) * (q . ((p1 /. p) /. 2))),(r . ((p1 /. p) /. 3))) is Element of the carrier of L
q1 is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of the carrier of L *
len q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of the carrier of L *
len r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom q1 is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Seg (len p1) is finite len p1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
q1 . p is set
p1 /. p is Relation-like NAT -defined NAT -valued Function-like finite 3 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 3 -tuples_on NAT
(p1 /. p) /. 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . ((p1 /. p) /. 1) is Element of the carrier of L
(p1 /. p) /. 2 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . ((p1 /. p) /. 2) is Element of the carrier of L
(p . ((p1 /. p) /. 1)) * (q . ((p1 /. p) /. 2)) is Element of the carrier of L
the multF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is set
the multF of L . ((p . ((p1 /. p) /. 1)),(q . ((p1 /. p) /. 2))) is Element of the carrier of L
(p1 /. p) /. 3 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r . ((p1 /. p) /. 3) is Element of the carrier of L
((p . ((p1 /. p) /. 1)) * (q . ((p1 /. p) /. 2))) * (r . ((p1 /. p) /. 3)) is Element of the carrier of L
the multF of L . (((p . ((p1 /. p) /. 1)) * (q . ((p1 /. p) /. 2))),(r . ((p1 /. p) /. 3))) is Element of the carrier of L
r1 . p is set
L is non empty multMagma
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
r is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p1 is Relation-like NAT -defined 3 -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 3 -tuples_on NAT
dom p1 is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
[:(dom p1),(dom p1):] is RAT -valued INT -valued finite V65() V66() V67() V68() set
bool [:(dom p1),(dom p1):] is finite V37() set
(L,p,q,r,p1) is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of the carrier of L *
the carrier of L * is functional non empty FinSequence-membered FinSequenceSet of the carrier of L
q1 is Relation-like dom p1 -defined dom p1 -valued Function-like one-to-one total quasi_total onto bijective finite V65() V66() V67() V68() finite-support Element of bool [:(dom p1),(dom p1):]
p1 * q1 is Relation-like dom p1 -defined 3 -tuples_on NAT -valued Function-like finite finite-support Element of bool [:(dom p1),(3 -tuples_on NAT):]
[:(dom p1),(3 -tuples_on NAT):] is set
bool [:(dom p1),(3 -tuples_on NAT):] is set
(L,p,q,r,p1) * q1 is Relation-like dom p1 -defined the carrier of L -valued Function-like finite finite-support Element of bool [:(dom p1), the carrier of L:]
[:(dom p1), the carrier of L:] is set
bool [:(dom p1), the carrier of L:] is set
r1 is Relation-like NAT -defined 3 -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 3 -tuples_on NAT
(L,p,q,r,r1) is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of the carrier of L *
rng q1 is finite V75() V76() V77() V78() V79() V80() Element of bool REAL
dom q1 is finite V75() V76() V77() V78() V79() V80() Element of bool (dom p1)
bool (dom p1) is finite V37() set
dom r1 is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
p is set
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L,p,q,r,r1) . q is set
r1 /. q is Relation-like NAT -defined NAT -valued Function-like finite 3 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 3 -tuples_on NAT
(r1 /. q) /. 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . ((r1 /. q) /. 1) is Element of the carrier of L
(r1 /. q) /. 2 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . ((r1 /. q) /. 2) is Element of the carrier of L
(p . ((r1 /. q) /. 1)) * (q . ((r1 /. q) /. 2)) is Element of the carrier of L
the multF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is set
the multF of L . ((p . ((r1 /. q) /. 1)),(q . ((r1 /. q) /. 2))) is Element of the carrier of L
(r1 /. q) /. 3 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r . ((r1 /. q) /. 3) is Element of the carrier of L
((p . ((r1 /. q) /. 1)) * (q . ((r1 /. q) /. 2))) * (r . ((r1 /. q) /. 3)) is Element of the carrier of L
the multF of L . (((p . ((r1 /. q) /. 1)) * (q . ((r1 /. q) /. 2))),(r . ((r1 /. q) /. 3))) is Element of the carrier of L
((L,p,q,r,p1) * q1) . p is set
q1 . p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L,p,q,r,p1) . (q1 . p) is set
q1 . q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 . q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
p1 . (q1 . q) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 /. p is Relation-like NAT -defined NAT -valued Function-like finite 3 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 3 -tuples_on NAT
(L,p,q,r,r1) . p is set
len (L,p,q,r,r1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (L,p,q,r,r1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Seg (len r1) is finite len r1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
len (L,p,q,r,p1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (L,p,q,r,p1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
dom ((L,p,q,r,p1) * q1) is finite V75() V76() V77() V78() V79() V80() Element of bool (dom p1)
L is set
L * is functional non empty FinSequence-membered FinSequenceSet of L
p is Relation-like NAT -defined L * -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of L *
Card p is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p | q is Relation-like NAT -defined L * -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of L *
Card (p | q) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
(Card p) | q is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
Seg q is finite q -element V75() V76() V77() V78() V79() V80() Element of bool NAT
p | (Seg q) is Relation-like NAT -defined L * -valued Function-like finite FinSubsequence-like finite-support Element of bool [:NAT,(L *):]
[:NAT,(L *):] is non trivial non finite set
bool [:NAT,(L *):] is non trivial non finite set
len p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
min (q,(len p)) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (Card (p | q)) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
dom (p | q) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
len (Card (p | q)) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len (p | q) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg r is finite r -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom (Card p) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
dom p is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(Card p) | (Seg q) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite FinSubsequence-like V65() V66() V67() V68() finite-support Element of bool [:NAT,NAT:]
bool [:NAT,NAT:] is non trivial non finite set
len (Card p) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
len ((Card p) | q) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom ((Card p) | q) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Seg (len (p | q)) is finite len (p | q) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(Card (p | q)) . p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p | q) . p1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
card ((p | q) . p1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p | q) /. p1 is Relation-like NAT -defined L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of L *
card ((p | q) /. p1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p /. p1 is Relation-like NAT -defined L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of L *
card (p /. p1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . p1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
card (p . p1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Card p) . p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q1 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
q1 /. p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q1 | q is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
(q1 | q) /. p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((Card p) | q) . p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Card (p | q)) . p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((Card p) | q) . p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len ((Card p) | q) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
min (q,(len (Card p))) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() finite-support FinSequence of REAL
p is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V195() finite-support FinSequence of NAT
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L | q is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() finite-support FinSequence of REAL
p | q is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
L is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V195() finite-support FinSequence of NAT
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L | p is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
Sum (L | p) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L | q is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
Sum (L | q) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
p + r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len (L | q) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p + p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V195() finite-support FinSequence of NAT
len q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V195() finite-support FinSequence of NAT
len r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q1 ^ r1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V195() finite-support FinSequence of NAT
len (L | p) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (L | p) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Seg p is finite p -element V75() V76() V77() V78() V79() V80() Element of bool NAT
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
p is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() finite-support FinSequence of REAL
p | p is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() finite-support FinSequence of REAL
(p | p) /. q is V45() V46() ext-real Element of REAL
L /. q is V45() V46() ext-real Element of REAL
dom q1 is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Seg q is finite q -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom (L | q) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
p | q is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() finite-support FinSequence of REAL
(p | q) /. q is V45() V46() ext-real Element of REAL
(L | p) . q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L | q) . q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q1 . q is V45() V46() ext-real set
Sum q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum q1) + 0 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Sum r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum q1) + (Sum r1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
p + q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V195() finite-support FinSequence of NAT
len r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V195() finite-support FinSequence of NAT
len p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 ^ p is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V195() finite-support FinSequence of NAT
len (L | p) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (L | p) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Seg p is finite p -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom r1 is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
dom L is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
q is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() finite-support FinSequence of REAL
q | p is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() finite-support FinSequence of REAL
(q | p) /. p is V45() V46() ext-real Element of REAL
L /. p is V45() V46() ext-real Element of REAL
(L | p) . p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L . p is V45() V46() ext-real set
r1 . p is V45() V46() ext-real set
Sum r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum r1) + 0 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Sum p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum r1) + (Sum p) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Sum L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L is set
p is Relation-like NAT -defined L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of L
len p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p | (q + 1) is Relation-like NAT -defined L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of L
p | q is Relation-like NAT -defined L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of L
p . (q + 1) is set
<*(p . (q + 1))*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like finite-support set
(p | q) ^ <*(p . (q + 1))*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
L is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() finite-support FinSequence of REAL
len L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L | (p + 1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() finite-support FinSequence of REAL
Sum (L | (p + 1)) is V45() V46() ext-real Element of REAL
L | p is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() finite-support FinSequence of REAL
Sum (L | p) is V45() V46() ext-real Element of REAL
L . (p + 1) is V45() V46() ext-real set
(Sum (L | p)) + (L . (p + 1)) is V45() V46() ext-real set
<*(L . (p + 1))*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like finite-support set
(L | p) ^ <*(L . (p + 1))*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
L is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V195() finite-support FinSequence of NAT
len L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L . (p + 1) is V45() V46() ext-real set
q + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L . (q + 1) is V45() V46() ext-real set
L | p is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
Sum (L | p) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum (L | p)) + r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L | q is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
Sum (L | q) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum (L | q)) + p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() finite-support FinSequence of REAL
q1 | p is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() finite-support FinSequence of REAL
Sum (q1 | p) is V45() V46() ext-real Element of REAL
(Sum (q1 | p)) + (L . (p + 1)) is V45() V46() ext-real set
q1 | q is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() finite-support FinSequence of REAL
Sum (q1 | q) is V45() V46() ext-real Element of REAL
(Sum (q1 | q)) + (L . (q + 1)) is V45() V46() ext-real set
q1 | (p + 1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() finite-support FinSequence of REAL
Sum (q1 | (p + 1)) is V45() V46() ext-real Element of REAL
q1 | (q + 1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() finite-support FinSequence of REAL
Sum (q1 | (q + 1)) is V45() V46() ext-real Element of REAL
L is set
L * is functional non empty FinSequence-membered FinSequenceSet of L
p is set
p * is functional non empty FinSequence-membered FinSequenceSet of p
q is Relation-like NAT -defined L * -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of L *
dom q is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Card q is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
r is Relation-like NAT -defined p * -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of p *
dom r is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Card r is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . p1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom (q . p1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r . q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom (r . q1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
p1 -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Card q) | (p1 -' 1) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
Sum ((Card q) | (p1 -' 1)) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum ((Card q) | (p1 -' 1))) + r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q1 -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Card r) | (q1 -' 1) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
Sum ((Card r) | (q1 -' 1)) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum ((Card r) | (q1 -' 1))) + p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 - 1 is V45() V46() V47() ext-real set
len (q . p1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Card q) . p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p1 -' 1) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Card q) . ((p1 -' 1) + 1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q1 - 1 is V45() V46() V47() ext-real set
dom (Card r) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
len (Card r) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (Card q) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
len (Card q) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(len q) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((len q) + 1) - 1 is V45() V46() V47() ext-real set
len (r . q1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Card r) . q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(q1 -' 1) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Card r) . ((q1 -' 1) + 1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(len r) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((len r) + 1) - 1 is V45() V46() V47() ext-real set
L is non empty ZeroStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
len p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
p . r is set
0. L is V105(L) Element of the carrier of L
the ZeroF of L is Element of the carrier of L
p . r is Element of the carrier of L
F₁() is non empty addLoopStr
the carrier of F₁() is non empty set
[:NAT, the carrier of F₁():] is non trivial non finite set
bool [:NAT, the carrier of F₁():] is non trivial non finite set
F₂() is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
0. F₁() is V105(F₁()) Element of the carrier of F₁()
the ZeroF of F₁() is Element of the carrier of F₁()
L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
F₃(L) is Element of the carrier of F₁()
L is Relation-like NAT -defined the carrier of F₁() -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of F₁():]
L is Relation-like NAT -defined the carrier of F₁() -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of F₁():]
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
L . p is Element of the carrier of F₁()
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
p is Relation-like NAT -defined the carrier of F₁() -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of F₁():]
len p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
p . q is Element of the carrier of F₁()
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . q is Element of the carrier of F₁()
F₃(q) is Element of the carrier of F₁()
L is non empty right_zeroed addLoopStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
p + q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
len p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(len p) + (len q) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
0. L is V105(L) Element of the carrier of L
the ZeroF of L is Element of the carrier of L
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
(p + q) . p1 is set
p . p1 is Element of the carrier of L
(p + q) . p1 is Element of the carrier of L
q . p1 is Element of the carrier of L
(p . p1) + (q . p1) is Element of the carrier of L
the addF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is set
the addF of L . ((p . p1),(q . p1)) is Element of the carrier of L
(0. L) + (0. L) is Element of the carrier of L
the addF of L . ((0. L),(0. L)) is Element of the carrier of L
L is non empty right_zeroed addLoopStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
p + q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
(p + q) . p1 is set
0. L is V105(L) Element of the carrier of L
the ZeroF of L is Element of the carrier of L
p . p1 is Element of the carrier of L
q . p1 is Element of the carrier of L
(p + q) . p1 is Element of the carrier of L
(0. L) + (0. L) is Element of the carrier of L
the addF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is set
the addF of L . ((0. L),(0. L)) is Element of the carrier of L
L is non empty right_zeroed addLoopStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
p + q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
support (p + q) is V75() V76() V77() V78() V79() V80() Element of bool NAT
len (p + q) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Segm (len (p + q)) is V75() V76() V77() V78() V79() V80() Element of bool NAT
support p is V75() V76() V77() V78() V79() V80() Element of bool NAT
len p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Segm (len p) is V75() V76() V77() V78() V79() V80() Element of bool NAT
support q is V75() V76() V77() V78() V79() V80() Element of bool NAT
len q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Segm (len q) is V75() V76() V77() V78() V79() V80() Element of bool NAT
(support p) \/ (support q) is V75() V76() V77() V78() V79() V80() Element of bool NAT
r is set
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
L is non empty Abelian addLoopStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
r is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
r + p1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p1 + r is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(r + p1) . q1 is Element of the carrier of L
r . q1 is Element of the carrier of L
p1 . q1 is Element of the carrier of L
(r . q1) + (p1 . q1) is Element of the carrier of L
the addF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is set
the addF of L . ((r . q1),(p1 . q1)) is Element of the carrier of L
(p1 + r) . q1 is Element of the carrier of L
L is non empty add-associative addLoopStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p + q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
r is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(p + q) + r is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q + r is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p + (q + r) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((p + q) + r) . p1 is Element of the carrier of L
(p + q) . p1 is Element of the carrier of L
r . p1 is Element of the carrier of L
((p + q) . p1) + (r . p1) is Element of the carrier of L
the addF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is set
the addF of L . (((p + q) . p1),(r . p1)) is Element of the carrier of L
p . p1 is Element of the carrier of L
q . p1 is Element of the carrier of L
(p . p1) + (q . p1) is Element of the carrier of L
the addF of L . ((p . p1),(q . p1)) is Element of the carrier of L
((p . p1) + (q . p1)) + (r . p1) is Element of the carrier of L
the addF of L . (((p . p1) + (q . p1)),(r . p1)) is Element of the carrier of L
(q . p1) + (r . p1) is Element of the carrier of L
the addF of L . ((q . p1),(r . p1)) is Element of the carrier of L
(p . p1) + ((q . p1) + (r . p1)) is Element of the carrier of L
the addF of L . ((p . p1),((q . p1) + (r . p1))) is Element of the carrier of L
(q + r) . p1 is Element of the carrier of L
(p . p1) + ((q + r) . p1) is Element of the carrier of L
the addF of L . ((p . p1),((q + r) . p1)) is Element of the carrier of L
(p + (q + r)) . p1 is Element of the carrier of L
L is non empty right_complementable add-associative right_zeroed addLoopStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
- p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
len p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
0. L is V105(L) Element of the carrier of L
the ZeroF of L is Element of the carrier of L
r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
(- p) . r is set
(- p) . r is Element of the carrier of L
p . r is Element of the carrier of L
- (p . r) is Element of the carrier of L
- (0. L) is Element of the carrier of L
L is non empty addLoopStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p - q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
- q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p + (- q) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p - q) . r is set
(p + (- q)) . r is set
(p - q) . r is Element of the carrier of L
p . r is Element of the carrier of L
q . r is Element of the carrier of L
(p . r) - (q . r) is Element of the carrier of L
- (q . r) is Element of the carrier of L
(p . r) + (- (q . r)) is Element of the carrier of L
the addF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is set
the addF of L . ((p . r),(- (q . r))) is Element of the carrier of L
(- q) . r is Element of the carrier of L
(p . r) + ((- q) . r) is Element of the carrier of L
the addF of L . ((p . r),((- q) . r)) is Element of the carrier of L
(p + (- q)) . r is Element of the carrier of L
L is non empty addLoopStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p - q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
- q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p + (- q) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
r is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
L is non empty right_complementable add-associative right_zeroed addLoopStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
p - q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
- q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
p + (- q) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
L is non empty addLoopStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p - q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
- q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p + (- q) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p - q) . r is Element of the carrier of L
p . r is Element of the carrier of L
q . r is Element of the carrier of L
(p . r) - (q . r) is Element of the carrier of L
- (q . r) is Element of the carrier of L
(p . r) + (- (q . r)) is Element of the carrier of L
the addF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is set
the addF of L . ((p . r),(- (q . r))) is Element of the carrier of L
L is non empty ZeroStr
the carrier of L is non empty set
0. L is V105(L) Element of the carrier of L
the ZeroF of L is Element of the carrier of L
NAT --> (0. L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total V30() Element of bool [:NAT, the carrier of L:]
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
L is non empty ZeroStr
(L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
0. L is V105(L) Element of the carrier of L
the ZeroF of L is Element of the carrier of L
NAT --> (0. L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total V30() Element of bool [:NAT, the carrier of L:]
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
(L) . p is set
L is non empty right_zeroed addLoopStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
(L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
0. L is V105(L) Element of the carrier of L
the ZeroF of L is Element of the carrier of L
NAT --> (0. L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total V30() Element of bool [:NAT, the carrier of L:]
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p + (L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p + (L)) . q is Element of the carrier of L
p . q is Element of the carrier of L
(L) . q is Element of the carrier of L
(p . q) + ((L) . q) is Element of the carrier of L
the addF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is set
the addF of L . ((p . q),((L) . q)) is Element of the carrier of L
(p . q) + (0. L) is Element of the carrier of L
the addF of L . ((p . q),(0. L)) is Element of the carrier of L
L is non empty right_complementable add-associative right_zeroed addLoopStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
(L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
0. L is V105(L) Element of the carrier of L
the ZeroF of L is Element of the carrier of L
NAT --> (0. L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total V30() Element of bool [:NAT, the carrier of L:]
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p - p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
- p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p + (- p) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p - p) . q is Element of the carrier of L
p . q is Element of the carrier of L
(p . q) - (p . q) is Element of the carrier of L
- (p . q) is Element of the carrier of L
(p . q) + (- (p . q)) is Element of the carrier of L
the addF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is set
the addF of L . ((p . q),(- (p . q))) is Element of the carrier of L
(L) . q is Element of the carrier of L
L is non empty multLoopStr_0
the carrier of L is non empty set
(L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
0. L is V105(L) Element of the carrier of L
the ZeroF of L is Element of the carrier of L
NAT --> (0. L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total V30() Element of bool [:NAT, the carrier of L:]
1. L is Element of the carrier of L
the OneF of L is Element of the carrier of L
(L) +* (0,(1. L)) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
L is non empty multLoopStr_0
(L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
(L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
0. L is V105(L) Element of the carrier of L
the ZeroF of L is Element of the carrier of L
NAT --> (0. L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total V30() Element of bool [:NAT, the carrier of L:]
1. L is Element of the carrier of L
the OneF of L is Element of the carrier of L
(L) +* (0,(1. L)) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
(L) . p is set
(L) . p is Element of the carrier of L
(L) . p is Element of the carrier of L
L is non empty multLoopStr_0
(L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
(L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
0. L is V105(L) Element of the carrier of L
the ZeroF of L is Element of the carrier of L
NAT --> (0. L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total V30() Element of bool [:NAT, the carrier of L:]
1. L is Element of the carrier of L
the OneF of L is Element of the carrier of L
(L) +* (0,(1. L)) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L) . 0 is Element of the carrier of L
dom (L) is V75() V76() V77() V78() V79() V80() Element of bool NAT
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
(L) . p is Element of the carrier of L
(L) . p is Element of the carrier of L
L is non empty doubleLoopStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
len p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom p1 is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Sum p1 is Element of the carrier of L
q1 is Element of the carrier of L
r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 . r1 is set
r1 -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . (r1 -' 1) is Element of the carrier of L
(r + 1) -' r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . ((r + 1) -' r1) is Element of the carrier of L
(p . (r1 -' 1)) * (q . ((r + 1) -' r1)) is Element of the carrier of L
the multF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is set
the multF of L . ((p . (r1 -' 1)),(q . ((r + 1) -' r1))) is Element of the carrier of L
r is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r . p1 is Element of the carrier of L
r is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q1 + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r . q1 is Element of the carrier of L
r1 is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
len r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Sum r1 is Element of the carrier of L
dom r1 is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
p1 . q1 is Element of the carrier of L
p is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
len p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Sum p is Element of the carrier of L
dom p is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Seg (len p) is finite len p -element V75() V76() V77() V78() V79() V80() Element of bool NAT
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
r1 . q is set
q -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . (q -' 1) is Element of the carrier of L
(q1 + 1) -' q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . ((q1 + 1) -' q) is Element of the carrier of L
(p . (q -' 1)) * (q . ((q1 + 1) -' q)) is Element of the carrier of L
the multF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is set
the multF of L . ((p . (q -' 1)),(q . ((q1 + 1) -' q))) is Element of the carrier of L
p . q is set
L is non empty right_complementable right-distributive left-distributive distributive add-associative right_zeroed doubleLoopStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
(L,p,q) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
len p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(len p) + (len q) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
0. L is V105(L) Element of the carrier of L
the ZeroF of L is Element of the carrier of L
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
(L,p,q) . p1 is set
p1 + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L,p,q) . p1 is Element of the carrier of L
q1 is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
len q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Sum q1 is Element of the carrier of L
dom q1 is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
p1 - (len q) is V45() V46() V47() ext-real set
- (p1 - (len q)) is V45() V46() V47() ext-real set
- (len p) is V45() V46() V47() ext-real non positive set
r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q1 . r1 is set
r1 -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . (r1 -' 1) is Element of the carrier of L
(p1 + 1) -' r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . ((p1 + 1) -' r1) is Element of the carrier of L
(p . (r1 -' 1)) * (q . ((p1 + 1) -' r1)) is Element of the carrier of L
the multF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is set
the multF of L . ((p . (r1 -' 1)),(q . ((p1 + 1) -' r1))) is Element of the carrier of L
(p1 + 1) - r1 is V45() V46() V47() ext-real set
r1 - 1 is V45() V46() V47() ext-real set
- (r1 - 1) is V45() V46() V47() ext-real set
1 - r1 is V45() V46() V47() ext-real set
(len q) - p1 is V45() V46() V47() ext-real set
p1 + (1 - r1) is V45() V46() V47() ext-real set
L is non empty right_complementable right-distributive Abelian add-associative right_zeroed doubleLoopStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
r is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,q,r) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,p,(L,q,r)) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,p,q) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,p,r) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,(L,p,q),(L,p,r)) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L,p,(L,q,r)) . p1 is Element of the carrier of L
q1 is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
len q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Sum q1 is Element of the carrier of L
dom q1 is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Seg (p1 + 1) is non empty finite p1 + 1 -element p1 + 1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
p1 + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L,p,r) . p1 is Element of the carrier of L
r1 is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
len r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Sum r1 is Element of the carrier of L
dom r1 is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(L,p,q) . p1 is Element of the carrier of L
p is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
len p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Sum p is Element of the carrier of L
dom p is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(p1 + 1) -tuples_on the carrier of L is functional non empty FinSequence-membered V196() V197() FinSequenceSet of the carrier of L
the carrier of L * is functional non empty FinSequence-membered FinSequenceSet of the carrier of L
{ b₁ where b₁ is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of the carrier of L * : len b₁ = p1 + 1 } is set
q is Relation-like NAT -defined the carrier of L -valued Function-like finite p1 + 1 -element FinSequence-like FinSubsequence-like finite-support Element of (p1 + 1) -tuples_on the carrier of L
p is Relation-like NAT -defined the carrier of L -valued Function-like finite p1 + 1 -element FinSequence-like FinSubsequence-like finite-support Element of (p1 + 1) -tuples_on the carrier of L
q + p is Relation-like NAT -defined the carrier of L -valued Function-like finite p1 + 1 -element FinSequence-like FinSubsequence-like finite-support Element of (p1 + 1) -tuples_on the carrier of L
len (q + p) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
p + r1 is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
dom (p + r1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
r1 . q is set
q -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . (q -' 1) is Element of the carrier of L
(p1 + 1) -' q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r . ((p1 + 1) -' q) is Element of the carrier of L
(p . (q -' 1)) * (r . ((p1 + 1) -' q)) is Element of the carrier of L
the multF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is set
the multF of L . ((p . (q -' 1)),(r . ((p1 + 1) -' q))) is Element of the carrier of L
p . q is set
q . ((p1 + 1) -' q) is Element of the carrier of L
(p . (q -' 1)) * (q . ((p1 + 1) -' q)) is Element of the carrier of L
the multF of L . ((p . (q -' 1)),(q . ((p1 + 1) -' q))) is Element of the carrier of L
q1 . q is set
(L,q,r) . ((p1 + 1) -' q) is Element of the carrier of L
(p . (q -' 1)) * ((L,q,r) . ((p1 + 1) -' q)) is Element of the carrier of L
the multF of L . ((p . (q -' 1)),((L,q,r) . ((p1 + 1) -' q))) is Element of the carrier of L
(q . ((p1 + 1) -' q)) + (r . ((p1 + 1) -' q)) is Element of the carrier of L
the addF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
the addF of L . ((q . ((p1 + 1) -' q)),(r . ((p1 + 1) -' q))) is Element of the carrier of L
(p . (q -' 1)) * ((q . ((p1 + 1) -' q)) + (r . ((p1 + 1) -' q))) is Element of the carrier of L
the multF of L . ((p . (q -' 1)),((q . ((p1 + 1) -' q)) + (r . ((p1 + 1) -' q)))) is Element of the carrier of L
((p . (q -' 1)) * (q . ((p1 + 1) -' q))) + ((p . (q -' 1)) * (r . ((p1 + 1) -' q))) is Element of the carrier of L
the addF of L . (((p . (q -' 1)) * (q . ((p1 + 1) -' q))),((p . (q -' 1)) * (r . ((p1 + 1) -' q)))) is Element of the carrier of L
(p + r1) . q is set
Sum (q + p) is Element of the carrier of L
(Sum p) + (Sum r1) is Element of the carrier of L
the addF of L . ((Sum p),(Sum r1)) is Element of the carrier of L
(L,(L,p,q),(L,p,r)) . p1 is Element of the carrier of L
L is non empty right_complementable left-distributive Abelian add-associative right_zeroed doubleLoopStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,p,q) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
r is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,(L,p,q),r) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,p,r) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,q,r) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,(L,p,r),(L,q,r)) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L,(L,p,q),r) . p1 is Element of the carrier of L
q1 is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
len q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Sum q1 is Element of the carrier of L
dom q1 is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Seg (p1 + 1) is non empty finite p1 + 1 -element p1 + 1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
p1 + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L,q,r) . p1 is Element of the carrier of L
r1 is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
len r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Sum r1 is Element of the carrier of L
dom r1 is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(L,p,r) . p1 is Element of the carrier of L
p is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
len p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Sum p is Element of the carrier of L
dom p is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(p1 + 1) -tuples_on the carrier of L is functional non empty FinSequence-membered V196() V197() FinSequenceSet of the carrier of L
the carrier of L * is functional non empty FinSequence-membered FinSequenceSet of the carrier of L
{ b₁ where b₁ is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of the carrier of L * : len b₁ = p1 + 1 } is set
q is Relation-like NAT -defined the carrier of L -valued Function-like finite p1 + 1 -element FinSequence-like FinSubsequence-like finite-support Element of (p1 + 1) -tuples_on the carrier of L
p is Relation-like NAT -defined the carrier of L -valued Function-like finite p1 + 1 -element FinSequence-like FinSubsequence-like finite-support Element of (p1 + 1) -tuples_on the carrier of L
q + p is Relation-like NAT -defined the carrier of L -valued Function-like finite p1 + 1 -element FinSequence-like FinSubsequence-like finite-support Element of (p1 + 1) -tuples_on the carrier of L
len (q + p) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
p + r1 is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
dom (p + r1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
r1 . q is set
q -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . (q -' 1) is Element of the carrier of L
(p1 + 1) -' q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r . ((p1 + 1) -' q) is Element of the carrier of L
(q . (q -' 1)) * (r . ((p1 + 1) -' q)) is Element of the carrier of L
the multF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is set
the multF of L . ((q . (q -' 1)),(r . ((p1 + 1) -' q))) is Element of the carrier of L
p . q is set
p . (q -' 1) is Element of the carrier of L
(p . (q -' 1)) * (r . ((p1 + 1) -' q)) is Element of the carrier of L
the multF of L . ((p . (q -' 1)),(r . ((p1 + 1) -' q))) is Element of the carrier of L
q1 . q is set
(L,p,q) . (q -' 1) is Element of the carrier of L
((L,p,q) . (q -' 1)) * (r . ((p1 + 1) -' q)) is Element of the carrier of L
the multF of L . (((L,p,q) . (q -' 1)),(r . ((p1 + 1) -' q))) is Element of the carrier of L
(p . (q -' 1)) + (q . (q -' 1)) is Element of the carrier of L
the addF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
the addF of L . ((p . (q -' 1)),(q . (q -' 1))) is Element of the carrier of L
((p . (q -' 1)) + (q . (q -' 1))) * (r . ((p1 + 1) -' q)) is Element of the carrier of L
the multF of L . (((p . (q -' 1)) + (q . (q -' 1))),(r . ((p1 + 1) -' q))) is Element of the carrier of L
((p . (q -' 1)) * (r . ((p1 + 1) -' q))) + ((q . (q -' 1)) * (r . ((p1 + 1) -' q))) is Element of the carrier of L
the addF of L . (((p . (q -' 1)) * (r . ((p1 + 1) -' q))),((q . (q -' 1)) * (r . ((p1 + 1) -' q)))) is Element of the carrier of L
(p + r1) . q is set
Sum (q + p) is Element of the carrier of L
(Sum p) + (Sum r1) is Element of the carrier of L
the addF of L . ((Sum p),(Sum r1)) is Element of the carrier of L
(L,(L,p,r),(L,q,r)) . p1 is Element of the carrier of L
L is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
<*L*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like finite-support set
1 -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = 1 } is set
<*L*> is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V69() V70() V71() V72() V195() finite-support Element of NAT *
L is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,p,q) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
r is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,(L,p,q),r) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,q,r) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,p,(L,q,r)) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
2 + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(2 + 1) -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = 2 + 1 } is set
((2 + 1) -tuples_on NAT) * is functional non empty FinSequence-membered FinSequenceSet of (2 + 1) -tuples_on NAT
q1 is Relation-like NAT -defined ((2 + 1) -tuples_on NAT) * -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of ((2 + 1) -tuples_on NAT) *
len q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom q1 is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Seg (p1 + 1) is non empty finite p1 + 1 -element p1 + 1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
p1 + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(3 -tuples_on NAT) * is functional non empty FinSequence-membered FinSequenceSet of 3 -tuples_on NAT
p1 + 2 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
1 + 2 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(1 + 2) -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = 1 + 2 } is set
((1 + 2) -tuples_on NAT) * is functional non empty FinSequence-membered FinSequenceSet of (1 + 2) -tuples_on NAT
p is Relation-like NAT -defined ((1 + 2) -tuples_on NAT) * -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of ((1 + 2) -tuples_on NAT) *
len p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom p is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(L,p,(L,q,r)) . p1 is Element of the carrier of L
p is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
len p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Sum p is Element of the carrier of L
dom p is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
r1 is Relation-like NAT -defined (3 -tuples_on NAT) * -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of (3 -tuples_on NAT) *
Card r1 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
dom (Card r1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
dom r1 is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
q is Relation-like NAT -defined (3 -tuples_on NAT) * -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of (3 -tuples_on NAT) *
len q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len q) is finite len q -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom q is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Card q is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
dom (Card q) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Rev (Card q) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
dom (Rev (Card q)) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
(p1 + 1) -' q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(((p1 + 1) -' q)) is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V69() V70() V71() V72() V195() finite-support Element of 1 -tuples_on NAT
q |-> (((p1 + 1) -' q)) is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like Function-yielding finite q -element FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of q -tuples_on (1 -tuples_on NAT)
q -tuples_on (1 -tuples_on NAT) is functional non empty FinSequence-membered V196() V197() FinSequenceSet of 1 -tuples_on NAT
(1 -tuples_on NAT) * is functional non empty FinSequence-membered FinSequenceSet of 1 -tuples_on NAT
{ b₁ where b₁ is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (1 -tuples_on NAT) * : len b₁ = q } is set
Seg q is finite q -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(Seg q) --> (((p1 + 1) -' q)) is Relation-like Seg q -defined {(((p1 + 1) -' q))} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like finite-support Element of bool [:(Seg q),{(((p1 + 1) -' q))}:]
{(((p1 + 1) -' q))} is functional non empty trivial finite V37() 1 -element set
[:(Seg q),{(((p1 + 1) -' q))}:] is finite set
bool [:(Seg q),{(((p1 + 1) -' q))}:] is finite V37() set
dom (q |-> (((p1 + 1) -' q))) is finite q -element V75() V76() V77() V78() V79() V80() Element of bool NAT
len (Rev (Card q)) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len (Rev (Card q))) is finite len (Rev (Card q)) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
q - 1 is V45() V46() V47() ext-real set
(p1 + 1) - (q - 1) is V45() V46() V47() ext-real set
len (Card q) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 . q is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
q -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(2,(q -' 1)) is Relation-like NAT -defined 2 -tuples_on NAT -valued Function-like one-to-one non empty Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 2 -tuples_on NAT
2 -tuples_on NAT is functional non empty FinSequence-membered V196() V197() FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of NAT * : len b₁ = 2 } is set
(NAT,2,1,(2,(q -' 1)),(q |-> (((p1 + 1) -' q)))) is Relation-like NAT -defined (2 + 1) -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of ((2 + 1) -tuples_on NAT) *
(p1 + 1) - q is V45() V46() V47() ext-real set
((p1 + 1) - q) + 1 is V45() V46() V47() ext-real set
((p1 + 1) -' q) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(len (Card q)) - q is V45() V46() V47() ext-real set
((len (Card q)) - q) + 1 is V45() V46() V47() ext-real set
(p1 + 1) - (((p1 + 1) - q) + 1) is V45() V46() V47() ext-real set
0 + (q - 1) is V45() V46() V47() ext-real set
P is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p1 + 1) -' P is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((p1 + 1) -' P) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(0 + (q - 1)) + 1 is V45() V46() V47() ext-real set
0 + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . P is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(p1 + 2) -' P is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
P -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((P -' 1)) is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V69() V70() V71() V72() V195() finite-support Element of 1 -tuples_on NAT
((p1 + 2) -' P) |-> ((P -' 1)) is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like Function-yielding finite (p1 + 2) -' P -element FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of ((p1 + 2) -' P) -tuples_on (1 -tuples_on NAT)
((p1 + 2) -' P) -tuples_on (1 -tuples_on NAT) is functional non empty FinSequence-membered V196() V197() FinSequenceSet of 1 -tuples_on NAT
{ b₁ where b₁ is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (1 -tuples_on NAT) * : len b₁ = (p1 + 2) -' P } is set
Seg ((p1 + 2) -' P) is finite (p1 + 2) -' P -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(Seg ((p1 + 2) -' P)) --> ((P -' 1)) is Relation-like Seg ((p1 + 2) -' P) -defined {((P -' 1))} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like finite-support Element of bool [:(Seg ((p1 + 2) -' P)),{((P -' 1))}:]
{((P -' 1))} is functional non empty trivial finite V37() 1 -element set
[:(Seg ((p1 + 2) -' P)),{((P -' 1))}:] is finite set
bool [:(Seg ((p1 + 2) -' P)),{((P -' 1))}:] is finite V37() set
(2,((p1 + 1) -' P)) is Relation-like NAT -defined 2 -tuples_on NAT -valued Function-like one-to-one non empty Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 2 -tuples_on NAT
(NAT,1,2,(((p1 + 2) -' P) |-> ((P -' 1))),(2,((p1 + 1) -' P))) is Relation-like NAT -defined (1 + 2) -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of ((1 + 2) -tuples_on NAT) *
(p1 + 1) - P is V45() V46() V47() ext-real set
((p1 + 1) - P) + 1 is V45() V46() V47() ext-real set
1 + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p1 + (1 + 1) is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p1 + (1 + 1)) - P is V45() V46() V47() ext-real set
dom (((p1 + 2) -' P) |-> ((P -' 1))) is finite (p1 + 2) -' P -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom (2,((p1 + 1) -' P)) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
len (2,((p1 + 1) -' P)) is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len (2,((p1 + 1) -' P))) is non empty finite len (2,((p1 + 1) -' P)) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
len (q . P) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len (q . P)) is finite len (q . P) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom (q . P) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(Seg q) /\ (Seg q) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
dom (2,(q -' 1)) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
len (2,(q -' 1)) is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len (2,(q -' 1))) is non empty finite len (2,(q -' 1)) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(q -' 1) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg ((q -' 1) + 1) is non empty finite (q -' 1) + 1 -element (q -' 1) + 1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(q -' 1) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len (r1 . q) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len (r1 . q)) is finite len (r1 . q) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom (r1 . q) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(Card r1) . q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Card q) . (((len (Card q)) - q) + 1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Rev (Card q)) . q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len (Card r1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
FlattenSeq r1 is Relation-like NAT -defined 3 -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of (3 -tuples_on NAT) *
len (FlattenSeq r1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len (FlattenSeq r1)) is finite len (FlattenSeq r1) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom (FlattenSeq r1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
P is set
rng (FlattenSeq r1) is functional finite FinSequence-membered Element of bool (3 -tuples_on NAT)
bool (3 -tuples_on NAT) is set
FlattenSeq q is Relation-like NAT -defined 3 -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of (3 -tuples_on NAT) *
rng (FlattenSeq q) is functional finite FinSequence-membered Element of bool (3 -tuples_on NAT)
r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
(FlattenSeq r1) . r1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
f1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
g1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom (r1 . f1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
f1 -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 | (f1 -' 1) is Relation-like NAT -defined (3 -tuples_on NAT) * -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of (3 -tuples_on NAT) *
Card (r1 | (f1 -' 1)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
Sum (Card (r1 | (f1 -' 1))) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum (Card (r1 | (f1 -' 1)))) + g1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(r1 . f1) . g1 is set
(2,(f1 -' 1)) is Relation-like NAT -defined 2 -tuples_on NAT -valued Function-like one-to-one non empty Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 2 -tuples_on NAT
(p1 + 1) -' f1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(((p1 + 1) -' f1)) is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V69() V70() V71() V72() V195() finite-support Element of 1 -tuples_on NAT
f1 |-> (((p1 + 1) -' f1)) is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like Function-yielding finite f1 -element FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of f1 -tuples_on (1 -tuples_on NAT)
f1 -tuples_on (1 -tuples_on NAT) is functional non empty FinSequence-membered V196() V197() FinSequenceSet of 1 -tuples_on NAT
{ b₁ where b₁ is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (1 -tuples_on NAT) * : len b₁ = f1 } is set
Seg f1 is finite f1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(Seg f1) --> (((p1 + 1) -' f1)) is Relation-like Seg f1 -defined {(((p1 + 1) -' f1))} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like finite-support Element of bool [:(Seg f1),{(((p1 + 1) -' f1))}:]
{(((p1 + 1) -' f1))} is functional non empty trivial finite V37() 1 -element set
[:(Seg f1),{(((p1 + 1) -' f1))}:] is finite set
bool [:(Seg f1),{(((p1 + 1) -' f1))}:] is finite V37() set
(NAT,2,1,(2,(f1 -' 1)),(f1 |-> (((p1 + 1) -' f1)))) is Relation-like NAT -defined (2 + 1) -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of ((2 + 1) -tuples_on NAT) *
dom (2,(f1 -' 1)) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
dom (f1 |-> (((p1 + 1) -' f1))) is finite f1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(dom (2,(f1 -' 1))) /\ (dom (f1 |-> (((p1 + 1) -' f1)))) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
f1 - g1 is V45() V46() V47() ext-real set
f1 -' g1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(f1 -' g1) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p1 + 2) -' g1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
g1 -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((g1 -' 1)) is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V69() V70() V71() V72() V195() finite-support Element of 1 -tuples_on NAT
((p1 + 2) -' g1) |-> ((g1 -' 1)) is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like Function-yielding finite (p1 + 2) -' g1 -element FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of ((p1 + 2) -' g1) -tuples_on (1 -tuples_on NAT)
((p1 + 2) -' g1) -tuples_on (1 -tuples_on NAT) is functional non empty FinSequence-membered V196() V197() FinSequenceSet of 1 -tuples_on NAT
{ b₁ where b₁ is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (1 -tuples_on NAT) * : len b₁ = (p1 + 2) -' g1 } is set
Seg ((p1 + 2) -' g1) is finite (p1 + 2) -' g1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(Seg ((p1 + 2) -' g1)) --> ((g1 -' 1)) is Relation-like Seg ((p1 + 2) -' g1) -defined {((g1 -' 1))} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like finite-support Element of bool [:(Seg ((p1 + 2) -' g1)),{((g1 -' 1))}:]
{((g1 -' 1))} is functional non empty trivial finite V37() 1 -element set
[:(Seg ((p1 + 2) -' g1)),{((g1 -' 1))}:] is finite set
bool [:(Seg ((p1 + 2) -' g1)),{((g1 -' 1))}:] is finite V37() set
dom (((p1 + 2) -' g1) |-> ((g1 -' 1))) is finite (p1 + 2) -' g1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(f1 -' 1) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg ((f1 -' 1) + 1) is non empty finite (f1 -' 1) + 1 -element (f1 -' 1) + 1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(f1 -' 1) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p1 + 1) - f1 is V45() V46() V47() ext-real set
(p1 + 1) - g1 is V45() V46() V47() ext-real set
(p1 + 1) -' g1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((p1 + 1) -' g1) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((p1 + 1) - g1) + 1 is V45() V46() V47() ext-real set
(p1 + (1 + 1)) - g1 is V45() V46() V47() ext-real set
(((p1 + 1) -' g1) + 1) - ((f1 -' g1) + 1) is V45() V46() V47() ext-real set
(((p1 + 1) -' g1) + 1) -' ((f1 -' g1) + 1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(f1 - g1) + 1 is V45() V46() V47() ext-real set
(((p1 + 1) -' g1) + 1) - ((f1 - g1) + 1) is V45() V46() V47() ext-real set
1 - g1 is V45() V46() V47() ext-real set
(1 - g1) + f1 is V45() V46() V47() ext-real set
(((p1 + 1) - g1) + 1) - ((1 - g1) + f1) is V45() V46() V47() ext-real set
q . g1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(2,((p1 + 1) -' g1)) is Relation-like NAT -defined 2 -tuples_on NAT -valued Function-like one-to-one non empty Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 2 -tuples_on NAT
(NAT,1,2,(((p1 + 2) -' g1) |-> ((g1 -' 1))),(2,((p1 + 1) -' g1))) is Relation-like NAT -defined (1 + 2) -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of ((1 + 2) -tuples_on NAT) *
Seg (((p1 + 1) -' g1) + 1) is non empty finite ((p1 + 1) -' g1) + 1 -element ((p1 + 1) -' g1) + 1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
((p1 + 1) -' g1) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (2,((p1 + 1) -' g1)) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
len (2,((p1 + 1) -' g1)) is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len (2,((p1 + 1) -' g1))) is non empty finite len (2,((p1 + 1) -' g1)) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom (q . g1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(Seg ((p1 + 2) -' g1)) /\ (Seg ((p1 + 2) -' g1)) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(q . g1) . ((f1 -' g1) + 1) is set
(((p1 + 2) -' g1) |-> ((g1 -' 1))) . ((f1 -' g1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(2,((p1 + 1) -' g1)) . ((f1 -' g1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((((p1 + 2) -' g1) |-> ((g1 -' 1))) . ((f1 -' g1) + 1)) ^ ((2,((p1 + 1) -' g1)) . ((f1 -' g1) + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((g1 -' 1)) ^ ((2,((p1 + 1) -' g1)) . ((f1 -' g1) + 1)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
((f1 -' g1) + 1) -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,(((f1 -' g1) + 1) -' 1),((((p1 + 1) -' g1) + 1) -' ((f1 -' g1) + 1))) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
(NAT,1,2,((g1 -' 1)),(NAT,(((f1 -' g1) + 1) -' 1),((((p1 + 1) -' g1) + 1) -' ((f1 -' g1) + 1)))) is Relation-like NAT -defined NAT -valued Function-like non empty finite 1 + 2 -element 1 + 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of (1 + 2) -tuples_on NAT
1 + 2 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
<*(g1 -' 1),(((f1 -' g1) + 1) -' 1),((((p1 + 1) -' g1) + 1) -' ((f1 -' g1) + 1))*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like finite-support set
<*(g1 -' 1),(f1 -' g1),((p1 + 1) -' f1)*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like finite-support set
q | (g1 -' 1) is Relation-like NAT -defined (3 -tuples_on NAT) * -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of (3 -tuples_on NAT) *
Card (q | (g1 -' 1)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
Sum (Card (q | (g1 -' 1))) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum (Card (q | (g1 -' 1)))) + ((f1 -' g1) + 1) is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (FlattenSeq q) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(FlattenSeq q) . ((Sum (Card (q | (g1 -' 1)))) + ((f1 -' g1) + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(2,(f1 -' 1)) . g1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(f1 |-> (((p1 + 1) -' f1))) . g1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((2,(f1 -' 1)) . g1) ^ ((f1 |-> (((p1 + 1) -' f1))) . g1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((2,(f1 -' 1)) . g1) ^ (((p1 + 1) -' f1)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
((f1 -' 1) + 1) -' g1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,(g1 -' 1),(((f1 -' 1) + 1) -' g1)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
(NAT,2,1,(NAT,(g1 -' 1),(((f1 -' 1) + 1) -' g1)),(((p1 + 1) -' f1))) is Relation-like NAT -defined NAT -valued Function-like non empty finite 2 + 1 -element 2 + 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of (2 + 1) -tuples_on NAT
2 + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,(g1 -' 1),(f1 -' g1)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
(NAT,2,1,(NAT,(g1 -' 1),(f1 -' g1)),(((p1 + 1) -' f1))) is Relation-like NAT -defined NAT -valued Function-like non empty finite 2 + 1 -element 2 + 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of (2 + 1) -tuples_on NAT
dom (FlattenSeq q) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
(FlattenSeq q) . r1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
f1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
g1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom (q . f1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
f1 -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q | (f1 -' 1) is Relation-like NAT -defined (3 -tuples_on NAT) * -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of (3 -tuples_on NAT) *
Card (q | (f1 -' 1)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
Sum (Card (q | (f1 -' 1))) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum (Card (q | (f1 -' 1)))) + g1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(q . f1) . g1 is set
(p1 + 2) -' f1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((f1 -' 1)) is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V69() V70() V71() V72() V195() finite-support Element of 1 -tuples_on NAT
((p1 + 2) -' f1) |-> ((f1 -' 1)) is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like Function-yielding finite (p1 + 2) -' f1 -element FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of ((p1 + 2) -' f1) -tuples_on (1 -tuples_on NAT)
((p1 + 2) -' f1) -tuples_on (1 -tuples_on NAT) is functional non empty FinSequence-membered V196() V197() FinSequenceSet of 1 -tuples_on NAT
{ b₁ where b₁ is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (1 -tuples_on NAT) * : len b₁ = (p1 + 2) -' f1 } is set
Seg ((p1 + 2) -' f1) is finite (p1 + 2) -' f1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(Seg ((p1 + 2) -' f1)) --> ((f1 -' 1)) is Relation-like Seg ((p1 + 2) -' f1) -defined {((f1 -' 1))} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like finite-support Element of bool [:(Seg ((p1 + 2) -' f1)),{((f1 -' 1))}:]
{((f1 -' 1))} is functional non empty trivial finite V37() 1 -element set
[:(Seg ((p1 + 2) -' f1)),{((f1 -' 1))}:] is finite set
bool [:(Seg ((p1 + 2) -' f1)),{((f1 -' 1))}:] is finite V37() set
(p1 + 1) -' f1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(2,((p1 + 1) -' f1)) is Relation-like NAT -defined 2 -tuples_on NAT -valued Function-like one-to-one non empty Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 2 -tuples_on NAT
(NAT,1,2,(((p1 + 2) -' f1) |-> ((f1 -' 1))),(2,((p1 + 1) -' f1))) is Relation-like NAT -defined (1 + 2) -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of ((1 + 2) -tuples_on NAT) *
dom (((p1 + 2) -' f1) |-> ((f1 -' 1))) is finite (p1 + 2) -' f1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom (2,((p1 + 1) -' f1)) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(dom (((p1 + 2) -' f1) |-> ((f1 -' 1)))) /\ (dom (2,((p1 + 1) -' f1))) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
g1 - 1 is V45() V46() V47() ext-real set
(p1 + 1) - f1 is V45() V46() V47() ext-real set
((p1 + 1) -' f1) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((p1 + 1) - f1) + 1 is V45() V46() V47() ext-real set
(p1 + (1 + 1)) - f1 is V45() V46() V47() ext-real set
Seg (((p1 + 1) -' f1) + 1) is non empty finite ((p1 + 1) -' f1) + 1 -element ((p1 + 1) -' f1) + 1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
((p1 + 1) -' f1) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(((p1 + 1) -' f1) + 1) - g1 is V45() V46() V47() ext-real set
(g1 - 1) + f1 is V45() V46() V47() ext-real set
g1 -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(g1 -' 1) + f1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p1 + 1) - ((g1 - 1) + f1) is V45() V46() V47() ext-real set
(p1 + 1) - ((g1 -' 1) + f1) is V45() V46() V47() ext-real set
(p1 + 1) -' ((g1 -' 1) + f1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(((p1 + 1) - f1) + 1) - g1 is V45() V46() V47() ext-real set
(((p1 + 1) -' f1) + 1) -' g1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(((p1 + 2) -' f1) |-> ((f1 -' 1))) . g1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(2,((p1 + 1) -' f1)) . g1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((((p1 + 2) -' f1) |-> ((f1 -' 1))) . g1) ^ ((2,((p1 + 1) -' f1)) . g1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((f1 -' 1)) ^ ((2,((p1 + 1) -' f1)) . g1) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
(NAT,(g1 -' 1),((((p1 + 1) -' f1) + 1) -' g1)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
(NAT,1,2,((f1 -' 1)),(NAT,(g1 -' 1),((((p1 + 1) -' f1) + 1) -' g1))) is Relation-like NAT -defined NAT -valued Function-like non empty finite 1 + 2 -element 1 + 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of (1 + 2) -tuples_on NAT
1 + 2 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
<*(f1 -' 1),(g1 -' 1),((((p1 + 1) -' f1) + 1) -' g1)*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like finite-support set
(((p1 + 1) -' ((g1 -' 1) + f1))) is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V69() V70() V71() V72() V195() finite-support Element of 1 -tuples_on NAT
((g1 -' 1) + f1) |-> (((p1 + 1) -' ((g1 -' 1) + f1))) is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like Function-yielding finite (g1 -' 1) + f1 -element FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of ((g1 -' 1) + f1) -tuples_on (1 -tuples_on NAT)
((g1 -' 1) + f1) -tuples_on (1 -tuples_on NAT) is functional non empty FinSequence-membered V196() V197() FinSequenceSet of 1 -tuples_on NAT
{ b₁ where b₁ is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (1 -tuples_on NAT) * : len b₁ = (g1 -' 1) + f1 } is set
Seg ((g1 -' 1) + f1) is finite (g1 -' 1) + f1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(Seg ((g1 -' 1) + f1)) --> (((p1 + 1) -' ((g1 -' 1) + f1))) is Relation-like Seg ((g1 -' 1) + f1) -defined {(((p1 + 1) -' ((g1 -' 1) + f1)))} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like finite-support Element of bool [:(Seg ((g1 -' 1) + f1)),{(((p1 + 1) -' ((g1 -' 1) + f1)))}:]
{(((p1 + 1) -' ((g1 -' 1) + f1)))} is functional non empty trivial finite V37() 1 -element set
[:(Seg ((g1 -' 1) + f1)),{(((p1 + 1) -' ((g1 -' 1) + f1)))}:] is finite set
bool [:(Seg ((g1 -' 1) + f1)),{(((p1 + 1) -' ((g1 -' 1) + f1)))}:] is finite V37() set
dom (((g1 -' 1) + f1) |-> (((p1 + 1) -' ((g1 -' 1) + f1)))) is finite (g1 -' 1) + f1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
((g1 -' 1) + f1) -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(((g1 -' 1) + f1) -' 1) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg ((((g1 -' 1) + f1) -' 1) + 1) is non empty finite (((g1 -' 1) + f1) -' 1) + 1 -element (((g1 -' 1) + f1) -' 1) + 1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(((g1 -' 1) + f1) -' 1) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 . ((g1 -' 1) + f1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(2,(((g1 -' 1) + f1) -' 1)) is Relation-like NAT -defined 2 -tuples_on NAT -valued Function-like one-to-one non empty Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 2 -tuples_on NAT
(NAT,2,1,(2,(((g1 -' 1) + f1) -' 1)),(((g1 -' 1) + f1) |-> (((p1 + 1) -' ((g1 -' 1) + f1))))) is Relation-like NAT -defined (2 + 1) -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of ((2 + 1) -tuples_on NAT) *
dom (2,(((g1 -' 1) + f1) -' 1)) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
len (2,(((g1 -' 1) + f1) -' 1)) is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len (2,(((g1 -' 1) + f1) -' 1))) is non empty finite len (2,(((g1 -' 1) + f1) -' 1)) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom (r1 . ((g1 -' 1) + f1)) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(Seg ((g1 -' 1) + f1)) /\ (Seg ((g1 -' 1) + f1)) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
r1 | (((g1 -' 1) + f1) -' 1) is Relation-like NAT -defined (3 -tuples_on NAT) * -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of (3 -tuples_on NAT) *
Card (r1 | (((g1 -' 1) + f1) -' 1)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
Sum (Card (r1 | (((g1 -' 1) + f1) -' 1))) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum (Card (r1 | (((g1 -' 1) + f1) -' 1)))) + f1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(r1 . ((g1 -' 1) + f1)) . f1 is set
(FlattenSeq r1) . ((Sum (Card (r1 | (((g1 -' 1) + f1) -' 1)))) + f1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(2,(((g1 -' 1) + f1) -' 1)) . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(((g1 -' 1) + f1) |-> (((p1 + 1) -' ((g1 -' 1) + f1)))) . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((2,(((g1 -' 1) + f1) -' 1)) . f1) ^ ((((g1 -' 1) + f1) |-> (((p1 + 1) -' ((g1 -' 1) + f1)))) . f1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((2,(((g1 -' 1) + f1) -' 1)) . f1) ^ (((p1 + 1) -' ((g1 -' 1) + f1))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
((((g1 -' 1) + f1) -' 1) + 1) -' f1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,(f1 -' 1),(((((g1 -' 1) + f1) -' 1) + 1) -' f1)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
(NAT,2,1,(NAT,(f1 -' 1),(((((g1 -' 1) + f1) -' 1) + 1) -' f1)),(((p1 + 1) -' ((g1 -' 1) + f1)))) is Relation-like NAT -defined NAT -valued Function-like non empty finite 2 + 1 -element 2 + 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of (2 + 1) -tuples_on NAT
2 + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
<*(f1 -' 1),(((((g1 -' 1) + f1) -' 1) + 1) -' f1),((p1 + 1) -' ((g1 -' 1) + f1))*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like finite-support set
((g1 -' 1) + f1) -' f1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
<*(f1 -' 1),(((g1 -' 1) + f1) -' f1),((p1 + 1) -' ((g1 -' 1) + f1))*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like finite-support set
(p1 + 1) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
P is set
r1 is set
(FlattenSeq q) . P is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(FlattenSeq q) . r1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
f1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
g1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom (q . f1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
f1 -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q | (f1 -' 1) is Relation-like NAT -defined (3 -tuples_on NAT) * -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of (3 -tuples_on NAT) *
Card (q | (f1 -' 1)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
Sum (Card (q | (f1 -' 1))) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum (Card (q | (f1 -' 1)))) + g1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(q . f1) . g1 is set
(p1 + 2) -' f1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((f1 -' 1)) is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V69() V70() V71() V72() V195() finite-support Element of 1 -tuples_on NAT
((p1 + 2) -' f1) |-> ((f1 -' 1)) is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like Function-yielding finite (p1 + 2) -' f1 -element FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of ((p1 + 2) -' f1) -tuples_on (1 -tuples_on NAT)
((p1 + 2) -' f1) -tuples_on (1 -tuples_on NAT) is functional non empty FinSequence-membered V196() V197() FinSequenceSet of 1 -tuples_on NAT
{ b₁ where b₁ is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (1 -tuples_on NAT) * : len b₁ = (p1 + 2) -' f1 } is set
Seg ((p1 + 2) -' f1) is finite (p1 + 2) -' f1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(Seg ((p1 + 2) -' f1)) --> ((f1 -' 1)) is Relation-like Seg ((p1 + 2) -' f1) -defined {((f1 -' 1))} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like finite-support Element of bool [:(Seg ((p1 + 2) -' f1)),{((f1 -' 1))}:]
{((f1 -' 1))} is functional non empty trivial finite V37() 1 -element set
[:(Seg ((p1 + 2) -' f1)),{((f1 -' 1))}:] is finite set
bool [:(Seg ((p1 + 2) -' f1)),{((f1 -' 1))}:] is finite V37() set
(p1 + 1) -' f1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(2,((p1 + 1) -' f1)) is Relation-like NAT -defined 2 -tuples_on NAT -valued Function-like one-to-one non empty Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 2 -tuples_on NAT
(NAT,1,2,(((p1 + 2) -' f1) |-> ((f1 -' 1))),(2,((p1 + 1) -' f1))) is Relation-like NAT -defined (1 + 2) -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of ((1 + 2) -tuples_on NAT) *
(p1 + 2) - f1 is V45() V46() V47() ext-real set
(p1 + 1) - f1 is V45() V46() V47() ext-real set
((p1 + 1) -' f1) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((p1 + 1) - f1) + 1 is V45() V46() V47() ext-real set
dom (((p1 + 2) -' f1) |-> ((f1 -' 1))) is finite (p1 + 2) -' f1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom (2,((p1 + 1) -' f1)) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
len (2,((p1 + 1) -' f1)) is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len (2,((p1 + 1) -' f1))) is non empty finite len (2,((p1 + 1) -' f1)) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(Seg ((p1 + 2) -' f1)) /\ (Seg ((p1 + 2) -' f1)) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
len (q . f1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len (q . f1)) is finite len (q . f1) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
P is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
j is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . P is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom (q . P) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
P -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q | (P -' 1) is Relation-like NAT -defined (3 -tuples_on NAT) * -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of (3 -tuples_on NAT) *
Card (q | (P -' 1)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
Sum (Card (q | (P -' 1))) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum (Card (q | (P -' 1)))) + j is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(q . P) . j is set
(p1 + 2) -' P is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((P -' 1)) is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V69() V70() V71() V72() V195() finite-support Element of 1 -tuples_on NAT
((p1 + 2) -' P) |-> ((P -' 1)) is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like Function-yielding finite (p1 + 2) -' P -element FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of ((p1 + 2) -' P) -tuples_on (1 -tuples_on NAT)
((p1 + 2) -' P) -tuples_on (1 -tuples_on NAT) is functional non empty FinSequence-membered V196() V197() FinSequenceSet of 1 -tuples_on NAT
{ b₁ where b₁ is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (1 -tuples_on NAT) * : len b₁ = (p1 + 2) -' P } is set
Seg ((p1 + 2) -' P) is finite (p1 + 2) -' P -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(Seg ((p1 + 2) -' P)) --> ((P -' 1)) is Relation-like Seg ((p1 + 2) -' P) -defined {((P -' 1))} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like finite-support Element of bool [:(Seg ((p1 + 2) -' P)),{((P -' 1))}:]
{((P -' 1))} is functional non empty trivial finite V37() 1 -element set
[:(Seg ((p1 + 2) -' P)),{((P -' 1))}:] is finite set
bool [:(Seg ((p1 + 2) -' P)),{((P -' 1))}:] is finite V37() set
(p1 + 1) -' P is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(2,((p1 + 1) -' P)) is Relation-like NAT -defined 2 -tuples_on NAT -valued Function-like one-to-one non empty Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 2 -tuples_on NAT
(NAT,1,2,(((p1 + 2) -' P) |-> ((P -' 1))),(2,((p1 + 1) -' P))) is Relation-like NAT -defined (1 + 2) -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of ((1 + 2) -tuples_on NAT) *
(p1 + 2) - P is V45() V46() V47() ext-real set
(p1 + 1) - P is V45() V46() V47() ext-real set
((p1 + 1) -' P) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((p1 + 1) - P) + 1 is V45() V46() V47() ext-real set
dom (((p1 + 2) -' P) |-> ((P -' 1))) is finite (p1 + 2) -' P -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom (2,((p1 + 1) -' P)) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
len (2,((p1 + 1) -' P)) is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len (2,((p1 + 1) -' P))) is non empty finite len (2,((p1 + 1) -' P)) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(Seg ((p1 + 2) -' P)) /\ (Seg ((p1 + 2) -' P)) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(((p1 + 2) -' P) |-> ((P -' 1))) . j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(2,((p1 + 1) -' P)) . j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((((p1 + 2) -' P) |-> ((P -' 1))) . j) ^ ((2,((p1 + 1) -' P)) . j) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((P -' 1)) ^ ((2,((p1 + 1) -' P)) . j) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
j -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(((p1 + 1) -' P) + 1) -' j is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,(j -' 1),((((p1 + 1) -' P) + 1) -' j)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
(NAT,1,2,((P -' 1)),(NAT,(j -' 1),((((p1 + 1) -' P) + 1) -' j))) is Relation-like NAT -defined NAT -valued Function-like non empty finite 1 + 2 -element 1 + 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of (1 + 2) -tuples_on NAT
<*(P -' 1),(j -' 1),((((p1 + 1) -' P) + 1) -' j)*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like finite-support set
len (q . P) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len (q . P)) is finite len (q . P) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(((p1 + 2) -' f1) |-> ((f1 -' 1))) . g1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(2,((p1 + 1) -' f1)) . g1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((((p1 + 2) -' f1) |-> ((f1 -' 1))) . g1) ^ ((2,((p1 + 1) -' f1)) . g1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((f1 -' 1)) ^ ((2,((p1 + 1) -' f1)) . g1) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
g1 -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(((p1 + 1) -' f1) + 1) -' g1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,(g1 -' 1),((((p1 + 1) -' f1) + 1) -' g1)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
(NAT,1,2,((f1 -' 1)),(NAT,(g1 -' 1),((((p1 + 1) -' f1) + 1) -' g1))) is Relation-like NAT -defined NAT -valued Function-like non empty finite 1 + 2 -element 1 + 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of (1 + 2) -tuples_on NAT
<*(f1 -' 1),(g1 -' 1),((((p1 + 1) -' f1) + 1) -' g1)*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like finite-support set
Sum (Card r1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V195() finite-support FinSequence of NAT
Sum q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len (FlattenSeq q) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
[:(dom (FlattenSeq q)),(dom (FlattenSeq q)):] is RAT -valued INT -valued finite V65() V66() V67() V68() set
bool [:(dom (FlattenSeq q)),(dom (FlattenSeq q)):] is finite V37() set
P is Relation-like dom (FlattenSeq q) -defined dom (FlattenSeq q) -valued Function-like one-to-one total quasi_total onto bijective finite V65() V66() V67() V68() finite-support Element of bool [:(dom (FlattenSeq q)),(dom (FlattenSeq q)):]
(FlattenSeq q) * P is Relation-like dom (FlattenSeq q) -defined 3 -tuples_on NAT -valued Function-like finite finite-support Element of bool [:(dom (FlattenSeq q)),(3 -tuples_on NAT):]
[:(dom (FlattenSeq q)),(3 -tuples_on NAT):] is set
bool [:(dom (FlattenSeq q)),(3 -tuples_on NAT):] is set
(L,(L,p,q),r) . p1 is Element of the carrier of L
r1 is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
len r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Sum r1 is Element of the carrier of L
dom r1 is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
the carrier of L * is functional non empty FinSequence-membered FinSequenceSet of the carrier of L
len r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
f1 is Relation-like NAT -defined the carrier of L * -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of the carrier of L *
len f1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom f1 is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Seg (len r1) is finite len r1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
g1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
(p1 + 1) -' g1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(((p1 + 1) -' g1)) is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V69() V70() V71() V72() V195() finite-support Element of 1 -tuples_on NAT
g1 |-> (((p1 + 1) -' g1)) is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like Function-yielding finite g1 -element FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of g1 -tuples_on (1 -tuples_on NAT)
g1 -tuples_on (1 -tuples_on NAT) is functional non empty FinSequence-membered V196() V197() FinSequenceSet of 1 -tuples_on NAT
{ b₁ where b₁ is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (1 -tuples_on NAT) * : len b₁ = g1 } is set
Seg g1 is finite g1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(Seg g1) --> (((p1 + 1) -' g1)) is Relation-like Seg g1 -defined {(((p1 + 1) -' g1))} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like finite-support Element of bool [:(Seg g1),{(((p1 + 1) -' g1))}:]
{(((p1 + 1) -' g1))} is functional non empty trivial finite V37() 1 -element set
[:(Seg g1),{(((p1 + 1) -' g1))}:] is finite set
bool [:(Seg g1),{(((p1 + 1) -' g1))}:] is finite V37() set
dom (g1 |-> (((p1 + 1) -' g1))) is finite g1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
g1 -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(g1 -' 1) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L,p,q) . (g1 -' 1) is Element of the carrier of L
P is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
len P is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Sum P is Element of the carrier of L
dom P is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(2,(g1 -' 1)) is Relation-like NAT -defined 2 -tuples_on NAT -valued Function-like one-to-one non empty Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 2 -tuples_on NAT
len (2,(g1 -' 1)) is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (2,(g1 -' 1)) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
f1 /. g1 is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of the carrier of L *
f1 . g1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
r1 /. g1 is Relation-like NAT -defined 3 -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of (3 -tuples_on NAT) *
(L,p,q,r,(r1 /. g1)) is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of the carrier of L *
r1 . g1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(NAT,2,1,(2,(g1 -' 1)),(g1 |-> (((p1 + 1) -' g1)))) is Relation-like NAT -defined (2 + 1) -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of ((2 + 1) -tuples_on NAT) *
dom (r1 /. g1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(dom (2,(g1 -' 1))) /\ (dom (g1 |-> (((p1 + 1) -' g1)))) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
len (L,p,q,r,(r1 /. g1)) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len (r1 /. g1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (L,p,q,r,(r1 /. g1)) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
r . ((p1 + 1) -' g1) is Element of the carrier of L
P * (r . ((p1 + 1) -' g1)) is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
dom (P * (r . ((p1 + 1) -' g1))) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
j is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
(r1 /. g1) /. j is Relation-like NAT -defined NAT -valued Function-like finite 3 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 3 -tuples_on NAT
(r1 /. g1) . j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(2,(g1 -' 1)) . j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(g1 |-> (((p1 + 1) -' g1))) . j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((2,(g1 -' 1)) . j) ^ ((g1 |-> (((p1 + 1) -' g1))) . j) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
j -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((g1 -' 1) + 1) -' j is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,(j -' 1),(((g1 -' 1) + 1) -' j)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
(NAT,(j -' 1),(((g1 -' 1) + 1) -' j)) ^ ((g1 |-> (((p1 + 1) -' g1))) . j) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
(NAT,2,1,(NAT,(j -' 1),(((g1 -' 1) + 1) -' j)),(((p1 + 1) -' g1))) is Relation-like NAT -defined NAT -valued Function-like non empty finite 2 + 1 -element 2 + 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of (2 + 1) -tuples_on NAT
<*(j -' 1),(((g1 -' 1) + 1) -' j),((p1 + 1) -' g1)*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like finite-support set
len ((r1 /. g1) /. j) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len ((r1 /. g1) /. j)) is finite len ((r1 /. g1) /. j) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom ((r1 /. g1) /. j) is finite 3 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
((r1 /. g1) /. j) /. 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((r1 /. g1) /. j) . 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
P /. j is Element of the carrier of L
P . j is set
p . (j -' 1) is Element of the carrier of L
q . (((g1 -' 1) + 1) -' j) is Element of the carrier of L
(p . (j -' 1)) * (q . (((g1 -' 1) + 1) -' j)) is Element of the carrier of L
the multF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is set
the multF of L . ((p . (j -' 1)),(q . (((g1 -' 1) + 1) -' j))) is Element of the carrier of L
((r1 /. g1) /. j) /. 3 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((r1 /. g1) /. j) . 3 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((r1 /. g1) /. j) /. 2 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((r1 /. g1) /. j) . 2 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L,p,q,r,(r1 /. g1)) . j is set
p . (((r1 /. g1) /. j) /. 1) is Element of the carrier of L
q . (((r1 /. g1) /. j) /. 2) is Element of the carrier of L
(p . (((r1 /. g1) /. j) /. 1)) * (q . (((r1 /. g1) /. j) /. 2)) is Element of the carrier of L
the multF of L . ((p . (((r1 /. g1) /. j) /. 1)),(q . (((r1 /. g1) /. j) /. 2))) is Element of the carrier of L
r . (((r1 /. g1) /. j) /. 3) is Element of the carrier of L
((p . (((r1 /. g1) /. j) /. 1)) * (q . (((r1 /. g1) /. j) /. 2))) * (r . (((r1 /. g1) /. j) /. 3)) is Element of the carrier of L
the multF of L . (((p . (((r1 /. g1) /. j) /. 1)) * (q . (((r1 /. g1) /. j) /. 2))),(r . (((r1 /. g1) /. j) /. 3))) is Element of the carrier of L
(P * (r . ((p1 + 1) -' g1))) /. j is Element of the carrier of L
(P * (r . ((p1 + 1) -' g1))) . j is set
Sum f1 is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
len (Sum f1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (Sum f1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
len (P * (r . ((p1 + 1) -' g1))) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((L,p,q) . (g1 -' 1)) * (r . ((p1 + 1) -' g1)) is Element of the carrier of L
the multF of L . (((L,p,q) . (g1 -' 1)),(r . ((p1 + 1) -' g1))) is Element of the carrier of L
Sum (P * (r . ((p1 + 1) -' g1))) is Element of the carrier of L
r1 . g1 is set
(Sum f1) /. g1 is Element of the carrier of L
(Sum f1) . g1 is set
g1 is Relation-like NAT -defined the carrier of L * -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of the carrier of L *
len g1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom g1 is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
P is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
(p1 + 2) -' P is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
P -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((P -' 1)) is Relation-like NAT -defined NAT -valued Function-like one-to-one constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V69() V70() V71() V72() V195() finite-support Element of 1 -tuples_on NAT
((p1 + 2) -' P) |-> ((P -' 1)) is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like Function-yielding finite (p1 + 2) -' P -element FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of ((p1 + 2) -' P) -tuples_on (1 -tuples_on NAT)
((p1 + 2) -' P) -tuples_on (1 -tuples_on NAT) is functional non empty FinSequence-membered V196() V197() FinSequenceSet of 1 -tuples_on NAT
{ b₁ where b₁ is Relation-like NAT -defined 1 -tuples_on NAT -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of (1 -tuples_on NAT) * : len b₁ = (p1 + 2) -' P } is set
Seg ((p1 + 2) -' P) is finite (p1 + 2) -' P -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(Seg ((p1 + 2) -' P)) --> ((P -' 1)) is Relation-like Seg ((p1 + 2) -' P) -defined {((P -' 1))} -valued Function-like total quasi_total finite FinSequence-like FinSubsequence-like finite-support Element of bool [:(Seg ((p1 + 2) -' P)),{((P -' 1))}:]
{((P -' 1))} is functional non empty trivial finite V37() 1 -element set
[:(Seg ((p1 + 2) -' P)),{((P -' 1))}:] is finite set
bool [:(Seg ((p1 + 2) -' P)),{((P -' 1))}:] is finite V37() set
dom (((p1 + 2) -' P) |-> ((P -' 1))) is finite (p1 + 2) -' P -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(p1 + 1) -' P is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((p1 + 1) -' P) + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L,q,r) . ((p1 + 1) -' P) is Element of the carrier of L
j is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
len j is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Sum j is Element of the carrier of L
dom j is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(p1 + 2) - P is V45() V46() V47() ext-real set
(p1 + 1) - P is V45() V46() V47() ext-real set
((p1 + 1) - P) + 1 is V45() V46() V47() ext-real set
(2,((p1 + 1) -' P)) is Relation-like NAT -defined 2 -tuples_on NAT -valued Function-like one-to-one non empty Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of 2 -tuples_on NAT
len (2,((p1 + 1) -' P)) is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (2,((p1 + 1) -' P)) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
g1 /. P is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of the carrier of L *
g1 . P is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
q /. P is Relation-like NAT -defined 3 -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of (3 -tuples_on NAT) *
(L,p,q,r,(q /. P)) is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of the carrier of L *
q . P is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(NAT,1,2,(((p1 + 2) -' P) |-> ((P -' 1))),(2,((p1 + 1) -' P))) is Relation-like NAT -defined (1 + 2) -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of ((1 + 2) -tuples_on NAT) *
dom (q /. P) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(dom (((p1 + 2) -' P) |-> ((P -' 1)))) /\ (dom (2,((p1 + 1) -' P))) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
len (L,p,q,r,(q /. P)) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len (q /. P) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (L,p,q,r,(q /. P)) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
p . (P -' 1) is Element of the carrier of L
(p . (P -' 1)) * j is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
dom ((p . (P -' 1)) * j) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
i1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
(q /. P) /. i1 is Relation-like NAT -defined NAT -valued Function-like finite 3 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 3 -tuples_on NAT
(q /. P) . i1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(((p1 + 2) -' P) |-> ((P -' 1))) . i1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(2,((p1 + 1) -' P)) . i1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
((((p1 + 2) -' P) |-> ((P -' 1))) . i1) ^ ((2,((p1 + 1) -' P)) . i1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
i1 -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(((p1 + 1) -' P) + 1) -' i1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(NAT,(i1 -' 1),((((p1 + 1) -' P) + 1) -' i1)) is Relation-like NAT -defined NAT -valued Function-like non empty non trivial finite 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 2 -tuples_on NAT
((((p1 + 2) -' P) |-> ((P -' 1))) . i1) ^ (NAT,(i1 -' 1),((((p1 + 1) -' P) + 1) -' i1)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
(NAT,1,2,((P -' 1)),(NAT,(i1 -' 1),((((p1 + 1) -' P) + 1) -' i1))) is Relation-like NAT -defined NAT -valued Function-like non empty finite 1 + 2 -element 1 + 2 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of (1 + 2) -tuples_on NAT
<*(P -' 1),(i1 -' 1),((((p1 + 1) -' P) + 1) -' i1)*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like finite-support set
len ((q /. P) /. i1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len ((q /. P) /. i1)) is finite len ((q /. P) /. i1) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom ((q /. P) /. i1) is finite 3 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
((q /. P) /. i1) /. 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((q /. P) /. i1) . 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
j /. i1 is Element of the carrier of L
j . i1 is set
q . (i1 -' 1) is Element of the carrier of L
r . ((((p1 + 1) -' P) + 1) -' i1) is Element of the carrier of L
(q . (i1 -' 1)) * (r . ((((p1 + 1) -' P) + 1) -' i1)) is Element of the carrier of L
the multF of L . ((q . (i1 -' 1)),(r . ((((p1 + 1) -' P) + 1) -' i1))) is Element of the carrier of L
((q /. P) /. i1) /. 3 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((q /. P) /. i1) . 3 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((q /. P) /. i1) /. 2 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((q /. P) /. i1) . 2 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L,p,q,r,(q /. P)) . i1 is set
p . (((q /. P) /. i1) /. 1) is Element of the carrier of L
q . (((q /. P) /. i1) /. 2) is Element of the carrier of L
(p . (((q /. P) /. i1) /. 1)) * (q . (((q /. P) /. i1) /. 2)) is Element of the carrier of L
the multF of L . ((p . (((q /. P) /. i1) /. 1)),(q . (((q /. P) /. i1) /. 2))) is Element of the carrier of L
r . (((q /. P) /. i1) /. 3) is Element of the carrier of L
((p . (((q /. P) /. i1) /. 1)) * (q . (((q /. P) /. i1) /. 2))) * (r . (((q /. P) /. i1) /. 3)) is Element of the carrier of L
the multF of L . (((p . (((q /. P) /. i1) /. 1)) * (q . (((q /. P) /. i1) /. 2))),(r . (((q /. P) /. i1) /. 3))) is Element of the carrier of L
(q . (((q /. P) /. i1) /. 2)) * (r . (((q /. P) /. i1) /. 3)) is Element of the carrier of L
the multF of L . ((q . (((q /. P) /. i1) /. 2)),(r . (((q /. P) /. i1) /. 3))) is Element of the carrier of L
(p . (((q /. P) /. i1) /. 1)) * ((q . (((q /. P) /. i1) /. 2)) * (r . (((q /. P) /. i1) /. 3))) is Element of the carrier of L
the multF of L . ((p . (((q /. P) /. i1) /. 1)),((q . (((q /. P) /. i1) /. 2)) * (r . (((q /. P) /. i1) /. 3)))) is Element of the carrier of L
((p . (P -' 1)) * j) /. i1 is Element of the carrier of L
((p . (P -' 1)) * j) . i1 is set
Sum g1 is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
len (Sum g1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (Sum g1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
len ((p . (P -' 1)) * j) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(p . (P -' 1)) * ((L,q,r) . ((p1 + 1) -' P)) is Element of the carrier of L
the multF of L . ((p . (P -' 1)),((L,q,r) . ((p1 + 1) -' P))) is Element of the carrier of L
Sum ((p . (P -' 1)) * j) is Element of the carrier of L
p . P is set
(Sum g1) /. P is Element of the carrier of L
(Sum g1) . P is set
P is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
g1 . P is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
q /. P is Relation-like NAT -defined 3 -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of (3 -tuples_on NAT) *
(L,p,q,r,(q /. P)) is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of the carrier of L *
len (g1 . P) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len (q /. P) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . P is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
len (q . P) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Card q) . P is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Card g1 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
(Card g1) . P is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (Card g1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
len (Card g1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
FlattenSeq g1 is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of the carrier of L *
len (FlattenSeq g1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (FlattenSeq g1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
[:(dom (FlattenSeq g1)),(dom (FlattenSeq g1)):] is RAT -valued INT -valued finite V65() V66() V67() V68() set
bool [:(dom (FlattenSeq g1)),(dom (FlattenSeq g1)):] is finite V37() set
Seg (len (FlattenSeq g1)) is finite len (FlattenSeq g1) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
j is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
(FlattenSeq g1) . j is set
i1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
j1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
g1 . i1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom (g1 . i1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
i1 -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
g1 | (i1 -' 1) is Relation-like NAT -defined the carrier of L * -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of the carrier of L *
Card (g1 | (i1 -' 1)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
Sum (Card (g1 | (i1 -' 1))) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum (Card (g1 | (i1 -' 1)))) + j1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(g1 . i1) . j1 is set
(FlattenSeq q) . j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
i2 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
j2 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . i2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom (q . i2) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
i2 -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q | (i2 -' 1) is Relation-like NAT -defined (3 -tuples_on NAT) * -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of (3 -tuples_on NAT) *
Card (q | (i2 -' 1)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
Sum (Card (q | (i2 -' 1))) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum (Card (q | (i2 -' 1)))) + j2 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(q . i2) . j2 is set
(Card g1) | (i1 -' 1) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
Sum ((Card g1) | (i1 -' 1)) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum ((Card g1) | (i1 -' 1))) + j1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Card q) | (i2 -' 1) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
Sum ((Card q) | (i2 -' 1)) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum ((Card q) | (i2 -' 1))) + j2 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q /. i1 is Relation-like NAT -defined 3 -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of (3 -tuples_on NAT) *
(L,p,q,r,(q /. i1)) is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of the carrier of L *
len (g1 . i1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len (q /. i1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . i1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
len (q . i1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len (q . i1)) is finite len (q . i1) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
Seg (len (q /. i1)) is finite len (q /. i1) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom (q /. i1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(q /. i1) /. j1 is Relation-like NAT -defined NAT -valued Function-like finite 3 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 3 -tuples_on NAT
(q /. i1) . j1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(q . i1) . j1 is set
(FlattenSeq q) /. j is Relation-like NAT -defined NAT -valued Function-like finite 3 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 3 -tuples_on NAT
((q /. i1) /. j1) /. 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . (((q /. i1) /. j1) /. 1) is Element of the carrier of L
((q /. i1) /. j1) /. 2 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . (((q /. i1) /. j1) /. 2) is Element of the carrier of L
(p . (((q /. i1) /. j1) /. 1)) * (q . (((q /. i1) /. j1) /. 2)) is Element of the carrier of L
the multF of L . ((p . (((q /. i1) /. j1) /. 1)),(q . (((q /. i1) /. j1) /. 2))) is Element of the carrier of L
((q /. i1) /. j1) /. 3 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r . (((q /. i1) /. j1) /. 3) is Element of the carrier of L
((p . (((q /. i1) /. j1) /. 1)) * (q . (((q /. i1) /. j1) /. 2))) * (r . (((q /. i1) /. j1) /. 3)) is Element of the carrier of L
the multF of L . (((p . (((q /. i1) /. j1) /. 1)) * (q . (((q /. i1) /. j1) /. 2))),(r . (((q /. i1) /. j1) /. 3))) is Element of the carrier of L
(L,p,q,r,(FlattenSeq q)) is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of the carrier of L *
(L,p,q,r,(FlattenSeq q)) . j is set
j is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
f1 . j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
r1 /. j is Relation-like NAT -defined 3 -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of (3 -tuples_on NAT) *
(L,p,q,r,(r1 /. j)) is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of the carrier of L *
len (f1 . j) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len (r1 /. j) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 . j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
len (r1 . j) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Card r1) . j is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Card f1 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
(Card f1) . j is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
dom (Card f1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
len (Card f1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
FlattenSeq f1 is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of the carrier of L *
len (FlattenSeq f1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len (FlattenSeq f1)) is finite len (FlattenSeq f1) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom (FlattenSeq f1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
j is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
(FlattenSeq f1) . j is set
i1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
j1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
f1 . i1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom (f1 . i1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
i1 -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
f1 | (i1 -' 1) is Relation-like NAT -defined the carrier of L * -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of the carrier of L *
Card (f1 | (i1 -' 1)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
Sum (Card (f1 | (i1 -' 1))) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum (Card (f1 | (i1 -' 1)))) + j1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(f1 . i1) . j1 is set
(FlattenSeq r1) . j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
i2 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
j2 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 . i2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom (r1 . i2) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
i2 -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 | (i2 -' 1) is Relation-like NAT -defined (3 -tuples_on NAT) * -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support FinSequence of (3 -tuples_on NAT) *
Card (r1 | (i2 -' 1)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
Sum (Card (r1 | (i2 -' 1))) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum (Card (r1 | (i2 -' 1)))) + j2 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(r1 . i2) . j2 is set
(Card f1) | (i1 -' 1) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
Sum ((Card f1) | (i1 -' 1)) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum ((Card f1) | (i1 -' 1))) + j1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Card r1) | (i2 -' 1) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support FinSequence of NAT
Sum ((Card r1) | (i2 -' 1)) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(Sum ((Card r1) | (i2 -' 1))) + j2 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 /. i1 is Relation-like NAT -defined 3 -tuples_on NAT -valued Function-like Function-yielding finite FinSequence-like FinSubsequence-like FinSequence-yielding finite-support Element of (3 -tuples_on NAT) *
(L,p,q,r,(r1 /. i1)) is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of the carrier of L *
len (f1 . i1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len (r1 /. i1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 . i1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
len (r1 . i1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len (r1 . i1)) is finite len (r1 . i1) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
Seg (len (r1 /. i1)) is finite len (r1 /. i1) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
dom (r1 /. i1) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(r1 /. i1) /. j1 is Relation-like NAT -defined NAT -valued Function-like finite 3 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 3 -tuples_on NAT
(r1 /. i1) . j1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(r1 . i1) . j1 is set
(FlattenSeq r1) /. j is Relation-like NAT -defined NAT -valued Function-like finite 3 -element FinSequence-like FinSubsequence-like V65() V66() V67() V68() V195() finite-support Element of 3 -tuples_on NAT
((r1 /. i1) /. j1) /. 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . (((r1 /. i1) /. j1) /. 1) is Element of the carrier of L
((r1 /. i1) /. j1) /. 2 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . (((r1 /. i1) /. j1) /. 2) is Element of the carrier of L
(p . (((r1 /. i1) /. j1) /. 1)) * (q . (((r1 /. i1) /. j1) /. 2)) is Element of the carrier of L
the multF of L . ((p . (((r1 /. i1) /. j1) /. 1)),(q . (((r1 /. i1) /. j1) /. 2))) is Element of the carrier of L
((r1 /. i1) /. j1) /. 3 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r . (((r1 /. i1) /. j1) /. 3) is Element of the carrier of L
((p . (((r1 /. i1) /. j1) /. 1)) * (q . (((r1 /. i1) /. j1) /. 2))) * (r . (((r1 /. i1) /. j1) /. 3)) is Element of the carrier of L
the multF of L . (((p . (((r1 /. i1) /. j1) /. 1)) * (q . (((r1 /. i1) /. j1) /. 2))),(r . (((r1 /. i1) /. j1) /. 3))) is Element of the carrier of L
((FlattenSeq r1) /. j) /. 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . (((FlattenSeq r1) /. j) /. 1) is Element of the carrier of L
((FlattenSeq r1) /. j) /. 2 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q . (((FlattenSeq r1) /. j) /. 2) is Element of the carrier of L
(p . (((FlattenSeq r1) /. j) /. 1)) * (q . (((FlattenSeq r1) /. j) /. 2)) is Element of the carrier of L
the multF of L . ((p . (((FlattenSeq r1) /. j) /. 1)),(q . (((FlattenSeq r1) /. j) /. 2))) is Element of the carrier of L
((FlattenSeq r1) /. j) /. 3 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r . (((FlattenSeq r1) /. j) /. 3) is Element of the carrier of L
((p . (((FlattenSeq r1) /. j) /. 1)) * (q . (((FlattenSeq r1) /. j) /. 2))) * (r . (((FlattenSeq r1) /. j) /. 3)) is Element of the carrier of L
the multF of L . (((p . (((FlattenSeq r1) /. j) /. 1)) * (q . (((FlattenSeq r1) /. j) /. 2))),(r . (((FlattenSeq r1) /. j) /. 3))) is Element of the carrier of L
(L,p,q,r,(FlattenSeq r1)) is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support Element of the carrier of L *
(L,p,q,r,(FlattenSeq r1)) . j is set
Sum (FlattenSeq g1) is Element of the carrier of L
len (L,p,q,r,(FlattenSeq q)) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
len (L,p,q,r,(FlattenSeq r1)) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
P is Relation-like dom (FlattenSeq g1) -defined dom (FlattenSeq g1) -valued Function-like one-to-one total quasi_total onto bijective finite V65() V66() V67() V68() finite-support Element of bool [:(dom (FlattenSeq g1)),(dom (FlattenSeq g1)):]
(FlattenSeq g1) * P is Relation-like dom (FlattenSeq g1) -defined the carrier of L -valued Function-like finite finite-support Element of bool [:(dom (FlattenSeq g1)), the carrier of L:]
[:(dom (FlattenSeq g1)), the carrier of L:] is set
bool [:(dom (FlattenSeq g1)), the carrier of L:] is set
Sum (FlattenSeq f1) is Element of the carrier of L
L is non empty commutative Abelian add-associative right_zeroed doubleLoopStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
r is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,r,p1) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,p1,r) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q1 + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L,r,p1) . q1 is Element of the carrier of L
r1 is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
len r1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Sum r1 is Element of the carrier of L
dom r1 is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
(L,p1,r) . q1 is Element of the carrier of L
p is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
len p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Sum p is Element of the carrier of L
dom p is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative set
q - 1 is V45() V46() V47() ext-real set
(q1 + 1) - q is V45() V46() V47() ext-real set
(len p) - q is V45() V46() V47() ext-real set
((len p) - q) + 1 is V45() V46() V47() ext-real set
(q1 + 1) -' q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
((q1 + 1) - q) + 1 is V45() V46() V47() ext-real set
(((q1 + 1) - q) + 1) - 1 is V45() V46() V47() ext-real set
p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
1 - q is V45() V46() V47() ext-real set
q1 + (1 - q) is V45() V46() V47() ext-real set
q1 + 0 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(q1 + 1) - p is V45() V46() V47() ext-real set
(q1 + 1) -' p is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(q1 + 1) - (q - 1) is V45() V46() V47() ext-real set
(q1 + 1) - ((q1 + 1) - (q - 1)) is V45() V46() V47() ext-real set
q -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
0 + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r1 . q is set
r . (q -' 1) is Element of the carrier of L
p1 . ((q1 + 1) -' q) is Element of the carrier of L
(r . (q -' 1)) * (p1 . ((q1 + 1) -' q)) is Element of the carrier of L
the multF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is set
the multF of L . ((r . (q -' 1)),(p1 . ((q1 + 1) -' q))) is Element of the carrier of L
p . (((len p) - q) + 1) is set
Rev p is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
L is non empty right_complementable right-distributive add-associative right_zeroed doubleLoopStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
(L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
0. L is V105(L) Element of the carrier of L
the ZeroF of L is Element of the carrier of L
NAT --> (0. L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total V30() Element of bool [:NAT, the carrier of L:]
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,p,(L)) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L,p,(L)) . q is Element of the carrier of L
r is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
len r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Sum r is Element of the carrier of L
dom r is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
r . p1 is set
p1 -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . (p1 -' 1) is Element of the carrier of L
(q + 1) -' p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L) . ((q + 1) -' p1) is Element of the carrier of L
(p . (p1 -' 1)) * ((L) . ((q + 1) -' p1)) is Element of the carrier of L
the multF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is set
the multF of L . ((p . (p1 -' 1)),((L) . ((q + 1) -' p1))) is Element of the carrier of L
(p . (p1 -' 1)) * (0. L) is Element of the carrier of L
the multF of L . ((p . (p1 -' 1)),(0. L)) is Element of the carrier of L
(L) . q is Element of the carrier of L
L is non empty right_complementable unital right-distributive right_unital well-unital left_unital add-associative right_zeroed doubleLoopStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
(L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
(L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
0. L is V105(L) Element of the carrier of L
the ZeroF of L is Element of the carrier of L
NAT --> (0. L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total V30() Element of bool [:NAT, the carrier of L:]
1. L is Element of the carrier of L
the OneF of L is Element of the carrier of L
(L) +* (0,(1. L)) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,p,(L)) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
q + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L,p,(L)) . q is Element of the carrier of L
r is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
len r is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Sum r is Element of the carrier of L
dom r is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
Seg (len r) is finite len r -element V75() V76() V77() V78() V79() V80() Element of bool NAT
p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
( the carrier of L,(q + 1),r) is Relation-like NAT -defined the carrier of L -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
dom ( the carrier of L,(q + 1),r) is finite V75() V76() V77() V78() V79() V80() Element of bool NAT
len ( the carrier of L,(q + 1),r) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (len ( the carrier of L,(q + 1),r)) is finite len ( the carrier of L,(q + 1),r) -element V75() V76() V77() V78() V79() V80() Element of bool NAT
Seg q is finite q -element V75() V76() V77() V78() V79() V80() Element of bool NAT
(q + 1) - p1 is V45() V46() V47() ext-real set
(q + 1) -' p1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
Seg (q + 1) is non empty finite q + 1 -element q + 1 -element V75() V76() V77() V78() V79() V80() Element of bool NAT
q + 1 is non empty V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real positive non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
( the carrier of L,(q + 1),r) . p1 is set
r . p1 is set
p1 -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . (p1 -' 1) is Element of the carrier of L
(L) . ((q + 1) -' p1) is Element of the carrier of L
(p . (p1 -' 1)) * ((L) . ((q + 1) -' p1)) is Element of the carrier of L
the multF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is set
the multF of L . ((p . (p1 -' 1)),((L) . ((q + 1) -' p1))) is Element of the carrier of L
(p . (p1 -' 1)) * (0. L) is Element of the carrier of L
the multF of L . ((p . (p1 -' 1)),(0. L)) is Element of the carrier of L
Sum ( the carrier of L,(q + 1),r) is Element of the carrier of L
r . (q + 1) is set
<*(r . (q + 1))*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like finite-support set
( the carrier of L,(q + 1),r) ^ <*(r . (q + 1))*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like finite-support set
r /. (q + 1) is Element of the carrier of L
<*(r /. (q + 1))*> is Relation-like NAT -defined the carrier of L -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like finite-support Element of the carrier of L *
the carrier of L * is functional non empty FinSequence-membered FinSequenceSet of the carrier of L
( the carrier of L,(q + 1),r) ^ <*(r /. (q + 1))*> is Relation-like NAT -defined the carrier of L -valued Function-like non empty finite FinSequence-like FinSubsequence-like finite-support FinSequence of the carrier of L
Sum <*(r /. (q + 1))*> is Element of the carrier of L
(Sum ( the carrier of L,(q + 1),r)) + (Sum <*(r /. (q + 1))*>) is Element of the carrier of L
the addF of L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like total quasi_total Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
the addF of L . ((Sum ( the carrier of L,(q + 1),r)),(Sum <*(r /. (q + 1))*>)) is Element of the carrier of L
(Sum ( the carrier of L,(q + 1),r)) + (r /. (q + 1)) is Element of the carrier of L
the addF of L . ((Sum ( the carrier of L,(q + 1),r)),(r /. (q + 1))) is Element of the carrier of L
(q + 1) -' 1 is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
p . ((q + 1) -' 1) is Element of the carrier of L
(q + 1) -' (q + 1) is V26() V27() V28() V32() finite cardinal V45() V46() V47() ext-real non negative V52() V75() V76() V77() V78() V79() V80() Element of NAT
(L) . ((q + 1) -' (q + 1)) is Element of the carrier of L
(p . ((q + 1) -' 1)) * ((L) . ((q + 1) -' (q + 1))) is Element of the carrier of L
the multF of L . ((p . ((q + 1) -' 1)),((L) . ((q + 1) -' (q + 1)))) is Element of the carrier of L
p . q is Element of the carrier of L
(p . q) * ((L) . ((q + 1) -' (q + 1))) is Element of the carrier of L
the multF of L . ((p . q),((L) . ((q + 1) -' (q + 1)))) is Element of the carrier of L
(L) . 0 is Element of the carrier of L
(p . q) * ((L) . 0) is Element of the carrier of L
the multF of L . ((p . q),((L) . 0)) is Element of the carrier of L
1_ L is Element of the carrier of L
(p . q) * (1_ L) is Element of the carrier of L
the multF of L . ((p . q),(1_ L)) is Element of the carrier of L
L is non empty right_complementable right-distributive left-distributive distributive add-associative right_zeroed doubleLoopStr
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
(L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
0. L is V105(L) Element of the carrier of L
the ZeroF of L is Element of the carrier of L
NAT --> (0. L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total V30() Element of bool [:NAT, the carrier of L:]
(L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
1. L is Element of the carrier of L
the OneF of L is Element of the carrier of L
(L) +* (0,(1. L)) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
{ b₁ where b₁ is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:] : verum } is set
p is non empty set
r is Element of p
p1 is Element of p
q1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
r1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
q1 + r1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
p is Element of p
[:p,p:] is set
[:[:p,p:],p:] is set
bool [:[:p,p:],p:] is set
r is Relation-like [:p,p:] -defined p -valued Function-like total quasi_total Element of bool [:[:p,p:],p:]
q1 is Element of p
r1 is Element of p
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
(L,p,q) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
p is Element of p
q1 is Relation-like [:p,p:] -defined p -valued Function-like total quasi_total Element of bool [:[:p,p:],p:]
p1 is Element of p
q is Element of p
doubleLoopStr(# p,r,q1,p1,q #) is strict doubleLoopStr
r1 is non empty strict doubleLoopStr
the carrier of r1 is non empty set
0. r1 is V105(r1) Element of the carrier of r1
the ZeroF of r1 is Element of the carrier of r1
1. r1 is Element of the carrier of r1
the OneF of r1 is Element of the carrier of r1
p is set
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
p is Element of the carrier of r1
q is Element of the carrier of r1
p + q is Element of the carrier of r1
the addF of r1 is Relation-like [: the carrier of r1, the carrier of r1:] -defined the carrier of r1 -valued Function-like total quasi_total Element of bool [:[: the carrier of r1, the carrier of r1:], the carrier of r1:]
[: the carrier of r1, the carrier of r1:] is set
[:[: the carrier of r1, the carrier of r1:], the carrier of r1:] is set
bool [:[: the carrier of r1, the carrier of r1:], the carrier of r1:] is set
the addF of r1 . (p,q) is Element of the carrier of r1
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p + q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
r . (p,q) is set
P is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
r1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
P + r1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
p is Element of the carrier of r1
q is Element of the carrier of r1
p * q is Element of the carrier of r1
the multF of r1 is Relation-like [: the carrier of r1, the carrier of r1:] -defined the carrier of r1 -valued Function-like total quasi_total Element of bool [:[: the carrier of r1, the carrier of r1:], the carrier of r1:]
[: the carrier of r1, the carrier of r1:] is set
[:[: the carrier of r1, the carrier of r1:], the carrier of r1:] is set
bool [:[: the carrier of r1, the carrier of r1:], the carrier of r1:] is set
the multF of r1 . (p,q) is Element of the carrier of r1
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,p,q) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q1 . (p,q) is set
P is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
r1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
(L,P,r1) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
p is non empty strict doubleLoopStr
the carrier of p is non empty set
0. p is V105(p) Element of the carrier of p
the ZeroF of p is Element of the carrier of p
1. p is Element of the carrier of p
the OneF of p is Element of the carrier of p
q is non empty strict doubleLoopStr
the carrier of q is non empty set
0. q is V105(q) Element of the carrier of q
the ZeroF of q is Element of the carrier of q
1. q is Element of the carrier of q
the OneF of q is Element of the carrier of q
r is set
p1 is Element of the carrier of q
r is Element of the carrier of p
the multF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like total quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
[: the carrier of p, the carrier of p:] is set
[:[: the carrier of p, the carrier of p:], the carrier of p:] is set
bool [:[: the carrier of p, the carrier of p:], the carrier of p:] is set
the multF of p . (r,p1) is set
q1 is Element of the carrier of p
r * q1 is Element of the carrier of p
the multF of p . (r,q1) is Element of the carrier of p
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,p,q) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
r1 is Element of the carrier of q
r1 * p1 is Element of the carrier of q
the multF of q is Relation-like [: the carrier of q, the carrier of q:] -defined the carrier of q -valued Function-like total quasi_total Element of bool [:[: the carrier of q, the carrier of q:], the carrier of q:]
[: the carrier of q, the carrier of q:] is set
[:[: the carrier of q, the carrier of q:], the carrier of q:] is set
bool [:[: the carrier of q, the carrier of q:], the carrier of q:] is set
the multF of q . (r1,p1) is Element of the carrier of q
the multF of q . (r,p1) is set
p1 is Element of the carrier of q
r is Element of the carrier of p
the addF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like total quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
the addF of p . (r,p1) is set
q1 is Element of the carrier of p
r + q1 is Element of the carrier of p
the addF of p . (r,q1) is Element of the carrier of p
p is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p + q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
r1 is Element of the carrier of q
r1 + p1 is Element of the carrier of q
the addF of q is Relation-like [: the carrier of q, the carrier of q:] -defined the carrier of q -valued Function-like total quasi_total Element of bool [:[: the carrier of q, the carrier of q:], the carrier of q:]
the addF of q . (r1,p1) is Element of the carrier of q
the addF of q . (r,p1) is set
L is non empty right_complementable right-distributive left-distributive distributive Abelian add-associative right_zeroed doubleLoopStr
(L) is non empty strict doubleLoopStr
the carrier of (L) is non empty set
p is Element of the carrier of (L)
q is Element of the carrier of (L)
p + q is Element of the carrier of (L)
the addF of (L) is Relation-like [: the carrier of (L), the carrier of (L):] -defined the carrier of (L) -valued Function-like total quasi_total Element of bool [:[: the carrier of (L), the carrier of (L):], the carrier of (L):]
[: the carrier of (L), the carrier of (L):] is set
[:[: the carrier of (L), the carrier of (L):], the carrier of (L):] is set
bool [:[: the carrier of (L), the carrier of (L):], the carrier of (L):] is set
the addF of (L) . (p,q) is Element of the carrier of (L)
q + p is Element of the carrier of (L)
the addF of (L) . (q,p) is Element of the carrier of (L)
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
r is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,r,p1) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
L is non empty right_complementable right-distributive left-distributive distributive add-associative right_zeroed doubleLoopStr
(L) is non empty strict doubleLoopStr
the carrier of (L) is non empty set
p is Element of the carrier of (L)
q is Element of the carrier of (L)
p + q is Element of the carrier of (L)
the addF of (L) is Relation-like [: the carrier of (L), the carrier of (L):] -defined the carrier of (L) -valued Function-like total quasi_total Element of bool [:[: the carrier of (L), the carrier of (L):], the carrier of (L):]
[: the carrier of (L), the carrier of (L):] is set
[:[: the carrier of (L), the carrier of (L):], the carrier of (L):] is set
bool [:[: the carrier of (L), the carrier of (L):], the carrier of (L):] is set
the addF of (L) . (p,q) is Element of the carrier of (L)
r is Element of the carrier of (L)
(p + q) + r is Element of the carrier of (L)
the addF of (L) . ((p + q),r) is Element of the carrier of (L)
q + r is Element of the carrier of (L)
the addF of (L) . (q,r) is Element of the carrier of (L)
p + (q + r) is Element of the carrier of (L)
the addF of (L) . (p,(q + r)) is Element of the carrier of (L)
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
q1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
r1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q1 + r1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p1 + q1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(p1 + q1) + r1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p1 + (q1 + r1) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
the carrier of (L) is non empty set
p is Element of the carrier of (L)
0. (L) is V105((L)) Element of the carrier of (L)
the ZeroF of (L) is Element of the carrier of (L)
p + (0. (L)) is Element of the carrier of (L)
the addF of (L) is Relation-like [: the carrier of (L), the carrier of (L):] -defined the carrier of (L) -valued Function-like total quasi_total Element of bool [:[: the carrier of (L), the carrier of (L):], the carrier of (L):]
[: the carrier of (L), the carrier of (L):] is set
[:[: the carrier of (L), the carrier of (L):], the carrier of (L):] is set
bool [:[: the carrier of (L), the carrier of (L):], the carrier of (L):] is set
the addF of (L) . (p,(0. (L))) is Element of the carrier of (L)
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
(L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
0. L is V105(L) Element of the carrier of L
the ZeroF of L is Element of the carrier of L
NAT --> (0. L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total V30() Element of bool [:NAT, the carrier of L:]
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q + (L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
the carrier of (L) is non empty set
p is Element of the carrier of (L)
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
- q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
r is Element of the carrier of (L)
p + r is Element of the carrier of (L)
the addF of (L) is Relation-like [: the carrier of (L), the carrier of (L):] -defined the carrier of (L) -valued Function-like total quasi_total Element of bool [:[: the carrier of (L), the carrier of (L):], the carrier of (L):]
[: the carrier of (L), the carrier of (L):] is set
[:[: the carrier of (L), the carrier of (L):], the carrier of (L):] is set
bool [:[: the carrier of (L), the carrier of (L):], the carrier of (L):] is set
the addF of (L) . (p,r) is Element of the carrier of (L)
0. (L) is V105((L)) Element of the carrier of (L)
the ZeroF of (L) is Element of the carrier of (L)
q - q is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
q + (- q) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
(L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
0. L is V105(L) Element of the carrier of L
the ZeroF of L is Element of the carrier of L
NAT --> (0. L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total V30() Element of bool [:NAT, the carrier of L:]
L is non empty right_complementable commutative right-distributive left-distributive distributive Abelian add-associative right_zeroed doubleLoopStr
(L) is non empty right_complementable strict Abelian add-associative right_zeroed doubleLoopStr
the carrier of (L) is non empty set
p is Element of the carrier of (L)
q is Element of the carrier of (L)
p * q is Element of the carrier of (L)
the multF of (L) is Relation-like [: the carrier of (L), the carrier of (L):] -defined the carrier of (L) -valued Function-like total quasi_total Element of bool [:[: the carrier of (L), the carrier of (L):], the carrier of (L):]
[: the carrier of (L), the carrier of (L):] is set
[:[: the carrier of (L), the carrier of (L):], the carrier of (L):] is set
bool [:[: the carrier of (L), the carrier of (L):], the carrier of (L):] is set
the multF of (L) . (p,q) is Element of the carrier of (L)
q * p is Element of the carrier of (L)
the multF of (L) . (q,p) is Element of the carrier of (L)
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
r is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,r,p1) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
L is non empty right_complementable unital associative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
(L) is non empty right_complementable strict Abelian add-associative right_zeroed doubleLoopStr
the carrier of (L) is non empty set
p is Element of the carrier of (L)
q is Element of the carrier of (L)
p * q is Element of the carrier of (L)
the multF of (L) is Relation-like [: the carrier of (L), the carrier of (L):] -defined the carrier of (L) -valued Function-like total quasi_total Element of bool [:[: the carrier of (L), the carrier of (L):], the carrier of (L):]
[: the carrier of (L), the carrier of (L):] is set
[:[: the carrier of (L), the carrier of (L):], the carrier of (L):] is set
bool [:[: the carrier of (L), the carrier of (L):], the carrier of (L):] is set
the multF of (L) . (p,q) is Element of the carrier of (L)
r is Element of the carrier of (L)
(p * q) * r is Element of the carrier of (L)
the multF of (L) . ((p * q),r) is Element of the carrier of (L)
q * r is Element of the carrier of (L)
the multF of (L) . (q,r) is Element of the carrier of (L)
p * (q * r) is Element of the carrier of (L)
the multF of (L) . (p,(q * r)) is Element of the carrier of (L)
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
q1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
r1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,q1,r1) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,p1,q1) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,(L,p1,q1),r1) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,p1,(L,q1,r1)) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
L is non empty right_complementable unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
(L) is non empty right_complementable strict commutative Abelian add-associative right_zeroed doubleLoopStr
the carrier of (L) is non empty set
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
q is Element of the carrier of (L)
r is Element of the carrier of (L)
1. (L) is Element of the carrier of (L)
the OneF of (L) is Element of the carrier of (L)
(L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
(L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
0. L is V105(L) Element of the carrier of L
the ZeroF of L is Element of the carrier of L
NAT --> (0. L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total V30() Element of bool [:NAT, the carrier of L:]
1. L is Element of the carrier of L
the OneF of L is Element of the carrier of L
(L) +* (0,(1. L)) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q * r is Element of the carrier of (L)
the multF of (L) is Relation-like [: the carrier of (L), the carrier of (L):] -defined the carrier of (L) -valued Function-like total quasi_total Element of bool [:[: the carrier of (L), the carrier of (L):], the carrier of (L):]
[: the carrier of (L), the carrier of (L):] is set
[:[: the carrier of (L), the carrier of (L):], the carrier of (L):] is set
bool [:[: the carrier of (L), the carrier of (L):], the carrier of (L):] is set
the multF of (L) . (q,r) is Element of the carrier of (L)
p1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
(L,p1,(L)) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
r * q is Element of the carrier of (L)
the multF of (L) . (r,q) is Element of the carrier of (L)
L is non empty right_complementable unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
(L) is non empty right_complementable strict commutative Abelian add-associative right_zeroed doubleLoopStr
the carrier of (L) is non empty set
p is Element of the carrier of (L)
1. (L) is Element of the carrier of (L)
the OneF of (L) is Element of the carrier of (L)
p * (1. (L)) is Element of the carrier of (L)
the multF of (L) is Relation-like [: the carrier of (L), the carrier of (L):] -defined the carrier of (L) -valued Function-like total quasi_total Element of bool [:[: the carrier of (L), the carrier of (L):], the carrier of (L):]
[: the carrier of (L), the carrier of (L):] is set
[:[: the carrier of (L), the carrier of (L):], the carrier of (L):] is set
bool [:[: the carrier of (L), the carrier of (L):], the carrier of (L):] is set
the multF of (L) . (p,(1. (L))) is Element of the carrier of (L)
(1. (L)) * p is Element of the carrier of (L)
the multF of (L) . ((1. (L)),p) is Element of the carrier of (L)
L is non empty right_complementable right-distributive left-distributive distributive Abelian add-associative right_zeroed doubleLoopStr
(L) is non empty right_complementable strict Abelian add-associative right_zeroed doubleLoopStr
the carrier of (L) is non empty set
p is Element of the carrier of (L)
q is Element of the carrier of (L)
r is Element of the carrier of (L)
q + r is Element of the carrier of (L)
the addF of (L) is Relation-like [: the carrier of (L), the carrier of (L):] -defined the carrier of (L) -valued Function-like total quasi_total Element of bool [:[: the carrier of (L), the carrier of (L):], the carrier of (L):]
[: the carrier of (L), the carrier of (L):] is set
[:[: the carrier of (L), the carrier of (L):], the carrier of (L):] is set
bool [:[: the carrier of (L), the carrier of (L):], the carrier of (L):] is set
the addF of (L) . (q,r) is Element of the carrier of (L)
p * (q + r) is Element of the carrier of (L)
the multF of (L) is Relation-like [: the carrier of (L), the carrier of (L):] -defined the carrier of (L) -valued Function-like total quasi_total Element of bool [:[: the carrier of (L), the carrier of (L):], the carrier of (L):]
the multF of (L) . (p,(q + r)) is Element of the carrier of (L)
p * q is Element of the carrier of (L)
the multF of (L) . (p,q) is Element of the carrier of (L)
p * r is Element of the carrier of (L)
the multF of (L) . (p,r) is Element of the carrier of (L)
(p * q) + (p * r) is Element of the carrier of (L)
the addF of (L) . ((p * q),(p * r)) is Element of the carrier of (L)
(q + r) * p is Element of the carrier of (L)
the multF of (L) . ((q + r),p) is Element of the carrier of (L)
q * p is Element of the carrier of (L)
the multF of (L) . (q,p) is Element of the carrier of (L)
r * p is Element of the carrier of (L)
the multF of (L) . (r,p) is Element of the carrier of (L)
(q * p) + (r * p) is Element of the carrier of (L)
the addF of (L) . ((q * p),(r * p)) is Element of the carrier of (L)
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
p1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,p1,q1) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
r1 is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,p1,r1) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
q + r is Element of the carrier of (L)
(L,q1,r1) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
p * (q + r) is Element of the carrier of (L)
the multF of (L) . (p,(q + r)) is Element of the carrier of (L)
(L,p1,(L,q1,r1)) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,(L,p1,q1),(L,p1,r1)) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(p * q) + (p * r) is Element of the carrier of (L)
(L,q1,p1) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,r1,p1) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(q + r) * p is Element of the carrier of (L)
the multF of (L) . ((q + r),p) is Element of the carrier of (L)
(L,(L,q1,r1),p1) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(L,(L,q1,p1),(L,r1,p1)) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]
(q * p) + (r * p) is Element of the carrier of (L)
L is non empty right_complementable unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
(L) is non empty right_complementable strict unital commutative right-distributive left-distributive right_unital well-unital distributive left_unital Abelian add-associative right_zeroed doubleLoopStr
1. (L) is Element of the carrier of (L)
the carrier of (L) is non empty set
the OneF of (L) is Element of the carrier of (L)
(L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
the carrier of L is non empty set
[:NAT, the carrier of L:] is non trivial non finite set
bool [:NAT, the carrier of L:] is non trivial non finite set
(L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total finite-Support Element of bool [:NAT, the carrier of L:]
0. L is V105(L) Element of the carrier of L
the ZeroF of L is Element of the carrier of L
NAT --> (0. L) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total V30() Element of bool [:NAT, the carrier of L:]
1. L is Element of the carrier of L
the OneF of L is Element of the carrier of L
(L) +* (0,(1. L)) is Relation-like NAT -defined the carrier of L -valued Function-like non empty total quasi_total Element of bool [:NAT, the carrier of L:]