:: INT_7 semantic presentation

REAL is V71() V72() V73() V77() set
NAT is non empty non trivial V4() V5() V6() non finite cardinal limit_cardinal V71() V72() V73() V74() V75() V76() V77() Element of bool REAL
bool REAL is non empty set
K703() is strict algebraic-closed doubleLoopStr
the carrier of K703() is set
COMPLEX is V71() V77() set
NAT is non empty non trivial V4() V5() V6() non finite cardinal limit_cardinal V71() V72() V73() V74() V75() V76() V77() set
bool NAT is non empty non trivial non finite set
bool NAT is non empty non trivial non finite set
RAT is V71() V72() V73() V74() V77() set
INT is V71() V72() V73() V74() V75() V77() set
{} is empty V4() V5() V6() V8() V9() V10() V11() V12() integer Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional Function-yielding finite finite-yielding V42() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-yielding ext-real-valued real-valued natural-valued V71() V72() V73() V74() V75() V76() V77() FinSequence-yielding finite-support set
1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
{{},1} is non empty finite V42() V71() V72() V73() V74() V75() V76() set
K340() is set
bool K340() is non empty set
K341() is Element of bool K340()
2 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
SetPrimes is non empty non trivial non finite V71() V72() V73() V74() V75() V76() Element of bool NAT
[:1,1:] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:1,1:] is non empty finite V42() set
[:[:1,1:],1:] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:1,1:],1:] is non empty finite V42() set
[:[:1,1:],REAL:] is Relation-like complex-yielding ext-real-valued real-valued set
bool [:[:1,1:],REAL:] is non empty set
[:REAL,REAL:] is Relation-like complex-yielding ext-real-valued real-valued set
[:[:REAL,REAL:],REAL:] is Relation-like complex-yielding ext-real-valued real-valued set
bool [:[:REAL,REAL:],REAL:] is non empty set
[:2,2:] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
[:[:2,2:],REAL:] is Relation-like complex-yielding ext-real-valued real-valued set
bool [:[:2,2:],REAL:] is non empty set
bool [:REAL,REAL:] is non empty set
K491(2) is V193() L15()
the carrier of K491(2) is set
K632() is non empty strict unital Group-like associative commutative cyclic multMagma
the carrier of K632() is non empty V71() V72() V73() V74() V75() set
INT.Ring is non empty non degenerated non trivial non finite left_add-cancelable right_add-cancelable add-cancelable right_complementable strict V181() V182() V183() unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital V238() left_unital V259() V260() V261() V262() V267() doubleLoopStr
addint is Relation-like [:INT,INT:] -defined INT -valued Function-like quasi_total complex-yielding ext-real-valued real-valued Element of bool [:[:INT,INT:],INT:]
[:INT,INT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued set
[:[:INT,INT:],INT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued set
bool [:[:INT,INT:],INT:] is non empty set
multint is Relation-like [:INT,INT:] -defined INT -valued Function-like quasi_total complex-yielding ext-real-valued real-valued Element of bool [:[:INT,INT:],INT:]
In (1,INT) is V11() V12() integer ext-real V52() Element of INT
0 is empty V4() V5() V6() V8() V9() V10() V11() V12() integer Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional Function-yielding finite finite-yielding V42() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative V52() complex-yielding ext-real-valued real-valued natural-valued V71() V72() V73() V74() V75() V76() V77() FinSequence-yielding finite-support Element of NAT
In (0,INT) is V11() V12() integer ext-real V52() Element of INT
doubleLoopStr(# INT,addint,multint,(In (1,INT)),(In (0,INT)) #) is strict doubleLoopStr
the carrier of INT.Ring is non empty non trivial non finite V71() V72() V73() V74() V75() set
[: the carrier of INT.Ring,NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued natural-valued set
bool [: the carrier of INT.Ring,NAT:] is non empty non trivial non finite set
[:NAT,NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:NAT,NAT:] is non empty non trivial non finite set
[:NAT,REAL:] is Relation-like complex-yielding ext-real-valued real-valued set
bool [:NAT,REAL:] is non empty set
K228(1,NAT) is M8( NAT )
[:NAT, the carrier of K703():] is Relation-like set
bool [:NAT, the carrier of K703():] is non empty set
[:COMPLEX,COMPLEX:] is Relation-like complex-yielding set
bool [:COMPLEX,COMPLEX:] is non empty set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is Relation-like complex-yielding set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty set
[:RAT,RAT:] is Relation-like RAT -valued complex-yielding ext-real-valued real-valued set
bool [:RAT,RAT:] is non empty set
[:[:RAT,RAT:],RAT:] is Relation-like RAT -valued complex-yielding ext-real-valued real-valued set
bool [:[:RAT,RAT:],RAT:] is non empty set
bool [:INT,INT:] is non empty set
[:[:NAT,NAT:],NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:NAT,NAT:],NAT:] is non empty non trivial non finite set
3 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
<*> REAL is empty V4() V5() V6() V8() V9() V10() V11() V12() integer Relation-like non-empty empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional Function-yielding finite finite-yielding V42() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-yielding ext-real-valued real-valued natural-valued V71() V72() V73() V74() V75() V76() V77() FinSequence-yielding finite-support FinSequence of REAL
Product (<*> REAL) is V11() V12() ext-real Element of REAL
- 1 is V11() V12() integer ext-real non positive set
p is set
a is set
a --> 0 is Relation-like a -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:a,NAT:]
[:a,NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:a,NAT:] is non empty set
ZP is set
(a --> 0) +* (p,ZP) is Relation-like a -defined Function-like total set
f is set
((a --> 0) +* (p,ZP)) . f is set
dom (a --> 0) is Element of bool a
bool a is non empty set
(a --> 0) . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(a --> 0) . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p is set
p --> 0 is Relation-like p -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:p,NAT:]
[:p,NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:p,NAT:] is non empty set
a is set
{a} is non empty trivial finite 1 -element set
ZP is Relation-like p -defined Function-like total set
support ZP is set
ZP . a is set
(p --> 0) +* (a,(ZP . a)) is Relation-like p -defined Function-like total set
dom ZP is Element of bool p
bool p is non empty set
f is set
ZP . f is set
((p --> 0) +* (a,(ZP . a))) . f is set
dom (p --> 0) is Element of bool p
dom ((p --> 0) +* (a,(ZP . a))) is Element of bool p
dom (p --> 0) is Element of bool p
p is set
a is Relation-like p -defined Function-like total complex-yielding ext-real-valued real-valued set
support a is set
ZP is Relation-like p -defined Function-like total complex-yielding ext-real-valued real-valued set
support ZP is set
(support a) /\ (support ZP) is set
(support a) \/ (support ZP) is set
f is Relation-like p -defined Function-like total complex-yielding ext-real-valued real-valued set
support f is set
a | (support a) is Relation-like support a -defined p -defined Function-like complex-yielding ext-real-valued real-valued set
f | (support a) is Relation-like support a -defined p -defined Function-like complex-yielding ext-real-valued real-valued set
ZP | (support ZP) is Relation-like support ZP -defined p -defined Function-like complex-yielding ext-real-valued real-valued set
f | (support ZP) is Relation-like support ZP -defined p -defined Function-like complex-yielding ext-real-valued real-valued set
a + ZP is Relation-like p -defined Function-like total set
g is set
f . g is V11() V12() ext-real set
a . g is V11() V12() ext-real set
ZP . g is V11() V12() ext-real set
(a . g) + (ZP . g) is V11() V12() ext-real set
(f | (support a)) . g is V11() V12() ext-real set
(a . g) + 0 is V11() V12() ext-real set
(f | (support ZP)) . g is V11() V12() ext-real set
0 + (ZP . g) is V11() V12() ext-real set
0 + (ZP . g) is V11() V12() ext-real set
p is set
a is Relation-like p -defined Function-like total set
support a is set
a | (support a) is Relation-like support a -defined p -defined Function-like set
ZP is Relation-like p -defined Function-like total set
support ZP is set
ZP | (support ZP) is Relation-like support ZP -defined p -defined Function-like set
dom (a | (support a)) is Element of bool (support a)
bool (support a) is non empty set
dom a is Element of bool p
bool p is non empty set
(dom a) /\ (support a) is Element of bool p
dom (ZP | (support ZP)) is Element of bool (support ZP)
bool (support ZP) is non empty set
dom ZP is Element of bool p
(dom ZP) /\ (support ZP) is Element of bool p
f is set
a . f is set
ZP . f is set
(a | (support a)) . f is set
p is set
a is Relation-like p -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support a is finite Element of bool p
bool p is non empty set
ZP is Relation-like p -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support ZP is finite Element of bool p
dom ZP is Element of bool p
(dom ZP) /\ {} is Relation-like finite V71() V72() V73() V74() V75() V76() Element of bool p
ZP | (support ZP) is Relation-like support ZP -defined p -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
dom (ZP | (support ZP)) is finite Element of bool (support ZP)
bool (support ZP) is non empty finite V42() set
a | (support a) is Relation-like support a -defined p -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
dom (a | (support a)) is finite Element of bool (support a)
bool (support a) is non empty finite V42() set
dom a is Element of bool p
(dom a) /\ (support a) is finite Element of bool p
f is set
(a | (support a)) . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(ZP | (support ZP)) . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support p is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
a is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support a is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
p | (support p) is Relation-like support p -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
a | (support p) is Relation-like support p -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
(support a) \ (support p) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
ZP is set
a . ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
[:SetPrimes,NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:SetPrimes,NAT:] is non empty non trivial non finite set
ZP is non empty Relation-like SetPrimes -defined NAT -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:SetPrimes,NAT:]
f is set
ZP . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
f is set
ZP . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
dom ZP is non empty V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
f is set
ZP . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support ZP is set
f is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support f is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(support p) \/ (support f) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(support p) \/ ((support a) \ (support p)) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(support p) \/ (support a) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
ZP | (support ZP) is Relation-like SetPrimes -defined support ZP -defined SetPrimes -defined NAT -valued RAT -valued Function-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:SetPrimes,NAT:]
dom (ZP | (support ZP)) is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
dom ZP is non empty V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(dom ZP) /\ (support ZP) is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
a | (support ZP) is Relation-like support ZP -defined SetPrimes -defined RAT -valued Function-like complex-yielding ext-real-valued real-valued natural-valued set
g is set
(ZP | (support ZP)) . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(a | (support ZP)) . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
dom (a | (support ZP)) is Element of bool (support ZP)
bool (support ZP) is non empty set
dom a is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(dom a) /\ (support ZP) is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(dom a) /\ ((support a) \ (support p)) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(dom a) /\ (support a) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
((dom a) /\ (support a)) \ (support p) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
g is set
(support p) /\ (support ZP) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
p + f is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
p is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support p is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
a is set
(support p) \ a is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
a --> 0 is Relation-like a -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:a,NAT:]
[:a,NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:a,NAT:] is non empty set
p +* (a --> 0) is Relation-like RAT -valued Function-like complex-yielding ext-real-valued real-valued natural-valued set
rng (p +* (a --> 0)) is V71() V72() V73() V74() V75() V76() Element of bool RAT
bool RAT is non empty set
rng p is V71() V72() V73() V74() V75() V76() Element of bool RAT
rng (a --> 0) is V71() V72() V73() V74() V75() V76() Element of bool RAT
(rng p) \/ (rng (a --> 0)) is V71() V72() V73() V74() V75() V76() Element of bool RAT
SetPrimes \ a is V71() V72() V73() V74() V75() V76() Element of bool NAT
(SetPrimes \ a) --> 0 is Relation-like SetPrimes \ a -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:(SetPrimes \ a),NAT:]
[:(SetPrimes \ a),NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:(SetPrimes \ a),NAT:] is non empty set
p +* ((SetPrimes \ a) --> 0) is Relation-like RAT -valued Function-like complex-yielding ext-real-valued real-valued natural-valued set
dom (p +* ((SetPrimes \ a) --> 0)) is set
dom p is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
dom ((SetPrimes \ a) --> 0) is V71() V72() V73() V74() V75() V76() Element of bool (SetPrimes \ a)
bool (SetPrimes \ a) is non empty set
(dom p) \/ (dom ((SetPrimes \ a) --> 0)) is V71() V72() V73() V74() V75() V76() set
(dom p) \/ (SetPrimes \ a) is V71() V72() V73() V74() V75() V76() set
SetPrimes \/ (SetPrimes \ a) is non empty V71() V72() V73() V74() V75() V76() Element of bool NAT
rng (p +* ((SetPrimes \ a) --> 0)) is V71() V72() V73() V74() V75() V76() Element of bool RAT
rng ((SetPrimes \ a) --> 0) is V71() V72() V73() V74() V75() V76() Element of bool RAT
(rng p) \/ (rng ((SetPrimes \ a) --> 0)) is V71() V72() V73() V74() V75() V76() Element of bool RAT
[:SetPrimes,NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:SetPrimes,NAT:] is non empty non trivial non finite set
g is non empty Relation-like SetPrimes -defined NAT -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:SetPrimes,NAT:]
y is set
g . y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
((SetPrimes \ a) --> 0) . y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
dom (a --> 0) is Element of bool a
bool a is non empty set
dom (p +* (a --> 0)) is set
(dom p) \/ a is set
SetPrimes \/ a is non empty set
y is non empty Relation-like SetPrimes -defined NAT -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:SetPrimes,NAT:]
support y is set
y | (support y) is Relation-like SetPrimes -defined support y -defined SetPrimes -defined NAT -valued RAT -valued Function-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:SetPrimes,NAT:]
dom (y | (support y)) is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
dom y is non empty V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(dom y) /\ (support y) is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
x is set
g . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
y . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
dom g is non empty V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
x is set
g . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
x is set
g . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
x is set
g . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support g is set
g | (support g) is Relation-like SetPrimes -defined support g -defined SetPrimes -defined NAT -valued RAT -valued Function-like complex-yielding ext-real-valued real-valued natural-valued Element of bool [:SetPrimes,NAT:]
dom (g | (support g)) is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
dom g is non empty V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(dom g) /\ (support g) is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
p | (support g) is Relation-like support g -defined SetPrimes -defined RAT -valued Function-like complex-yielding ext-real-valued real-valued natural-valued set
x is set
(g | (support g)) . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(p | (support g)) . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
g . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
dom (p | (support g)) is Element of bool (support g)
bool (support g) is non empty set
(dom p) /\ (support g) is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(dom p) /\ a is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
x is set
y . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(a --> 0) . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
x is set
y . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p | (support y) is Relation-like support y -defined SetPrimes -defined RAT -valued Function-like complex-yielding ext-real-valued real-valued natural-valued set
dom (p | (support y)) is Element of bool (support y)
bool (support y) is non empty set
(dom p) /\ (support y) is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(dom p) /\ ((support p) \ a) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(dom p) /\ (support p) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
((dom p) /\ (support p)) \ a is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(support y) /\ (support g) is set
gg is set
p . gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
y . gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
gg is set
(y | (support y)) . gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(p | (support y)) . gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p . gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
y . gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(support g) \/ (support y) is set
(support p) \ (support g) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(support g) \/ ((support p) \ (support g)) is set
(support g) \/ (support p) is set
x is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
x is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
x + x is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
p is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
prime_factorization p is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
a is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
support (prime_factorization p) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
(prime_factorization p) . a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a |-count p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a |^ (a |-count p) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
prime_exponents p is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support (prime_exponents p) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
p is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
a is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
a |^ ZP is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
f * (a |^ ZP) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
p is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
a is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support a is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
Product a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a . p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
p |^ ZP is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
rng a is V71() V72() V73() V74() V75() V76() Element of bool RAT
bool RAT is non empty set
canFS (support a) is Relation-like NAT -defined support a -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued finite-support FinSequence of support a
rng (canFS (support a)) is finite V71() V72() V73() V74() V75() V76() Element of bool (support a)
bool (support a) is non empty finite V42() set
dom (canFS (support a)) is finite V71() V72() V73() V74() V75() V76() Element of bool NAT
f is set
(canFS (support a)) . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(canFS (support a)) * a is Relation-like NAT -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
g is Relation-like NAT -defined COMPLEX -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding finite-support FinSequence of COMPLEX
Product g is V11() Element of COMPLEX
rng g is finite V71() Element of bool COMPLEX
bool COMPLEX is non empty set
dom a is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
y is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued V93() finite-support FinSequence of NAT
dom y is finite V71() V72() V73() V74() V75() V76() Element of bool NAT
((canFS (support a)) * a) . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
rng y is finite V71() V72() V73() V74() V75() V76() Element of bool NAT
Product y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued V93() finite-support FinSequence of NAT
len p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
<*a*> is non empty trivial Relation-like NAT -defined NAT -valued Function-like one-to-one constant finite 1 -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued V65() decreasing non-decreasing non-increasing V93() finite-support M9( NAT ,K227(NAT))
K227(NAT) is non empty functional FinSequence-membered M8( NAT )
[1,a] is set
{1,a} is non empty finite V42() V71() V72() V73() V74() V75() V76() set
{1} is non empty trivial finite V42() 1 -element V71() V72() V73() V74() V75() V76() set
{{1,a},{1}} is non empty finite V42() set
{[1,a]} is non empty trivial Relation-like Function-like constant finite 1 -element finite-support set
p ^ <*a*> is non empty Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued V93() finite-support FinSequence of NAT
ZP is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support ZP is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
canFS (support ZP) is Relation-like NAT -defined support ZP -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued finite-support FinSequence of support ZP
(canFS (support ZP)) * ZP is Relation-like NAT -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
rng (canFS (support ZP)) is finite V71() V72() V73() V74() V75() V76() Element of bool (support ZP)
bool (support ZP) is non empty finite V42() set
dom ZP is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
dom ((canFS (support ZP)) * ZP) is finite V71() V72() V73() V74() V75() V76() Element of bool NAT
dom (canFS (support ZP)) is finite V71() V72() V73() V74() V75() V76() Element of bool NAT
dom p is finite V71() V72() V73() V74() V75() V76() Element of bool NAT
((canFS (support ZP)) * ZP) | (dom p) is Relation-like dom p -defined NAT -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
(dom ((canFS (support ZP)) * ZP)) /\ (dom p) is finite V71() V72() V73() V74() V75() V76() Element of bool NAT
(canFS (support ZP)) | (dom p) is Relation-like NAT -defined dom p -defined NAT -defined RAT -valued support ZP -valued Function-like finite FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:NAT,(support ZP):]
[:NAT,(support ZP):] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:NAT,(support ZP):] is non empty set
dom ((canFS (support ZP)) | (dom p)) is finite V71() V72() V73() V74() V75() V76() Element of bool NAT
card (support ZP) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
len (canFS (support ZP)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(len p) + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Seg ((len p) + 1) is non empty finite (len p) + 1 -element (len p) + 1 -element V71() V72() V73() V74() V75() V76() Element of bool NAT
(len p) + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
{ b₁ where b₁ is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT : ( 1 <= b₁ & b₁ <= (len p) + 1 ) } is set
len <*a*> is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
len (p ^ <*a*>) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(p ^ <*a*>) . ((len p) + 1) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(canFS (support ZP)) . ((len p) + 1) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP . ((canFS (support ZP)) . ((len p) + 1)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
f is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
{f} is non empty trivial finite V42() 1 -element V71() V72() V73() V74() V75() V76() set
(support ZP) \ {f} is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
g is Relation-like SetPrimes -defined Function-like total set
rng g is set
y is set
dom g is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
x is set
g . x is set
x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of SetPrimes
g . x is set
ZP . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
y is set
support g is set
dom g is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
g . y is set
x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of SetPrimes
g . x is set
y is set
x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of SetPrimes
g . x is set
ZP . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
f |^ x is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
card (dom ((canFS (support ZP)) * ZP)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
card (dom (canFS (support ZP))) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Seg (len (canFS (support ZP))) is finite len (canFS (support ZP)) -element V71() V72() V73() V74() V75() V76() Element of bool NAT
{ b₁ where b₁ is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT : ( 1 <= b₁ & b₁ <= len (canFS (support ZP)) ) } is set
card (Seg (len (canFS (support ZP)))) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
card (len (canFS (support ZP))) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Seg (len (p ^ <*a*>)) is non empty finite len (p ^ <*a*>) -element V71() V72() V73() V74() V75() V76() Element of bool NAT
{ b₁ where b₁ is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT : ( 1 <= b₁ & b₁ <= len (p ^ <*a*>) ) } is set
card (Seg (len (p ^ <*a*>))) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
card (len (p ^ <*a*>)) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
card ((support ZP) \ {f}) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
card {f} is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(card (support ZP)) - (card {f}) is V11() V12() integer ext-real set
(card (support ZP)) - 1 is V11() V12() integer ext-real set
y is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support y is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
canFS (support y) is Relation-like NAT -defined support y -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued finite-support FinSequence of support y
len (canFS (support y)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
dom (canFS (support y)) is finite V71() V72() V73() V74() V75() V76() Element of bool NAT
Seg (len p) is finite len p -element V71() V72() V73() V74() V75() V76() Element of bool NAT
{ b₁ where b₁ is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT : ( 1 <= b₁ & b₁ <= len p ) } is set
gg is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
ZP . gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
gg |^ n is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
m0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
y . gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
gg |^ m0 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
(canFS (support y)) * y is Relation-like NAT -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
Seg (len (canFS (support y))) is finite len (canFS (support y)) -element V71() V72() V73() V74() V75() V76() Element of bool NAT
{ b₁ where b₁ is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT : ( 1 <= b₁ & b₁ <= len (canFS (support y)) ) } is set
Seg 0 is empty proper V4() V5() V6() V8() V9() V10() V11() V12() integer Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional Function-yielding finite finite-yielding V42() cardinal 0 -element {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-yielding ext-real-valued real-valued natural-valued V71() V72() V73() V74() V75() V76() V77() FinSequence-yielding finite-support Element of bool NAT
{ b₁ where b₁ is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT : ( 1 <= b₁ & b₁ <= 0 ) } is set
<*> NAT is empty V4() V5() V6() V8() V9() V10() V11() V12() integer Relation-like non-empty empty-yielding NAT -defined NAT -valued Function-like one-to-one constant functional Function-yielding finite finite-yielding V42() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-yielding ext-real-valued real-valued natural-valued V71() V72() V73() V74() V75() V76() V77() V93() FinSequence-yielding finite-support M9( NAT ,K227(NAT))
n is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued V93() finite-support FinSequence of NAT
len n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
f |^ x is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
gg is set
n is set
(canFS (support ZP)) . n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
m0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(dom (canFS (support ZP))) /\ (dom p) is finite V71() V72() V73() V74() V75() V76() Element of bool NAT
((canFS (support ZP)) | (dom p)) . n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
rng ((canFS (support ZP)) | (dom p)) is finite V71() V72() V73() V74() V75() V76() Element of bool RAT
bool RAT is non empty set
gg is set
n is set
((canFS (support ZP)) | (dom p)) . n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(canFS (support ZP)) . n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
1 + (len p) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(len p) + 0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
[:(dom p),((support ZP) \ {f}):] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(dom p),((support ZP) \ {f}):] is non empty finite V42() set
gg is Relation-like dom p -defined (support ZP) \ {f} -valued Function-like quasi_total finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:(dom p),((support ZP) \ {f}):]
gg " is Relation-like Function-like set
dom (gg ") is set
dom gg is finite V71() V72() V73() V74() V75() V76() Element of bool (dom p)
bool (dom p) is non empty finite V42() set
rng (gg ") is set
[:((support ZP) \ {f}),(dom p):] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:((support ZP) \ {f}),(dom p):] is non empty finite V42() set
rng (canFS (support y)) is finite V71() V72() V73() V74() V75() V76() Element of bool (support y)
bool (support y) is non empty finite V42() set
[:(dom p),(dom p):] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(dom p),(dom p):] is non empty finite V42() set
n is Relation-like (support ZP) \ {f} -defined dom p -valued Function-like quasi_total finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:((support ZP) \ {f}),(dom p):]
n * (canFS (support y)) is Relation-like NAT -defined RAT -valued dom p -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:NAT,(dom p):]
[:NAT,(dom p):] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:NAT,(dom p):] is non empty set
m0 is Relation-like dom p -defined dom p -valued Function-like total quasi_total finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:(dom p),(dom p):]
rng m0 is finite V71() V72() V73() V74() V75() V76() Element of bool (dom p)
n0 is Relation-like dom p -defined dom p -valued Function-like one-to-one total quasi_total onto bijective finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:(dom p),(dom p):]
((canFS (support ZP)) | (dom p)) * n0 is Relation-like dom p -defined RAT -valued support ZP -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:(dom p),(support ZP):]
[:(dom p),(support ZP):] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(dom p),(support ZP):] is non empty finite V42() set
((canFS (support ZP)) | (dom p)) * n is Relation-like (support ZP) \ {f} -defined RAT -valued support ZP -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:((support ZP) \ {f}),(support ZP):]
[:((support ZP) \ {f}),(support ZP):] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:((support ZP) \ {f}),(support ZP):] is non empty finite V42() set
(((canFS (support ZP)) | (dom p)) * n) * (canFS (support y)) is Relation-like NAT -defined RAT -valued support ZP -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:NAT,(support ZP):]
id (support y) is Relation-like support y -defined support y -valued RAT -valued INT -valued Function-like one-to-one total quasi_total finite complex-yielding ext-real-valued real-valued natural-valued V65() non-decreasing finite-support Element of bool [:(support y),(support y):]
[:(support y),(support y):] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(support y),(support y):] is non empty finite V42() set
(id (support y)) * (canFS (support y)) is Relation-like NAT -defined NAT -valued RAT -valued INT -valued Function-like one-to-one finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:NAT,NAT:]
n0 " is Relation-like dom p -defined dom p -valued Function-like one-to-one total quasi_total onto bijective finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:(dom p),(dom p):]
(canFS (support y)) * (n0 ") is Relation-like dom p -defined RAT -valued support y -valued Function-like one-to-one finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:(dom p),(support y):]
[:(dom p),(support y):] is Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:(dom p),(support y):] is non empty finite V42() set
n0 * (n0 ") is Relation-like dom p -defined RAT -valued dom p -valued Function-like one-to-one total quasi_total onto bijective finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:(dom p),(dom p):]
((canFS (support ZP)) | (dom p)) * (n0 * (n0 ")) is Relation-like dom p -defined RAT -valued support ZP -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:(dom p),(support ZP):]
u is Relation-like dom p -defined dom p -valued Function-like one-to-one total quasi_total onto bijective finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:(dom p),(dom p):]
rng u is finite V71() V72() V73() V74() V75() V76() Element of bool (dom p)
j is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom j is finite V71() V72() V73() V74() V75() V76() Element of bool NAT
u * j is Relation-like dom p -defined Function-like finite finite-support set
dom (u * j) is finite V71() V72() V73() V74() V75() V76() Element of bool (dom p)
dom u is finite V71() V72() V73() V74() V75() V76() Element of bool (dom p)
j * y is Relation-like NAT -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
dom y is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
dom (j * y) is finite V71() V72() V73() V74() V75() V76() Element of bool NAT
rng (u * j) is finite set
rng j is finite set
(u * j) * y is Relation-like dom p -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
dom ((u * j) * y) is finite V71() V72() V73() V74() V75() V76() Element of bool (dom p)
rng n0 is finite V71() V72() V73() V74() V75() V76() Element of bool (dom p)
id (dom p) is Relation-like dom p -defined dom p -valued RAT -valued INT -valued Function-like one-to-one total quasi_total finite complex-yielding ext-real-valued real-valued natural-valued V65() non-decreasing finite-support Element of bool [:(dom p),(dom p):]
((canFS (support ZP)) | (dom p)) * (id (dom p)) is Relation-like dom p -defined RAT -valued support ZP -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:(dom p),(support ZP):]
dom (p ^ <*a*>) is non empty finite V71() V72() V73() V74() V75() V76() Element of bool NAT
d1 is set
(u * j) . d1 is set
p . d1 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(p ^ <*a*>) . d1 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(canFS (support ZP)) . d1 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP . ((canFS (support ZP)) . d1) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
((canFS (support ZP)) | (dom p)) . d1 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP . (((canFS (support ZP)) | (dom p)) . d1) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP . ((u * j) . d1) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
y . ((u * j) . d1) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
((u * j) * y) . d1 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
u * (j * y) is Relation-like dom p -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
rng (j * y) is finite V71() V72() V73() V74() V75() V76() Element of bool RAT
d1 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued V93() finite-support FinSequence of NAT
len d1 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product d1 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
f |^ x is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
(canFS (support y)) * y is Relation-like NAT -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
Seg (len d1) is finite len d1 -element V71() V72() V73() V74() V75() V76() Element of bool NAT
{ b₁ where b₁ is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT : ( 1 <= b₁ & b₁ <= len d1 ) } is set
p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued V93() finite-support FinSequence of NAT
len a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
Product ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support ZP is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
canFS (support ZP) is Relation-like NAT -defined support ZP -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued finite-support FinSequence of support ZP
(canFS (support ZP)) * ZP is Relation-like NAT -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
f is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
a | p is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued V93() finite-support FinSequence of NAT
Seg p is finite p -element V71() V72() V73() V74() V75() V76() Element of bool NAT
{ b₁ where b₁ is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT : ( 1 <= b₁ & b₁ <= p ) } is set
a | (Seg p) is Relation-like NAT -defined Seg p -defined NAT -defined NAT -valued RAT -valued Function-like finite FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued finite-support set
a . (p + 1) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
g is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued V93() finite-support FinSequence of NAT
len g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a /. (len a) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
<*(a /. (len a))*> is non empty trivial Relation-like NAT -defined NAT -valued Function-like one-to-one constant finite 1 -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued V65() decreasing non-decreasing non-increasing V93() finite-support M9( NAT ,K227(NAT))
K227(NAT) is non empty functional FinSequence-membered M8( NAT )
[1,(a /. (len a))] is set
{1,(a /. (len a))} is non empty finite V42() V71() V72() V73() V74() V75() V76() set
{1} is non empty trivial finite V42() 1 -element V71() V72() V73() V74() V75() V76() set
{{1,(a /. (len a))},{1}} is non empty finite V42() set
{[1,(a /. (len a))]} is non empty trivial Relation-like Function-like constant finite 1 -element finite-support set
(a | p) ^ <*(a /. (len a))*> is non empty Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued V93() finite-support FinSequence of NAT
y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
<*y*> is non empty trivial Relation-like NAT -defined NAT -valued Function-like one-to-one constant finite 1 -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued V65() decreasing non-decreasing non-increasing V93() finite-support M9( NAT ,K227(NAT))
[1,y] is set
{1,y} is non empty finite V42() V71() V72() V73() V74() V75() V76() set
{{1,y},{1}} is non empty finite V42() set
{[1,y]} is non empty trivial Relation-like Function-like constant finite 1 -element finite-support set
g ^ <*y*> is non empty Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued V93() finite-support FinSequence of NAT
Product g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
n is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
x is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
support n is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
{x} is non empty trivial finite V42() 1 -element V71() V72() V73() V74() V75() V76() set
(support ZP) \ {x} is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
x |^ gg is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
x is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued V93() finite-support FinSequence of NAT
len x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
canFS (support n) is Relation-like NAT -defined support n -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued finite-support FinSequence of support n
(canFS (support n)) * n is Relation-like NAT -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
(Product x) * y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
rng x is finite V71() V72() V73() V74() V75() V76() Element of bool NAT
Product n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
m0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
x * m0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued V93() finite-support FinSequence of NAT
len p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
Product a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support a is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
canFS (support a) is Relation-like NAT -defined support a -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued finite-support FinSequence of support a
(canFS (support a)) * a is Relation-like NAT -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
ZP is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
<*> NAT is empty V4() V5() V6() V8() V9() V10() V11() V12() integer Relation-like non-empty empty-yielding NAT -defined NAT -valued Function-like one-to-one constant functional Function-yielding finite finite-yielding V42() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-yielding ext-real-valued real-valued natural-valued V71() V72() V73() V74() V75() V76() V77() V93() FinSequence-yielding finite-support M9( NAT ,K227(NAT))
K227(NAT) is non empty functional FinSequence-membered M8( NAT )
a is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued V93() finite-support FinSequence of NAT
len a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
Product ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
f is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
Product a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support ZP is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
canFS (support ZP) is Relation-like NAT -defined support ZP -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued finite-support FinSequence of support ZP
(canFS (support ZP)) * ZP is Relation-like NAT -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
p is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued V93() finite-support FinSequence of NAT
Product p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
Product a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support a is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
canFS (support a) is Relation-like NAT -defined support a -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued finite-support FinSequence of support a
(canFS (support a)) * a is Relation-like NAT -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
ZP is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
len p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
a is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
Product a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support a is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
rng a is V71() V72() V73() V74() V75() V76() Element of bool RAT
bool RAT is non empty set
canFS (support a) is Relation-like NAT -defined support a -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued finite-support FinSequence of support a
(canFS (support a)) * a is Relation-like NAT -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
ZP is Relation-like NAT -defined COMPLEX -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding finite-support FinSequence of COMPLEX
Product ZP is V11() Element of COMPLEX
rng ZP is finite V71() Element of bool COMPLEX
bool COMPLEX is non empty set
f is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued V93() finite-support FinSequence of NAT
Product f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support p is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
a is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support a is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
p | (support p) is Relation-like support p -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
a | (support p) is Relation-like support p -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
Product p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(support a) \ (support p) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
ZP is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support ZP is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
ZP | (support ZP) is Relation-like support ZP -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
a | (support ZP) is Relation-like support ZP -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
p + ZP is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
Product ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(Product p) * (Product ZP) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
a is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
Product p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support p is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
ZP is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
p is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
a is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
p lcm a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
prime_factorization ZP is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support () set
support (prime_factorization ZP) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
prime_factorization p is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support () set
support (prime_factorization p) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
prime_factorization a is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support () set
support (prime_factorization a) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(support (prime_factorization p)) \/ (support (prime_factorization a)) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
prime_exponents p is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support (prime_exponents p) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
prime_exponents a is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support (prime_exponents a) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(support (prime_exponents p)) \/ (support (prime_exponents a)) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
max ((prime_exponents p),(prime_exponents a)) is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support (max ((prime_exponents p),(prime_exponents a))) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
f is set
(prime_exponents p) . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(max ((prime_exponents p),(prime_exponents a))) . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(prime_exponents a) . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(prime_exponents a) . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(prime_exponents a) . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(prime_exponents a) . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(max ((prime_exponents p),(prime_exponents a))) . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(prime_exponents p) . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(prime_exponents p) . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(prime_exponents p) . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
prime_exponents ZP is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support (prime_exponents ZP) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
p is set
a is Relation-like p -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
ZP is Relation-like p -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
min (a,ZP) is Relation-like p -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support (min (a,ZP)) is finite Element of bool p
bool p is non empty set
support a is finite Element of bool p
support ZP is finite Element of bool p
(support a) /\ (support ZP) is finite Element of bool p
g is set
a . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(min (a,ZP)) . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(min (a,ZP)) . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
g is set
ZP . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(min (a,ZP)) . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
p is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
a is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
p gcd a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
prime_factorization ZP is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support () set
support (prime_factorization ZP) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
prime_factorization p is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support () set
support (prime_factorization p) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
prime_factorization a is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support () set
support (prime_factorization a) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(support (prime_factorization p)) /\ (support (prime_factorization a)) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
prime_exponents p is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support (prime_exponents p) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
prime_exponents a is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support (prime_exponents a) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
prime_exponents ZP is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support (prime_exponents ZP) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
min ((prime_exponents p),(prime_exponents a)) is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support (min ((prime_exponents p),(prime_exponents a))) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
p is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
a is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support p is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
support a is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
Product p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
SetPrimes --> 0 is non empty Relation-like SetPrimes -defined NAT -valued RAT -valued INT -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:SetPrimes,NAT:]
[:SetPrimes,NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:SetPrimes,NAT:] is non empty non trivial non finite set
p is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
{p} is non empty trivial finite V42() 1 -element V71() V72() V73() V74() V75() V76() set
a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(SetPrimes --> 0) +* (p,a) is non empty Relation-like SetPrimes -defined NAT -valued RAT -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:SetPrimes,NAT:]
dom (SetPrimes --> 0) is non empty V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
f is Relation-like SetPrimes -defined Function-like total set
f . p is set
g is set
f . g is set
g is set
support f is set
dom f is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
f . g is set
y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of SetPrimes
f . y is set
g is set
g is set
g is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support g is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
dom g is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
g . p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
canFS (support g) is Relation-like NAT -defined support g -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued finite-support FinSequence of support g
(canFS (support g)) * g is Relation-like NAT -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
y is Relation-like NAT -defined COMPLEX -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding finite-support FinSequence of COMPLEX
Product y is V11() Element of COMPLEX
<*p*> is non empty trivial Relation-like NAT -defined Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support set
[1,p] is set
{1,p} is non empty finite V42() V71() V72() V73() V74() V75() V76() set
{1} is non empty trivial finite V42() 1 -element V71() V72() V73() V74() V75() V76() set
{{1,p},{1}} is non empty finite V42() set
{[1,p]} is non empty trivial Relation-like Function-like constant finite 1 -element finite-support set
<*p*> * g is Relation-like NAT -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
g . p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
<*(g . p)*> is non empty trivial Relation-like NAT -defined NAT -valued Function-like one-to-one constant finite 1 -element FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued V65() decreasing non-decreasing non-increasing V93() finite-support M9( NAT ,K227(NAT))
K227(NAT) is non empty functional FinSequence-membered M8( NAT )
[1,(g . p)] is set
{1,(g . p)} is non empty finite V42() V71() V72() V73() V74() V75() V76() set
{{1,(g . p)},{1}} is non empty finite V42() set
{[1,(g . p)]} is non empty trivial Relation-like Function-like constant finite 1 -element finite-support set
p is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support p is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
Product p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
p . a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
{a} is non empty trivial finite V42() 1 -element V71() V72() V73() V74() V75() V76() set
(support p) \ {a} is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
a |^ ZP is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
f + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
0 + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a to_power ZP is V11() V12() ext-real set
a to_power 1 is V11() V12() ext-real set
a |^ 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
g is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support g is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
y is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support y is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
g | (support g) is Relation-like support g -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
p | (support g) is Relation-like support g -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
y | (support y) is Relation-like support y -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
p | (support y) is Relation-like support y -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
g + y is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
y . a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(SetPrimes --> 0) +* (a,(y . a)) is non empty Relation-like SetPrimes -defined NAT -valued RAT -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:SetPrimes,NAT:]
x is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
p . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
x |^ x is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
g . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(g | (support g)) . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
x |^ gg is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
(y | (support y)) . a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(Product g) * (Product y) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
x is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support x is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
Product x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support p is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
Product p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
p . a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
{a} is non empty trivial finite V42() 1 -element V71() V72() V73() V74() V75() V76() set
ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
a |^ ZP is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
f + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
dom (SetPrimes --> 0) is non empty V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(SetPrimes --> 0) +* (a,a) is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued set
(support p) \ {a} is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
y is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support y is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
x is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support x is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
y | (support y) is Relation-like support y -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
p | (support y) is Relation-like support y -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
x | (support x) is Relation-like support x -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
p | (support x) is Relation-like support x -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
y + x is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
x . a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(x | (support x)) . a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(x . a) / a is V11() V12() ext-real non negative set
a |^ f is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
(a |^ f) * a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
((a |^ f) * a) / a is V11() V12() ext-real non negative set
x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(SetPrimes --> 0) +* (a,x) is non empty Relation-like SetPrimes -defined NAT -valued RAT -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:SetPrimes,NAT:]
x * a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
n is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support n is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
Product n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
y + n is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
(SetPrimes --> 0) +* (a,(x . a)) is non empty Relation-like SetPrimes -defined NAT -valued RAT -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:SetPrimes,NAT:]
n0 is set
(y + n) . n0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
y . n0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
n . n0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(y . n0) + (n . n0) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support (y + n) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(support (y + n)) \ {a} is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(support y) \/ (support n) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(y | (support y)) . n0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p . n0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
dom (y + n) is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
dom p is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(y + n) | ((support (y + n)) \ {a}) is Relation-like (support (y + n)) \ {a} -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
p | ((support (y + n)) \ {a}) is Relation-like (support (y + n)) \ {a} -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
(support y) /\ (support x) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
n0 is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
(y + n) . n0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
y . n0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
n . n0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(y . n0) + (n . n0) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(y | (support y)) . n0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p . n0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
j is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
0 + (n . n0) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
n0 |^ j is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
(y + n) . a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
y . a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
n . a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(y . a) + (n . a) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
0 + (n . a) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
((y + n) . a) * a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
x * a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(Product n) * a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(Product y) * ((Product n) * a) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(Product y) * (Product n) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
((Product y) * (Product n)) * a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product (y + n) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(Product (y + n)) * a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
n0 is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support n0 is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
Product n0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
((support p) \ {a}) \/ {a} is non empty finite V71() V72() V73() V74() V75() V76() set
(support p) \/ {a} is non empty finite V71() V72() V73() V74() V75() V76() set
n0 is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support n0 is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
Product n0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
Product p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support p is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
canFS (support p) is Relation-like NAT -defined support p -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued finite-support FinSequence of support p
rng (canFS (support p)) is finite V71() V72() V73() V74() V75() V76() Element of bool (support p)
bool (support p) is non empty finite V42() set
(canFS (support p)) * p is Relation-like NAT -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
a is Relation-like NAT -defined COMPLEX -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding finite-support FinSequence of COMPLEX
Product a is V11() Element of COMPLEX
ZP is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding finite-support set
dom ZP is finite V71() V72() V73() V74() V75() V76() Element of bool NAT
f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
ZP . f is V11() set
dom (canFS (support p)) is finite V71() V72() V73() V74() V75() V76() Element of bool NAT
(canFS (support p)) . f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
g is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
p . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
g |^ y is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
p is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
Product p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support p is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
a is set
ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
f is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
canFS (support p) is Relation-like NAT -defined support p -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued natural-valued finite-support FinSequence of support p
(canFS (support p)) * p is Relation-like NAT -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
a is Relation-like NAT -defined COMPLEX -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding finite-support FinSequence of COMPLEX
Product a is V11() Element of COMPLEX
p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
2 |^ p is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
ZP is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
Product a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
2 |^ (p + 1) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support a is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
support ZP is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
support a is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
f is set
g is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
support ZP is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
a . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
{g} is non empty trivial finite V42() 1 -element V71() V72() V73() V74() V75() V76() set
y is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
x is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support x is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
Product x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support y is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(support y) \ {g} is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
y | ((support y) \ {g}) is Relation-like (support y) \ {g} -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
a | ((support y) \ {g}) is Relation-like (support y) \ {g} -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
y . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(y . g) * g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(Product y) * g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
1 + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(2 |^ (p + 1)) / g is V11() V12() ext-real non negative set
(2 |^ (p + 1)) / 2 is V11() V12() ext-real non negative set
x is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
gg is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support gg is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
Product gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support x is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(support x) \ {g} is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
x | ((support x) \ {g}) is Relation-like (support x) \ {g} -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
ZP | ((support x) \ {g}) is Relation-like (support x) \ {g} -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
x . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(x . g) * g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(Product x) * g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
((Product y) * g) / g is V11() V12() ext-real non negative set
2 |^ 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(2 |^ p) * (2 |^ 1) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
((2 |^ p) * (2 |^ 1)) / 2 is V11() V12() ext-real non negative set
(2 |^ p) * 2 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
((2 |^ p) * 2) / 2 is V11() V12() ext-real non negative set
n is set
a . n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(a | ((support y) \ {g})) . n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP . n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a . n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP . n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
dom a is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
dom ZP is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
a | (support a) is Relation-like support a -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
ZP | (support ZP) is Relation-like support ZP -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
ZP . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
1 + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(2 |^ (p + 1)) / g is V11() V12() ext-real non negative set
(2 |^ (p + 1)) / 2 is V11() V12() ext-real non negative set
((Product y) * g) / g is V11() V12() ext-real non negative set
2 |^ 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(2 |^ p) * (2 |^ 1) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
((2 |^ p) * (2 |^ 1)) / 2 is V11() V12() ext-real non negative set
(2 |^ p) * 2 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
((2 |^ p) * 2) / 2 is V11() V12() ext-real non negative set
(support ZP) \ {g} is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
x is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
gg is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support gg is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
Product gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support x is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
x | (support x) is Relation-like support x -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
ZP | (support x) is Relation-like support x -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
Product x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(Product x) * g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
{g} is non empty trivial finite V42() 1 -element V71() V72() V73() V74() V75() V76() set
(support a) \ {g} is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
y is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
x is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support x is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
Product x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support y is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
y | (support y) is Relation-like support y -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
a | (support y) is Relation-like support y -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
Product y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(Product y) * g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
1 + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(2 |^ (p + 1)) / g is V11() V12() ext-real non negative set
(2 |^ (p + 1)) / 2 is V11() V12() ext-real non negative set
((Product y) * g) / g is V11() V12() ext-real non negative set
2 |^ 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(2 |^ p) * (2 |^ 1) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
((2 |^ p) * (2 |^ 1)) / 2 is V11() V12() ext-real non negative set
(2 |^ p) * 2 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
((2 |^ p) * 2) / 2 is V11() V12() ext-real non negative set
x is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
gg is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support gg is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
Product gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support x is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(support x) \ {g} is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
x | ((support x) \ {g}) is Relation-like (support x) \ {g} -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
ZP | ((support x) \ {g}) is Relation-like (support x) \ {g} -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
x . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(x . g) * g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(Product x) * g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
1 + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(2 |^ (p + 1)) / g is V11() V12() ext-real non negative set
(2 |^ (p + 1)) / 2 is V11() V12() ext-real non negative set
(support ZP) \ {g} is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
x is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
gg is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support gg is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
Product gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support x is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
x | (support x) is Relation-like support x -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
ZP | (support x) is Relation-like support x -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
Product x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(Product x) * g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
((Product y) * g) / g is V11() V12() ext-real non negative set
2 |^ 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(2 |^ p) * (2 |^ 1) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
((2 |^ p) * (2 |^ 1)) / 2 is V11() V12() ext-real non negative set
(2 |^ p) * 2 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
((2 |^ p) * 2) / 2 is V11() V12() ext-real non negative set
(support a) \/ {g} is non empty finite V71() V72() V73() V74() V75() V76() set
((support ZP) \ {g}) \/ {g} is non empty finite V71() V72() V73() V74() V75() V76() set
(support ZP) \/ {g} is non empty finite V71() V72() V73() V74() V75() V76() set
n is set
a . n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(y | (support y)) . n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP . n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a . n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP . n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
dom a is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
dom ZP is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
a | (support a) is Relation-like support a -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
ZP | (support a) is Relation-like support a -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
ZP | (support ZP) is Relation-like support ZP -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
ZP . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a . g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support a is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
a is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
ZP is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
Product a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
2 |^ 0 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
a is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
Product p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
0 + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support p is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
support a is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
a is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
ZP is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
Product a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
2 |^ p is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
a is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
Product p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
2 |^ ZP is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
Product p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
prime_factorization a is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support () set
Product (prime_factorization a) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p lcm a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
ZP is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
prime_factorization ZP is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support () set
support (prime_factorization ZP) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
bool SetPrimes is non empty non trivial non finite set
y is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
prime_exponents y is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
prime_exponents ZP is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
{ b₁ where b₁ is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT : ( b₁ in support (prime_factorization ZP) & (prime_exponents y) . b₁ = (prime_exponents ZP) . b₁ ) } is set
prime_factorization y is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support () set
support (prime_factorization y) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(support (prime_factorization y)) \ { b₁ where b₁ is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT : ( b₁ in support (prime_factorization ZP) & (prime_exponents y) . b₁ = (prime_exponents ZP) . b₁ ) } is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
gg is set
n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(prime_exponents y) . n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(prime_exponents ZP) . n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
f is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
prime_exponents f is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
gg is set
(prime_exponents y) . gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(prime_exponents f) . gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(prime_exponents ZP) . gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
max ((prime_exponents ZP),(prime_exponents f)) is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
(max ((prime_exponents ZP),(prime_exponents f))) . gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support (prime_exponents ZP) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
prime_factorization f is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support () set
Product (prime_factorization f) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support (prime_factorization f) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(support (prime_factorization ZP)) \/ (support (prime_factorization f)) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
gg is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support gg is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
n is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
support n is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
gg | (support gg) is Relation-like support gg -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
(prime_factorization y) | (support gg) is Relation-like support gg -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
n | (support n) is Relation-like support n -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
(prime_factorization y) | (support n) is Relation-like support n -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
gg + n is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
Product n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product (prime_factorization ZP) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
j is set
(prime_exponents ZP) . j is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(prime_exponents f) . j is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
max ((prime_exponents ZP),(prime_exponents f)) is Relation-like SetPrimes -defined RAT -valued Function-like total complex-yielding ext-real-valued real-valued natural-valued finite-support set
(max ((prime_exponents ZP),(prime_exponents f))) . j is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support (prime_exponents y) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(prime_exponents y) . j is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
support (prime_exponents f) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
{ b₁ where b₁ is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT : ( b₁ in support (prime_factorization ZP) & (prime_exponents y) . b₁ = (prime_exponents ZP) . b₁ ) } \/ ((support (prime_factorization y)) \ { b₁ where b₁ is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT : ( b₁ in support (prime_factorization ZP) & (prime_exponents y) . b₁ = (prime_exponents ZP) . b₁ ) } ) is set
j is set
support (prime_exponents f) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
support (prime_exponents y) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(prime_factorization y) . j is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
u is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
u |-count y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
u |^ (u |-count y) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
(prime_exponents y) . u is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
u |^ ((prime_exponents y) . u) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
(prime_exponents f) . u is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
u |^ ((prime_exponents f) . u) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
u |-count f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
u |^ (u |-count f) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
(prime_factorization f) . j is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
dom (prime_factorization y) is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
dom (prime_factorization f) is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
gg | ((support (prime_factorization y)) \ { b₁ where b₁ is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT : ( b₁ in support (prime_factorization ZP) & (prime_exponents y) . b₁ = (prime_exponents ZP) . b₁ ) } ) is Relation-like (support (prime_factorization y)) \ { b₁ where b₁ is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT : ( b₁ in support (prime_factorization ZP) & (prime_exponents y) . b₁ = (prime_exponents ZP) . b₁ ) } -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
(prime_factorization f) | ((support (prime_factorization y)) \ { b₁ where b₁ is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT : ( b₁ in support (prime_factorization ZP) & (prime_exponents y) . b₁ = (prime_exponents ZP) . b₁ ) } ) is Relation-like (support (prime_factorization y)) \ { b₁ where b₁ is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT : ( b₁ in support (prime_factorization ZP) & (prime_exponents y) . b₁ = (prime_exponents ZP) . b₁ ) } -defined SetPrimes -defined RAT -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
n0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
m0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
m0 * n0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Product (prime_factorization y) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
j is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
(prime_factorization y) . j is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
j |-count y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
j |^ (j |-count y) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
(prime_exponents y) . j is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
gg . j is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(gg | (support gg)) . j is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
j is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
(prime_factorization y) . j is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
j |-count y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
j |^ (j |-count y) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
(prime_exponents y) . j is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
n . j is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(n | (support n)) . j is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
m0 gcd n0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
j is set
(prime_exponents y) . j is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(prime_exponents ZP) . j is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
u is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(prime_exponents y) . u is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(prime_exponents ZP) . u is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
j is set
support (prime_exponents ZP) is finite V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
(prime_factorization y) . j is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
u is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
u |-count y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
u |^ (u |-count y) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
(prime_exponents y) . u is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
u |^ ((prime_exponents y) . u) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
(prime_exponents ZP) . u is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
u |^ ((prime_exponents ZP) . u) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
u |-count ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
u |^ (u |-count ZP) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
(prime_factorization ZP) . j is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
dom (prime_factorization ZP) is V71() V72() V73() V74() V75() V76() Element of bool SetPrimes
n | { b₁ where b₁ is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT : ( b₁ in support (prime_factorization ZP) & (prime_exponents y) . b₁ = (prime_exponents ZP) . b₁ ) } is Relation-like { b₁ where b₁ is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT : ( b₁ in support (prime_factorization ZP) & (prime_exponents y) . b₁ = (prime_exponents ZP) . b₁ ) } -defined SetPrimes -defined RAT -valued Function-like complex-yielding ext-real-valued real-valued natural-valued set
(prime_factorization ZP) | { b₁ where b₁ is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT : ( b₁ in support (prime_factorization ZP) & (prime_exponents y) . b₁ = (prime_exponents ZP) . b₁ ) } is Relation-like { b₁ where b₁ is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT : ( b₁ in support (prime_factorization ZP) & (prime_exponents y) . b₁ = (prime_exponents ZP) . b₁ ) } -defined SetPrimes -defined RAT -valued Function-like complex-yielding ext-real-valued real-valued natural-valued set
p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
Segm p is V71() V72() V73() V74() V75() V76() Element of bool NAT
{0} is non empty trivial functional finite V42() 1 -element V71() V72() V73() V74() V75() V76() Element of bool NAT
(Segm p) \ {0} is V71() V72() V73() V74() V75() V76() Element of bool NAT
p is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
(p) is non empty finite V71() V72() V73() V74() V75() V76() Element of bool NAT
card (p) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p - 1 is V11() V12() integer ext-real set
Segm p is V71() V72() V73() V74() V75() V76() Element of bool NAT
card (Segm p) is V4() V5() V6() cardinal set
card {0} is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(Segm p) \ {0} is V71() V72() V73() V74() V75() V76() Element of bool NAT
p is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
multint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
Segm p is non empty V71() V72() V73() V74() V75() V76() Element of bool NAT
[:(Segm p),(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
[:[:(Segm p),(Segm p):],(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
(p) is non empty finite V71() V72() V73() V74() V75() V76() Element of bool NAT
(multint p) || (p) is set
[:(p),(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
(multint p) | [:(p),(p):] is Relation-like [:(p),(p):] -defined [:(Segm p),(Segm p):] -defined RAT -valued Segm p -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
[:[:(p),(p):],(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(p),(p):],(p):] is non empty finite V42() set
(Segm p) \ {0} is V71() V72() V73() V74() V75() V76() Element of bool NAT
bool (Segm p) is non empty set
a is V71() V72() V73() V74() V75() V76() Element of bool (Segm p)
ZP is set
[:a,a:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
(multint p) . ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
f is set
g is set
[f,g] is set
{f,g} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,g},{f}} is non empty finite V42() set
INT.Ring p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict V181() V182() V183() unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital V238() left_unital V259() V260() V261() V262() V267() doubleLoopStr
addint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
In (1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of Segm p
In (0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),(In (1,(Segm p))),(In (0,(Segm p))) #) is non empty strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial set
0. (INT.Ring p) is V110( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(multint p) . (f,g) is set
(multint p) . [f,g] is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
y is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
x * y is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is non empty Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like total quasi_total associative Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty Relation-like set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty Relation-like set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty set
the multF of (INT.Ring p) . (x,y) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[x,y] is set
{x,y} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,y},{x}} is non empty finite V42() set
the multF of (INT.Ring p) . [x,y] is set
(multint p) . ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
(p) is non empty finite V71() V72() V73() V74() V75() V76() Element of bool NAT
(p) is non empty Relation-like [:(p),(p):] -defined (p) -valued Function-like total quasi_total finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:[:(p),(p):],(p):]
[:(p),(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
[:[:(p),(p):],(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(p),(p):],(p):] is non empty finite V42() set
multint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
Segm p is non empty V71() V72() V73() V74() V75() V76() Element of bool NAT
[:(Segm p),(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
[:[:(Segm p),(Segm p):],(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
(multint p) || (p) is set
(multint p) | [:(p),(p):] is Relation-like [:(p),(p):] -defined [:(Segm p),(Segm p):] -defined RAT -valued Segm p -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
multMagma(# (p),(p) #) is non empty strict multMagma
the carrier of multMagma(# (p),(p) #) is non empty set
INT.Ring p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict V181() V182() V183() unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital V238() left_unital V259() V260() V261() V262() V267() doubleLoopStr
addint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
In (1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of Segm p
In (0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),(In (1,(Segm p))),(In (0,(Segm p))) #) is non empty strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial set
a is Element of the carrier of multMagma(# (p),(p) #)
ZP is Element of the carrier of multMagma(# (p),(p) #)
a * ZP is Element of the carrier of multMagma(# (p),(p) #)
the multF of multMagma(# (p),(p) #) is non empty Relation-like [: the carrier of multMagma(# (p),(p) #), the carrier of multMagma(# (p),(p) #):] -defined the carrier of multMagma(# (p),(p) #) -valued Function-like total quasi_total Element of bool [:[: the carrier of multMagma(# (p),(p) #), the carrier of multMagma(# (p),(p) #):], the carrier of multMagma(# (p),(p) #):]
[: the carrier of multMagma(# (p),(p) #), the carrier of multMagma(# (p),(p) #):] is non empty Relation-like set
[:[: the carrier of multMagma(# (p),(p) #), the carrier of multMagma(# (p),(p) #):], the carrier of multMagma(# (p),(p) #):] is non empty Relation-like set
bool [:[: the carrier of multMagma(# (p),(p) #), the carrier of multMagma(# (p),(p) #):], the carrier of multMagma(# (p),(p) #):] is non empty set
the multF of multMagma(# (p),(p) #) . (a,ZP) is Element of the carrier of multMagma(# (p),(p) #)
[a,ZP] is set
{a,ZP} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,ZP},{a}} is non empty finite V42() set
the multF of multMagma(# (p),(p) #) . [a,ZP] is set
f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
f * g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is non empty Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like total quasi_total associative Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty Relation-like set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty Relation-like set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty set
the multF of (INT.Ring p) . (f,g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[f,g] is set
{f,g} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,g},{f}} is non empty finite V42() set
the multF of (INT.Ring p) . [f,g] is set
[a,ZP] is Element of [: the carrier of multMagma(# (p),(p) #), the carrier of multMagma(# (p),(p) #):]
(multint p) . [a,ZP] is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
(p) is non empty finite V71() V72() V73() V74() V75() V76() Element of bool NAT
(p) is non empty Relation-like [:(p),(p):] -defined (p) -valued Function-like total quasi_total finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:[:(p),(p):],(p):]
[:(p),(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
[:[:(p),(p):],(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(p),(p):],(p):] is non empty finite V42() set
multint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
Segm p is non empty V71() V72() V73() V74() V75() V76() Element of bool NAT
[:(Segm p),(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
[:[:(Segm p),(Segm p):],(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
(multint p) || (p) is set
(multint p) | [:(p),(p):] is Relation-like [:(p),(p):] -defined [:(Segm p),(Segm p):] -defined RAT -valued Segm p -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
multMagma(# (p),(p) #) is non empty strict multMagma
(Segm p) \ {0} is V71() V72() V73() V74() V75() V76() Element of bool NAT
the carrier of multMagma(# (p),(p) #) is non empty set
INT.Ring p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict V181() V182() V183() unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital V238() left_unital V259() V260() V261() V262() V267() doubleLoopStr
addint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
In (1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of Segm p
In (0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),(In (1,(Segm p))),(In (0,(Segm p))) #) is non empty strict doubleLoopStr
1. (INT.Ring p) is V110( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the carrier of (INT.Ring p) is non empty non trivial set
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
f is Element of the carrier of multMagma(# (p),(p) #)
g is Element of the carrier of multMagma(# (p),(p) #)
f * g is Element of the carrier of multMagma(# (p),(p) #)
the multF of multMagma(# (p),(p) #) is non empty Relation-like [: the carrier of multMagma(# (p),(p) #), the carrier of multMagma(# (p),(p) #):] -defined the carrier of multMagma(# (p),(p) #) -valued Function-like total quasi_total Element of bool [:[: the carrier of multMagma(# (p),(p) #), the carrier of multMagma(# (p),(p) #):], the carrier of multMagma(# (p),(p) #):]
[: the carrier of multMagma(# (p),(p) #), the carrier of multMagma(# (p),(p) #):] is non empty Relation-like set
[:[: the carrier of multMagma(# (p),(p) #), the carrier of multMagma(# (p),(p) #):], the carrier of multMagma(# (p),(p) #):] is non empty Relation-like set
bool [:[: the carrier of multMagma(# (p),(p) #), the carrier of multMagma(# (p),(p) #):], the carrier of multMagma(# (p),(p) #):] is non empty set
the multF of multMagma(# (p),(p) #) . (f,g) is Element of the carrier of multMagma(# (p),(p) #)
[f,g] is set
{f,g} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,g},{f}} is non empty finite V42() set
the multF of multMagma(# (p),(p) #) . [f,g] is set
y is Element of the carrier of multMagma(# (p),(p) #)
(f * g) * y is Element of the carrier of multMagma(# (p),(p) #)
the multF of multMagma(# (p),(p) #) . ((f * g),y) is Element of the carrier of multMagma(# (p),(p) #)
[(f * g),y] is set
{(f * g),y} is non empty finite set
{(f * g)} is non empty trivial finite 1 -element set
{{(f * g),y},{(f * g)}} is non empty finite V42() set
the multF of multMagma(# (p),(p) #) . [(f * g),y] is set
g * y is Element of the carrier of multMagma(# (p),(p) #)
the multF of multMagma(# (p),(p) #) . (g,y) is Element of the carrier of multMagma(# (p),(p) #)
[g,y] is set
{g,y} is non empty finite set
{g} is non empty trivial finite 1 -element set
{{g,y},{g}} is non empty finite V42() set
the multF of multMagma(# (p),(p) #) . [g,y] is set
f * (g * y) is Element of the carrier of multMagma(# (p),(p) #)
the multF of multMagma(# (p),(p) #) . (f,(g * y)) is Element of the carrier of multMagma(# (p),(p) #)
[f,(g * y)] is set
{f,(g * y)} is non empty finite set
{{f,(g * y)},{f}} is non empty finite V42() set
the multF of multMagma(# (p),(p) #) . [f,(g * y)] is set
x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
gg is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
x * gg is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is non empty Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like total quasi_total associative Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty Relation-like set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty Relation-like set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty set
the multF of (INT.Ring p) . (x,gg) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[x,gg] is set
{x,gg} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,gg},{x}} is non empty finite V42() set
the multF of (INT.Ring p) . [x,gg] is set
x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
x * x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (x,x) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[x,x] is set
{x,x} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,x},{x}} is non empty finite V42() set
the multF of (INT.Ring p) . [x,x] is set
(x * x) * gg is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((x * x),gg) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(x * x),gg] is set
{(x * x),gg} is non empty finite set
{(x * x)} is non empty trivial finite 1 -element set
{{(x * x),gg},{(x * x)}} is non empty finite V42() set
the multF of (INT.Ring p) . [(x * x),gg] is set
x * (x * gg) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (x,(x * gg)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[x,(x * gg)] is set
{x,(x * gg)} is non empty finite set
{{x,(x * gg)},{x}} is non empty finite V42() set
the multF of (INT.Ring p) . [x,(x * gg)] is set
f is Element of the carrier of multMagma(# (p),(p) #)
ZP is Element of the carrier of multMagma(# (p),(p) #)
f * ZP is Element of the carrier of multMagma(# (p),(p) #)
the multF of multMagma(# (p),(p) #) is non empty Relation-like [: the carrier of multMagma(# (p),(p) #), the carrier of multMagma(# (p),(p) #):] -defined the carrier of multMagma(# (p),(p) #) -valued Function-like total quasi_total Element of bool [:[: the carrier of multMagma(# (p),(p) #), the carrier of multMagma(# (p),(p) #):], the carrier of multMagma(# (p),(p) #):]
[: the carrier of multMagma(# (p),(p) #), the carrier of multMagma(# (p),(p) #):] is non empty Relation-like set
[:[: the carrier of multMagma(# (p),(p) #), the carrier of multMagma(# (p),(p) #):], the carrier of multMagma(# (p),(p) #):] is non empty Relation-like set
bool [:[: the carrier of multMagma(# (p),(p) #), the carrier of multMagma(# (p),(p) #):], the carrier of multMagma(# (p),(p) #):] is non empty set
the multF of multMagma(# (p),(p) #) . (f,ZP) is Element of the carrier of multMagma(# (p),(p) #)
[f,ZP] is set
{f,ZP} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,ZP},{f}} is non empty finite V42() set
the multF of multMagma(# (p),(p) #) . [f,ZP] is set
g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
1_ (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
g * (1_ (INT.Ring p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is non empty Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like total quasi_total associative Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty Relation-like set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty Relation-like set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty set
the multF of (INT.Ring p) . (g,(1_ (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[g,(1_ (INT.Ring p))] is set
{g,(1_ (INT.Ring p))} is non empty finite set
{g} is non empty trivial finite 1 -element set
{{g,(1_ (INT.Ring p))},{g}} is non empty finite V42() set
the multF of (INT.Ring p) . [g,(1_ (INT.Ring p))] is set
ZP * f is Element of the carrier of multMagma(# (p),(p) #)
the multF of multMagma(# (p),(p) #) . (ZP,f) is Element of the carrier of multMagma(# (p),(p) #)
[ZP,f] is set
{ZP,f} is non empty finite set
{ZP} is non empty trivial finite 1 -element set
{{ZP,f},{ZP}} is non empty finite V42() set
the multF of multMagma(# (p),(p) #) . [ZP,f] is set
(1_ (INT.Ring p)) * g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((1_ (INT.Ring p)),g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(1_ (INT.Ring p)),g] is set
{(1_ (INT.Ring p)),g} is non empty finite set
{(1_ (INT.Ring p))} is non empty trivial finite 1 -element set
{{(1_ (INT.Ring p)),g},{(1_ (INT.Ring p))}} is non empty finite V42() set
the multF of (INT.Ring p) . [(1_ (INT.Ring p)),g] is set
0. (INT.Ring p) is V110( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
y is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
y * g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (y,g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[y,g] is set
{y,g} is non empty finite set
{y} is non empty trivial finite 1 -element set
{{y,g},{y}} is non empty finite V42() set
the multF of (INT.Ring p) . [y,g] is set
x is Element of the carrier of multMagma(# (p),(p) #)
x * f is Element of the carrier of multMagma(# (p),(p) #)
the multF of multMagma(# (p),(p) #) . (x,f) is Element of the carrier of multMagma(# (p),(p) #)
[x,f] is set
{x,f} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,f},{x}} is non empty finite V42() set
the multF of multMagma(# (p),(p) #) . [x,f] is set
f * x is Element of the carrier of multMagma(# (p),(p) #)
the multF of multMagma(# (p),(p) #) . (f,x) is Element of the carrier of multMagma(# (p),(p) #)
[f,x] is set
{f,x} is non empty finite set
{{f,x},{f}} is non empty finite V42() set
the multF of multMagma(# (p),(p) #) . [f,x] is set
f is Element of the carrier of multMagma(# (p),(p) #)
g is Element of the carrier of multMagma(# (p),(p) #)
f * g is Element of the carrier of multMagma(# (p),(p) #)
the multF of multMagma(# (p),(p) #) . (f,g) is Element of the carrier of multMagma(# (p),(p) #)
[f,g] is set
{f,g} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,g},{f}} is non empty finite V42() set
the multF of multMagma(# (p),(p) #) . [f,g] is set
g * f is Element of the carrier of multMagma(# (p),(p) #)
the multF of multMagma(# (p),(p) #) . (g,f) is Element of the carrier of multMagma(# (p),(p) #)
[g,f] is set
{g,f} is non empty finite set
{g} is non empty trivial finite 1 -element set
{{g,f},{g}} is non empty finite V42() set
the multF of multMagma(# (p),(p) #) . [g,f] is set
y is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
y * x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . (y,x) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[y,x] is set
{y,x} is non empty finite set
{y} is non empty trivial finite 1 -element set
{{y,x},{y}} is non empty finite V42() set
the multF of (INT.Ring p) . [y,x] is set
p is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
(p) is non empty finite V71() V72() V73() V74() V75() V76() Element of bool NAT
(p) is non empty Relation-like [:(p),(p):] -defined (p) -valued Function-like total quasi_total finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:[:(p),(p):],(p):]
[:(p),(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
[:[:(p),(p):],(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(p),(p):],(p):] is non empty finite V42() set
multint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
Segm p is non empty V71() V72() V73() V74() V75() V76() Element of bool NAT
[:(Segm p),(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
[:[:(Segm p),(Segm p):],(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
(multint p) || (p) is set
(multint p) | [:(p),(p):] is Relation-like [:(p),(p):] -defined [:(Segm p),(Segm p):] -defined RAT -valued Segm p -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
multMagma(# (p),(p) #) is non empty strict multMagma
p is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
(p) is non empty unital Group-like associative commutative multMagma
(p) is non empty finite V71() V72() V73() V74() V75() V76() Element of bool NAT
(p) is non empty Relation-like [:(p),(p):] -defined (p) -valued Function-like total quasi_total finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:[:(p),(p):],(p):]
[:(p),(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
[:[:(p),(p):],(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(p),(p):],(p):] is non empty finite V42() set
multint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
Segm p is non empty V71() V72() V73() V74() V75() V76() Element of bool NAT
[:(Segm p),(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
[:[:(Segm p),(Segm p):],(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
(multint p) || (p) is set
(multint p) | [:(p),(p):] is Relation-like [:(p),(p):] -defined [:(Segm p),(Segm p):] -defined RAT -valued Segm p -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
multMagma(# (p),(p) #) is non empty strict multMagma
the carrier of (p) is non empty set
INT.Ring p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict V181() V182() V183() unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital V238() left_unital V259() V260() V261() V262() V267() doubleLoopStr
addint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
In (1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of Segm p
In (0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),(In (1,(Segm p))),(In (0,(Segm p))) #) is non empty strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial set
a is Element of the carrier of (p)
f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
ZP is Element of the carrier of (p)
g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
a * ZP is Element of the carrier of (p)
the multF of (p) is non empty Relation-like [: the carrier of (p), the carrier of (p):] -defined the carrier of (p) -valued Function-like total quasi_total associative Element of bool [:[: the carrier of (p), the carrier of (p):], the carrier of (p):]
[: the carrier of (p), the carrier of (p):] is non empty Relation-like set
[:[: the carrier of (p), the carrier of (p):], the carrier of (p):] is non empty Relation-like set
bool [:[: the carrier of (p), the carrier of (p):], the carrier of (p):] is non empty set
the multF of (p) . (a,ZP) is Element of the carrier of (p)
[a,ZP] is set
{a,ZP} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,ZP},{a}} is non empty finite V42() set
the multF of (p) . [a,ZP] is set
f * g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is non empty Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like total quasi_total associative Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty Relation-like set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty Relation-like set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty set
the multF of (INT.Ring p) . (f,g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[f,g] is set
{f,g} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,g},{f}} is non empty finite V42() set
the multF of (INT.Ring p) . [f,g] is set
p is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
(p) is non empty unital Group-like associative commutative multMagma
(p) is non empty finite V71() V72() V73() V74() V75() V76() Element of bool NAT
(p) is non empty Relation-like [:(p),(p):] -defined (p) -valued Function-like total quasi_total finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:[:(p),(p):],(p):]
[:(p),(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
[:[:(p),(p):],(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(p),(p):],(p):] is non empty finite V42() set
multint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
Segm p is non empty V71() V72() V73() V74() V75() V76() Element of bool NAT
[:(Segm p),(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
[:[:(Segm p),(Segm p):],(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
(multint p) || (p) is set
(multint p) | [:(p),(p):] is Relation-like [:(p),(p):] -defined [:(Segm p),(Segm p):] -defined RAT -valued Segm p -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
multMagma(# (p),(p) #) is non empty strict multMagma
1_ (p) is non being_of_order_0 Element of the carrier of (p)
the carrier of (p) is non empty set
INT.Ring p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict V181() V182() V183() unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital V238() left_unital V259() V260() V261() V262() V267() doubleLoopStr
addint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
In (1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of Segm p
In (0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),(In (1,(Segm p))),(In (0,(Segm p))) #) is non empty strict doubleLoopStr
1. (INT.Ring p) is V110( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the carrier of (INT.Ring p) is non empty non trivial set
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(Segm p) \ {0} is V71() V72() V73() V74() V75() V76() Element of bool NAT
ZP is Element of the carrier of (p)
a is Element of the carrier of (p)
ZP * a is Element of the carrier of (p)
the multF of (p) is non empty Relation-like [: the carrier of (p), the carrier of (p):] -defined the carrier of (p) -valued Function-like total quasi_total associative Element of bool [:[: the carrier of (p), the carrier of (p):], the carrier of (p):]
[: the carrier of (p), the carrier of (p):] is non empty Relation-like set
[:[: the carrier of (p), the carrier of (p):], the carrier of (p):] is non empty Relation-like set
bool [:[: the carrier of (p), the carrier of (p):], the carrier of (p):] is non empty set
the multF of (p) . (ZP,a) is Element of the carrier of (p)
[ZP,a] is set
{ZP,a} is non empty finite set
{ZP} is non empty trivial finite 1 -element set
{{ZP,a},{ZP}} is non empty finite V42() set
the multF of (p) . [ZP,a] is set
f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
1_ (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
f * (1_ (INT.Ring p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is non empty Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like total quasi_total associative Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty Relation-like set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty Relation-like set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty set
the multF of (INT.Ring p) . (f,(1_ (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[f,(1_ (INT.Ring p))] is set
{f,(1_ (INT.Ring p))} is non empty finite set
{f} is non empty trivial finite 1 -element set
{{f,(1_ (INT.Ring p))},{f}} is non empty finite V42() set
the multF of (INT.Ring p) . [f,(1_ (INT.Ring p))] is set
a * ZP is Element of the carrier of (p)
the multF of (p) . (a,ZP) is Element of the carrier of (p)
[a,ZP] is set
{a,ZP} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,ZP},{a}} is non empty finite V42() set
the multF of (p) . [a,ZP] is set
(1_ (INT.Ring p)) * f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) . ((1_ (INT.Ring p)),f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[(1_ (INT.Ring p)),f] is set
{(1_ (INT.Ring p)),f} is non empty finite set
{(1_ (INT.Ring p))} is non empty trivial finite 1 -element set
{{(1_ (INT.Ring p)),f},{(1_ (INT.Ring p))}} is non empty finite V42() set
the multF of (INT.Ring p) . [(1_ (INT.Ring p)),f] is set
p is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
(p) is non empty unital Group-like associative commutative multMagma
(p) is non empty finite V71() V72() V73() V74() V75() V76() Element of bool NAT
(p) is non empty Relation-like [:(p),(p):] -defined (p) -valued Function-like total quasi_total finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:[:(p),(p):],(p):]
[:(p),(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
[:[:(p),(p):],(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(p),(p):],(p):] is non empty finite V42() set
multint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
Segm p is non empty V71() V72() V73() V74() V75() V76() Element of bool NAT
[:(Segm p),(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
[:[:(Segm p),(Segm p):],(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
(multint p) || (p) is set
(multint p) | [:(p),(p):] is Relation-like [:(p),(p):] -defined [:(Segm p),(Segm p):] -defined RAT -valued Segm p -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
multMagma(# (p),(p) #) is non empty strict multMagma
the carrier of (p) is non empty set
INT.Ring p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict V181() V182() V183() unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital V238() left_unital V259() V260() V261() V262() V267() doubleLoopStr
addint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
In (1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of Segm p
In (0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),(In (1,(Segm p))),(In (0,(Segm p))) #) is non empty strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial set
a is Element of the carrier of (p)
a " is Element of the carrier of (p)
ZP is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
ZP " is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(Segm p) \ {0} is V71() V72() V73() V74() V75() V76() Element of bool NAT
0. (INT.Ring p) is V110( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the ZeroF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
ZP * (ZP ") is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is non empty Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like total quasi_total associative Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty Relation-like set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty Relation-like set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty set
the multF of (INT.Ring p) . (ZP,(ZP ")) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[ZP,(ZP ")] is set
{ZP,(ZP ")} is non empty finite set
{ZP} is non empty trivial finite 1 -element set
{{ZP,(ZP ")},{ZP}} is non empty finite V42() set
the multF of (INT.Ring p) . [ZP,(ZP ")] is set
1. (INT.Ring p) is V110( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
g is Element of the carrier of (p)
a * g is Element of the carrier of (p)
the multF of (p) is non empty Relation-like [: the carrier of (p), the carrier of (p):] -defined the carrier of (p) -valued Function-like total quasi_total associative Element of bool [:[: the carrier of (p), the carrier of (p):], the carrier of (p):]
[: the carrier of (p), the carrier of (p):] is non empty Relation-like set
[:[: the carrier of (p), the carrier of (p):], the carrier of (p):] is non empty Relation-like set
bool [:[: the carrier of (p), the carrier of (p):], the carrier of (p):] is non empty set
the multF of (p) . (a,g) is Element of the carrier of (p)
[a,g] is set
{a,g} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,g},{a}} is non empty finite V42() set
the multF of (p) . [a,g] is set
1_ (p) is non being_of_order_0 Element of the carrier of (p)
p is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
(p) is non empty unital Group-like associative commutative multMagma
(p) is non empty finite V71() V72() V73() V74() V75() V76() Element of bool NAT
(p) is non empty Relation-like [:(p),(p):] -defined (p) -valued Function-like total quasi_total finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:[:(p),(p):],(p):]
[:(p),(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
[:[:(p),(p):],(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(p),(p):],(p):] is non empty finite V42() set
multint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
Segm p is non empty V71() V72() V73() V74() V75() V76() Element of bool NAT
[:(Segm p),(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
[:[:(Segm p),(Segm p):],(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
(multint p) || (p) is set
(multint p) | [:(p),(p):] is Relation-like [:(p),(p):] -defined [:(Segm p),(Segm p):] -defined RAT -valued Segm p -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
multMagma(# (p),(p) #) is non empty strict multMagma
p is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
(p) is non empty finite unital Group-like associative commutative multMagma
(p) is non empty finite V71() V72() V73() V74() V75() V76() Element of bool NAT
(p) is non empty Relation-like [:(p),(p):] -defined (p) -valued Function-like total quasi_total finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:[:(p),(p):],(p):]
[:(p),(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
[:[:(p),(p):],(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(p),(p):],(p):] is non empty finite V42() set
multint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
Segm p is non empty V71() V72() V73() V74() V75() V76() Element of bool NAT
[:(Segm p),(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
[:[:(Segm p),(Segm p):],(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
(multint p) || (p) is set
(multint p) | [:(p),(p):] is Relation-like [:(p),(p):] -defined [:(Segm p),(Segm p):] -defined RAT -valued Segm p -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
multMagma(# (p),(p) #) is non empty strict multMagma
card (p) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
the carrier of (p) is non empty finite set
card the carrier of (p) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
p - 1 is V11() V12() integer ext-real set
p is non empty unital Group-like associative multMagma
the carrier of p is non empty set
a is Element of the carrier of p
ord a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP is V11() V12() integer ext-real set
a |^ ZP is Element of the carrier of p
abs ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(abs ZP) * (ord a) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
((abs ZP) * (ord a)) + ZP is V11() V12() integer ext-real set
(abs ZP) + ZP is V11() V12() integer ext-real set
- ZP is V11() V12() integer ext-real set
a |^ (((abs ZP) * (ord a)) + ZP) is Element of the carrier of p
a |^ ((abs ZP) * (ord a)) is Element of the carrier of p
power p is non empty Relation-like [: the carrier of p,NAT:] -defined the carrier of p -valued Function-like total quasi_total Element of bool [:[: the carrier of p,NAT:], the carrier of p:]
[: the carrier of p,NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued natural-valued set
[:[: the carrier of p,NAT:], the carrier of p:] is non empty non trivial Relation-like non finite set
bool [:[: the carrier of p,NAT:], the carrier of p:] is non empty non trivial non finite set
(power p) . (a,((abs ZP) * (ord a))) is set
[a,((abs ZP) * (ord a))] is set
{a,((abs ZP) * (ord a))} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,((abs ZP) * (ord a))},{a}} is non empty finite V42() set
(power p) . [a,((abs ZP) * (ord a))] is set
(a |^ ((abs ZP) * (ord a))) * (a |^ ZP) is Element of the carrier of p
the multF of p is non empty Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like total quasi_total associative Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
[: the carrier of p, the carrier of p:] is non empty Relation-like set
[:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty Relation-like set
bool [:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
the multF of p . ((a |^ ((abs ZP) * (ord a))),(a |^ ZP)) is Element of the carrier of p
[(a |^ ((abs ZP) * (ord a))),(a |^ ZP)] is set
{(a |^ ((abs ZP) * (ord a))),(a |^ ZP)} is non empty finite set
{(a |^ ((abs ZP) * (ord a)))} is non empty trivial finite 1 -element set
{{(a |^ ((abs ZP) * (ord a))),(a |^ ZP)},{(a |^ ((abs ZP) * (ord a)))}} is non empty finite V42() set
the multF of p . [(a |^ ((abs ZP) * (ord a))),(a |^ ZP)] is set
a |^ (ord a) is Element of the carrier of p
(power p) . (a,(ord a)) is set
[a,(ord a)] is set
{a,(ord a)} is non empty finite set
{{a,(ord a)},{a}} is non empty finite V42() set
(power p) . [a,(ord a)] is set
(a |^ (ord a)) |^ (abs ZP) is Element of the carrier of p
(power p) . ((a |^ (ord a)),(abs ZP)) is set
[(a |^ (ord a)),(abs ZP)] is set
{(a |^ (ord a)),(abs ZP)} is non empty finite set
{(a |^ (ord a))} is non empty trivial finite 1 -element set
{{(a |^ (ord a)),(abs ZP)},{(a |^ (ord a))}} is non empty finite V42() set
(power p) . [(a |^ (ord a)),(abs ZP)] is set
((a |^ (ord a)) |^ (abs ZP)) * (a |^ ZP) is Element of the carrier of p
the multF of p . (((a |^ (ord a)) |^ (abs ZP)),(a |^ ZP)) is Element of the carrier of p
[((a |^ (ord a)) |^ (abs ZP)),(a |^ ZP)] is set
{((a |^ (ord a)) |^ (abs ZP)),(a |^ ZP)} is non empty finite set
{((a |^ (ord a)) |^ (abs ZP))} is non empty trivial finite 1 -element set
{{((a |^ (ord a)) |^ (abs ZP)),(a |^ ZP)},{((a |^ (ord a)) |^ (abs ZP))}} is non empty finite V42() set
the multF of p . [((a |^ (ord a)) |^ (abs ZP)),(a |^ ZP)] is set
1_ p is non being_of_order_0 Element of the carrier of p
(1_ p) |^ (abs ZP) is Element of the carrier of p
(power p) . ((1_ p),(abs ZP)) is set
[(1_ p),(abs ZP)] is set
{(1_ p),(abs ZP)} is non empty finite set
{(1_ p)} is non empty trivial finite 1 -element set
{{(1_ p),(abs ZP)},{(1_ p)}} is non empty finite V42() set
(power p) . [(1_ p),(abs ZP)] is set
((1_ p) |^ (abs ZP)) * (a |^ ZP) is Element of the carrier of p
the multF of p . (((1_ p) |^ (abs ZP)),(a |^ ZP)) is Element of the carrier of p
[((1_ p) |^ (abs ZP)),(a |^ ZP)] is set
{((1_ p) |^ (abs ZP)),(a |^ ZP)} is non empty finite set
{((1_ p) |^ (abs ZP))} is non empty trivial finite 1 -element set
{{((1_ p) |^ (abs ZP)),(a |^ ZP)},{((1_ p) |^ (abs ZP))}} is non empty finite V42() set
the multF of p . [((1_ p) |^ (abs ZP)),(a |^ ZP)] is set
(1_ p) * (a |^ ZP) is Element of the carrier of p
the multF of p . ((1_ p),(a |^ ZP)) is Element of the carrier of p
[(1_ p),(a |^ ZP)] is set
{(1_ p),(a |^ ZP)} is non empty finite set
{{(1_ p),(a |^ ZP)},{(1_ p)}} is non empty finite V42() set
the multF of p . [(1_ p),(a |^ ZP)] is set
p is non empty unital Group-like associative commutative multMagma
the carrier of p is non empty set
a is Element of the carrier of p
ord a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP is Element of the carrier of p
ord ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a * ZP is Element of the carrier of p
the multF of p is non empty Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like total quasi_total associative Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
[: the carrier of p, the carrier of p:] is non empty Relation-like set
[:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty Relation-like set
bool [:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
the multF of p . (a,ZP) is Element of the carrier of p
[a,ZP] is set
{a,ZP} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,ZP},{a}} is non empty finite V42() set
the multF of p . [a,ZP] is set
ord (a * ZP) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
f gcd g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
f * g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
(a * ZP) |^ (f * g) is Element of the carrier of p
power p is non empty Relation-like [: the carrier of p,NAT:] -defined the carrier of p -valued Function-like total quasi_total Element of bool [:[: the carrier of p,NAT:], the carrier of p:]
[: the carrier of p,NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued natural-valued set
[:[: the carrier of p,NAT:], the carrier of p:] is non empty non trivial Relation-like non finite set
bool [:[: the carrier of p,NAT:], the carrier of p:] is non empty non trivial non finite set
(power p) . ((a * ZP),(f * g)) is set
[(a * ZP),(f * g)] is set
{(a * ZP),(f * g)} is non empty finite set
{(a * ZP)} is non empty trivial finite 1 -element set
{{(a * ZP),(f * g)},{(a * ZP)}} is non empty finite V42() set
(power p) . [(a * ZP),(f * g)] is set
a |^ (f * g) is Element of the carrier of p
(power p) . (a,(f * g)) is set
[a,(f * g)] is set
{a,(f * g)} is non empty finite set
{{a,(f * g)},{a}} is non empty finite V42() set
(power p) . [a,(f * g)] is set
ZP |^ (f * g) is Element of the carrier of p
(power p) . (ZP,(f * g)) is set
[ZP,(f * g)] is set
{ZP,(f * g)} is non empty finite set
{ZP} is non empty trivial finite 1 -element set
{{ZP,(f * g)},{ZP}} is non empty finite V42() set
(power p) . [ZP,(f * g)] is set
(a |^ (f * g)) * (ZP |^ (f * g)) is Element of the carrier of p
the multF of p . ((a |^ (f * g)),(ZP |^ (f * g))) is Element of the carrier of p
[(a |^ (f * g)),(ZP |^ (f * g))] is set
{(a |^ (f * g)),(ZP |^ (f * g))} is non empty finite set
{(a |^ (f * g))} is non empty trivial finite 1 -element set
{{(a |^ (f * g)),(ZP |^ (f * g))},{(a |^ (f * g))}} is non empty finite V42() set
the multF of p . [(a |^ (f * g)),(ZP |^ (f * g))] is set
a |^ f is Element of the carrier of p
(power p) . (a,f) is set
[a,f] is set
{a,f} is non empty finite set
{{a,f},{a}} is non empty finite V42() set
(power p) . [a,f] is set
(a |^ f) |^ g is Element of the carrier of p
(power p) . ((a |^ f),g) is set
[(a |^ f),g] is set
{(a |^ f),g} is non empty finite set
{(a |^ f)} is non empty trivial finite 1 -element set
{{(a |^ f),g},{(a |^ f)}} is non empty finite V42() set
(power p) . [(a |^ f),g] is set
((a |^ f) |^ g) * (ZP |^ (f * g)) is Element of the carrier of p
the multF of p . (((a |^ f) |^ g),(ZP |^ (f * g))) is Element of the carrier of p
[((a |^ f) |^ g),(ZP |^ (f * g))] is set
{((a |^ f) |^ g),(ZP |^ (f * g))} is non empty finite set
{((a |^ f) |^ g)} is non empty trivial finite 1 -element set
{{((a |^ f) |^ g),(ZP |^ (f * g))},{((a |^ f) |^ g)}} is non empty finite V42() set
the multF of p . [((a |^ f) |^ g),(ZP |^ (f * g))] is set
ZP |^ g is Element of the carrier of p
(power p) . (ZP,g) is set
[ZP,g] is set
{ZP,g} is non empty finite set
{{ZP,g},{ZP}} is non empty finite V42() set
(power p) . [ZP,g] is set
(ZP |^ g) |^ f is Element of the carrier of p
(power p) . ((ZP |^ g),f) is set
[(ZP |^ g),f] is set
{(ZP |^ g),f} is non empty finite set
{(ZP |^ g)} is non empty trivial finite 1 -element set
{{(ZP |^ g),f},{(ZP |^ g)}} is non empty finite V42() set
(power p) . [(ZP |^ g),f] is set
((a |^ f) |^ g) * ((ZP |^ g) |^ f) is Element of the carrier of p
the multF of p . (((a |^ f) |^ g),((ZP |^ g) |^ f)) is Element of the carrier of p
[((a |^ f) |^ g),((ZP |^ g) |^ f)] is set
{((a |^ f) |^ g),((ZP |^ g) |^ f)} is non empty finite set
{{((a |^ f) |^ g),((ZP |^ g) |^ f)},{((a |^ f) |^ g)}} is non empty finite V42() set
the multF of p . [((a |^ f) |^ g),((ZP |^ g) |^ f)] is set
1_ p is non being_of_order_0 Element of the carrier of p
(1_ p) |^ g is Element of the carrier of p
(power p) . ((1_ p),g) is set
[(1_ p),g] is set
{(1_ p),g} is non empty finite set
{(1_ p)} is non empty trivial finite 1 -element set
{{(1_ p),g},{(1_ p)}} is non empty finite V42() set
(power p) . [(1_ p),g] is set
((1_ p) |^ g) * ((ZP |^ g) |^ f) is Element of the carrier of p
the multF of p . (((1_ p) |^ g),((ZP |^ g) |^ f)) is Element of the carrier of p
[((1_ p) |^ g),((ZP |^ g) |^ f)] is set
{((1_ p) |^ g),((ZP |^ g) |^ f)} is non empty finite set
{((1_ p) |^ g)} is non empty trivial finite 1 -element set
{{((1_ p) |^ g),((ZP |^ g) |^ f)},{((1_ p) |^ g)}} is non empty finite V42() set
the multF of p . [((1_ p) |^ g),((ZP |^ g) |^ f)] is set
(1_ p) |^ f is Element of the carrier of p
(power p) . ((1_ p),f) is set
[(1_ p),f] is set
{(1_ p),f} is non empty finite set
{{(1_ p),f},{(1_ p)}} is non empty finite V42() set
(power p) . [(1_ p),f] is set
((1_ p) |^ g) * ((1_ p) |^ f) is Element of the carrier of p
the multF of p . (((1_ p) |^ g),((1_ p) |^ f)) is Element of the carrier of p
[((1_ p) |^ g),((1_ p) |^ f)] is set
{((1_ p) |^ g),((1_ p) |^ f)} is non empty finite set
{{((1_ p) |^ g),((1_ p) |^ f)},{((1_ p) |^ g)}} is non empty finite V42() set
the multF of p . [((1_ p) |^ g),((1_ p) |^ f)] is set
(1_ p) * ((1_ p) |^ f) is Element of the carrier of p
the multF of p . ((1_ p),((1_ p) |^ f)) is Element of the carrier of p
[(1_ p),((1_ p) |^ f)] is set
{(1_ p),((1_ p) |^ f)} is non empty finite set
{{(1_ p),((1_ p) |^ f)},{(1_ p)}} is non empty finite V42() set
the multF of p . [(1_ p),((1_ p) |^ f)] is set
(1_ p) * (1_ p) is Element of the carrier of p
the multF of p . ((1_ p),(1_ p)) is Element of the carrier of p
[(1_ p),(1_ p)] is set
{(1_ p),(1_ p)} is non empty finite set
{{(1_ p),(1_ p)},{(1_ p)}} is non empty finite V42() set
the multF of p . [(1_ p),(1_ p)] is set
g * f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
y is V11() V12() integer ext-real set
x is V11() V12() integer ext-real set
x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
(a * ZP) |^ x is Element of the carrier of p
(power p) . ((a * ZP),x) is set
[(a * ZP),x] is set
{(a * ZP),x} is non empty finite set
{{(a * ZP),x},{(a * ZP)}} is non empty finite V42() set
(power p) . [(a * ZP),x] is set
x * f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
(a * ZP) |^ (x * f) is Element of the carrier of p
(power p) . ((a * ZP),(x * f)) is set
[(a * ZP),(x * f)] is set
{(a * ZP),(x * f)} is non empty finite set
{{(a * ZP),(x * f)},{(a * ZP)}} is non empty finite V42() set
(power p) . [(a * ZP),(x * f)] is set
a |^ (x * f) is Element of the carrier of p
(power p) . (a,(x * f)) is set
[a,(x * f)] is set
{a,(x * f)} is non empty finite set
{{a,(x * f)},{a}} is non empty finite V42() set
(power p) . [a,(x * f)] is set
ZP |^ (x * f) is Element of the carrier of p
(power p) . (ZP,(x * f)) is set
[ZP,(x * f)] is set
{ZP,(x * f)} is non empty finite set
{{ZP,(x * f)},{ZP}} is non empty finite V42() set
(power p) . [ZP,(x * f)] is set
(a |^ (x * f)) * (ZP |^ (x * f)) is Element of the carrier of p
the multF of p . ((a |^ (x * f)),(ZP |^ (x * f))) is Element of the carrier of p
[(a |^ (x * f)),(ZP |^ (x * f))] is set
{(a |^ (x * f)),(ZP |^ (x * f))} is non empty finite set
{(a |^ (x * f))} is non empty trivial finite 1 -element set
{{(a |^ (x * f)),(ZP |^ (x * f))},{(a |^ (x * f))}} is non empty finite V42() set
the multF of p . [(a |^ (x * f)),(ZP |^ (x * f))] is set
(a |^ f) |^ x is Element of the carrier of p
(power p) . ((a |^ f),x) is set
[(a |^ f),x] is set
{(a |^ f),x} is non empty finite set
{{(a |^ f),x},{(a |^ f)}} is non empty finite V42() set
(power p) . [(a |^ f),x] is set
((a |^ f) |^ x) * (ZP |^ (x * f)) is Element of the carrier of p
the multF of p . (((a |^ f) |^ x),(ZP |^ (x * f))) is Element of the carrier of p
[((a |^ f) |^ x),(ZP |^ (x * f))] is set
{((a |^ f) |^ x),(ZP |^ (x * f))} is non empty finite set
{((a |^ f) |^ x)} is non empty trivial finite 1 -element set
{{((a |^ f) |^ x),(ZP |^ (x * f))},{((a |^ f) |^ x)}} is non empty finite V42() set
the multF of p . [((a |^ f) |^ x),(ZP |^ (x * f))] is set
(1_ p) |^ x is Element of the carrier of p
(power p) . ((1_ p),x) is set
[(1_ p),x] is set
{(1_ p),x} is non empty finite set
{{(1_ p),x},{(1_ p)}} is non empty finite V42() set
(power p) . [(1_ p),x] is set
((1_ p) |^ x) * (ZP |^ (x * f)) is Element of the carrier of p
the multF of p . (((1_ p) |^ x),(ZP |^ (x * f))) is Element of the carrier of p
[((1_ p) |^ x),(ZP |^ (x * f))] is set
{((1_ p) |^ x),(ZP |^ (x * f))} is non empty finite set
{((1_ p) |^ x)} is non empty trivial finite 1 -element set
{{((1_ p) |^ x),(ZP |^ (x * f))},{((1_ p) |^ x)}} is non empty finite V42() set
the multF of p . [((1_ p) |^ x),(ZP |^ (x * f))] is set
(1_ p) * (ZP |^ (x * f)) is Element of the carrier of p
the multF of p . ((1_ p),(ZP |^ (x * f))) is Element of the carrier of p
[(1_ p),(ZP |^ (x * f))] is set
{(1_ p),(ZP |^ (x * f))} is non empty finite set
{{(1_ p),(ZP |^ (x * f))},{(1_ p)}} is non empty finite V42() set
the multF of p . [(1_ p),(ZP |^ (x * f))] is set
gg is V11() V12() integer ext-real set
n is V11() V12() integer ext-real set
x * n is V11() V12() integer ext-real set
x * g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
(a * ZP) |^ (x * g) is Element of the carrier of p
(power p) . ((a * ZP),(x * g)) is set
[(a * ZP),(x * g)] is set
{(a * ZP),(x * g)} is non empty finite set
{{(a * ZP),(x * g)},{(a * ZP)}} is non empty finite V42() set
(power p) . [(a * ZP),(x * g)] is set
a |^ (x * g) is Element of the carrier of p
(power p) . (a,(x * g)) is set
[a,(x * g)] is set
{a,(x * g)} is non empty finite set
{{a,(x * g)},{a}} is non empty finite V42() set
(power p) . [a,(x * g)] is set
ZP |^ (x * g) is Element of the carrier of p
(power p) . (ZP,(x * g)) is set
[ZP,(x * g)] is set
{ZP,(x * g)} is non empty finite set
{{ZP,(x * g)},{ZP}} is non empty finite V42() set
(power p) . [ZP,(x * g)] is set
(a |^ (x * g)) * (ZP |^ (x * g)) is Element of the carrier of p
the multF of p . ((a |^ (x * g)),(ZP |^ (x * g))) is Element of the carrier of p
[(a |^ (x * g)),(ZP |^ (x * g))] is set
{(a |^ (x * g)),(ZP |^ (x * g))} is non empty finite set
{(a |^ (x * g))} is non empty trivial finite 1 -element set
{{(a |^ (x * g)),(ZP |^ (x * g))},{(a |^ (x * g))}} is non empty finite V42() set
the multF of p . [(a |^ (x * g)),(ZP |^ (x * g))] is set
(ZP |^ g) |^ x is Element of the carrier of p
(power p) . ((ZP |^ g),x) is set
[(ZP |^ g),x] is set
{(ZP |^ g),x} is non empty finite set
{{(ZP |^ g),x},{(ZP |^ g)}} is non empty finite V42() set
(power p) . [(ZP |^ g),x] is set
(a |^ (x * g)) * ((ZP |^ g) |^ x) is Element of the carrier of p
the multF of p . ((a |^ (x * g)),((ZP |^ g) |^ x)) is Element of the carrier of p
[(a |^ (x * g)),((ZP |^ g) |^ x)] is set
{(a |^ (x * g)),((ZP |^ g) |^ x)} is non empty finite set
{{(a |^ (x * g)),((ZP |^ g) |^ x)},{(a |^ (x * g))}} is non empty finite V42() set
the multF of p . [(a |^ (x * g)),((ZP |^ g) |^ x)] is set
(a |^ (x * g)) * ((1_ p) |^ x) is Element of the carrier of p
the multF of p . ((a |^ (x * g)),((1_ p) |^ x)) is Element of the carrier of p
[(a |^ (x * g)),((1_ p) |^ x)] is set
{(a |^ (x * g)),((1_ p) |^ x)} is non empty finite set
{{(a |^ (x * g)),((1_ p) |^ x)},{(a |^ (x * g))}} is non empty finite V42() set
the multF of p . [(a |^ (x * g)),((1_ p) |^ x)] is set
(a |^ (x * g)) * (1_ p) is Element of the carrier of p
the multF of p . ((a |^ (x * g)),(1_ p)) is Element of the carrier of p
[(a |^ (x * g)),(1_ p)] is set
{(a |^ (x * g)),(1_ p)} is non empty finite set
{{(a |^ (x * g)),(1_ p)},{(a |^ (x * g))}} is non empty finite V42() set
the multF of p . [(a |^ (x * g)),(1_ p)] is set
m0 is V11() V12() integer ext-real set
y * m0 is V11() V12() integer ext-real set
x * y is V11() V12() integer ext-real set
(x * y) * m0 is V11() V12() integer ext-real set
x / (g * f) is V11() V12() ext-real non negative set
(g * f) * 1 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(g * f) * m0 is V11() V12() integer ext-real set
p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible V181() V182() V183() unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital V238() left_unital V259() V260() V261() V262() V267() doubleLoopStr
the carrier of p is non empty non trivial set
[:NAT, the carrier of p:] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of p:] is non empty non trivial non finite set
a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) non-zero Element of bool [:NAT, the carrier of p:]
0_. p is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) with_roots Element of bool [:NAT, the carrier of p:]
0. p is V110(p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the ZeroF of p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
NAT --> (0. p) is non empty V8() Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total Element of bool [:NAT, the carrier of p:]
deg ZP is V11() V12() integer ext-real set
len ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(len ZP) - 1 is V11() V12() integer ext-real set
a + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Roots ZP is finite Element of bool the carrier of p
bool the carrier of p is non empty set
card (Roots ZP) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
g is set
y is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
rpoly (1,y) is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) Element of bool [:NAT, the carrier of p:]
power p is non empty Relation-like [: the carrier of p,NAT:] -defined the carrier of p -valued Function-like total quasi_total Element of bool [:[: the carrier of p,NAT:], the carrier of p:]
[: the carrier of p,NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued natural-valued set
[:[: the carrier of p,NAT:], the carrier of p:] is non empty non trivial Relation-like non finite set
bool [:[: the carrier of p,NAT:], the carrier of p:] is non empty non trivial non finite set
(power p) . (y,1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[y,1] is set
{y,1} is non empty finite set
{y} is non empty trivial finite 1 -element set
{{y,1},{y}} is non empty finite V42() set
(power p) . [y,1] is set
- ((power p) . (y,1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
1_ p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
1. p is V110(p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the OneF of p is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
(0,1) --> ((- ((power p) . (y,1))),(1_ p)) is non empty Relation-like {0,1} -defined the carrier of p -valued Function-like total quasi_total finite finite-support Element of bool [:{0,1}, the carrier of p:]
{0,1} is non empty finite V42() V71() V72() V73() V74() V75() V76() set
[:{0,1}, the carrier of p:] is non empty Relation-like set
bool [:{0,1}, the carrier of p:] is non empty set
(0_. p) +* ((0,1) --> ((- ((power p) . (y,1))),(1_ p))) is Relation-like Function-like set
ZP div (rpoly (1,y)) is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) Element of bool [:NAT, the carrier of p:]
ZP mod (rpoly (1,y)) is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) Element of bool [:NAT, the carrier of p:]
(ZP div (rpoly (1,y))) *' (rpoly (1,y)) is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) Element of bool [:NAT, the carrier of p:]
ZP - ((ZP div (rpoly (1,y))) *' (rpoly (1,y))) is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) Element of bool [:NAT, the carrier of p:]
- ((ZP div (rpoly (1,y))) *' (rpoly (1,y))) is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) Element of bool [:NAT, the carrier of p:]
K680(p,ZP,(- ((ZP div (rpoly (1,y))) *' (rpoly (1,y))))) is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) Element of bool [:NAT, the carrier of p:]
(ZP - ((ZP div (rpoly (1,y))) *' (rpoly (1,y)))) + ((ZP div (rpoly (1,y))) *' (rpoly (1,y))) is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) Element of bool [:NAT, the carrier of p:]
(- ((ZP div (rpoly (1,y))) *' (rpoly (1,y)))) + ((ZP div (rpoly (1,y))) *' (rpoly (1,y))) is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) Element of bool [:NAT, the carrier of p:]
ZP + ((- ((ZP div (rpoly (1,y))) *' (rpoly (1,y)))) + ((ZP div (rpoly (1,y))) *' (rpoly (1,y)))) is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) Element of bool [:NAT, the carrier of p:]
((ZP div (rpoly (1,y))) *' (rpoly (1,y))) - ((ZP div (rpoly (1,y))) *' (rpoly (1,y))) is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) Element of bool [:NAT, the carrier of p:]
K680(p,((ZP div (rpoly (1,y))) *' (rpoly (1,y))),(- ((ZP div (rpoly (1,y))) *' (rpoly (1,y))))) is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) Element of bool [:NAT, the carrier of p:]
ZP + (((ZP div (rpoly (1,y))) *' (rpoly (1,y))) - ((ZP div (rpoly (1,y))) *' (rpoly (1,y)))) is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) Element of bool [:NAT, the carrier of p:]
ZP + (0_. p) is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) Element of bool [:NAT, the carrier of p:]
x is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) non-zero Element of bool [:NAT, the carrier of p:]
Roots x is finite Element of bool the carrier of p
deg x is V11() V12() integer ext-real set
len x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(len x) - 1 is V11() V12() integer ext-real set
(a + 1) - 1 is V11() V12() integer ext-real set
card (Roots x) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(card (Roots x)) + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
{y} is non empty trivial finite 1 -element Element of bool the carrier of p
(Roots x) \/ {y} is non empty finite Element of bool the carrier of p
n is set
m0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
eval (ZP,m0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
eval (x,m0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
eval ((rpoly (1,y)),m0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
(eval (x,m0)) * (eval ((rpoly (1,y)),m0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p is non empty Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like total quasi_total associative Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
[: the carrier of p, the carrier of p:] is non empty Relation-like set
[:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty Relation-like set
bool [:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
the multF of p . ((eval (x,m0)),(eval ((rpoly (1,y)),m0))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(eval (x,m0)),(eval ((rpoly (1,y)),m0))] is set
{(eval (x,m0)),(eval ((rpoly (1,y)),m0))} is non empty finite set
{(eval (x,m0))} is non empty trivial finite 1 -element set
{{(eval (x,m0)),(eval ((rpoly (1,y)),m0))},{(eval (x,m0))}} is non empty finite V42() set
the multF of p . [(eval (x,m0)),(eval ((rpoly (1,y)),m0))] is set
m0 - y is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
- y is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
m0 + (- y) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the addF of p is non empty 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 . (m0,(- y)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[m0,(- y)] is set
{m0,(- y)} is non empty finite set
{m0} is non empty trivial finite 1 -element set
{{m0,(- y)},{m0}} is non empty finite V42() set
the addF of p . [m0,(- y)] is set
(eval (x,m0)) * (m0 - y) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
the multF of p . ((eval (x,m0)),(m0 - y)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
[(eval (x,m0)),(m0 - y)] is set
{(eval (x,m0)),(m0 - y)} is non empty finite set
{{(eval (x,m0)),(m0 - y)},{(eval (x,m0))}} is non empty finite V42() set
the multF of p . [(eval (x,m0)),(m0 - y)] is set
card ((Roots x) \/ {y}) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
card {y} is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(card (Roots x)) + (card {y}) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) non-zero Element of bool [:NAT, the carrier of p:]
deg ZP is V11() V12() integer ext-real set
len ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(len ZP) - 1 is V11() V12() integer ext-real set
Roots ZP is finite Element of bool the carrier of p
card (Roots ZP) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) non-zero Element of bool [:NAT, the carrier of p:]
deg a is V11() V12() integer ext-real set
len a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(len a) - 1 is V11() V12() integer ext-real set
Roots a is finite Element of bool the carrier of p
card (Roots a) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a . 0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
<%(0. p)%> is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) Element of bool [:NAT, the carrier of p:]
ZP is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
<%ZP%> is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) Element of bool [:NAT, the carrier of p:]
f is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
eval (<%ZP%>,f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
<%ZP,(0. p)%> is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) Element of bool [:NAT, the carrier of p:]
eval (<%ZP,(0. p)%>,f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
f is set
g is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
eval (<%ZP%>,g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of p
ZP is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) non-zero Element of bool [:NAT, the carrier of p:]
deg ZP is V11() V12() integer ext-real set
len ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(len ZP) - 1 is V11() V12() integer ext-real set
a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
Roots ZP is finite Element of bool the carrier of p
card (Roots ZP) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p is non empty ZeroStr
the carrier of p is non empty set
[:NAT, the carrier of p:] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of p:] is non empty non trivial non finite set
a is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) Element of bool [:NAT, the carrier of p:]
deg a is V11() V12() integer ext-real set
len a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(len a) - 1 is V11() V12() integer ext-real set
0_. p is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) Element of bool [:NAT, the carrier of p:]
0. p is V110(p) Element of the carrier of p
the ZeroF of p is Element of the carrier of p
NAT --> (0. p) is non empty V8() Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total Element of bool [:NAT, the carrier of p:]
p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible V181() V182() V183() unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital V238() left_unital V259() V260() V261() V262() V267() doubleLoopStr
the carrier of p is non empty non trivial set
[:NAT, the carrier of p:] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of p:] is non empty non trivial non finite set
a is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) Element of bool [:NAT, the carrier of p:]
deg a is V11() V12() integer ext-real set
len a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(len a) - 1 is V11() V12() integer ext-real set
Roots a is Element of bool the carrier of p
bool the carrier of p is non empty set
card (Roots a) is V4() V5() V6() cardinal set
f is non empty Relation-like NAT -defined the carrier of p -valued Function-like total quasi_total V249(p) non-zero Element of bool [:NAT, the carrier of p:]
Roots f is finite Element of bool the carrier of p
card (Roots f) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
(p) is non empty finite unital Group-like associative commutative multMagma
(p) is non empty finite V71() V72() V73() V74() V75() V76() Element of bool NAT
(p) is non empty Relation-like [:(p),(p):] -defined (p) -valued Function-like total quasi_total finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:[:(p),(p):],(p):]
[:(p),(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
[:[:(p),(p):],(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(p),(p):],(p):] is non empty finite V42() set
multint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
Segm p is non empty V71() V72() V73() V74() V75() V76() Element of bool NAT
[:(Segm p),(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
[:[:(Segm p),(Segm p):],(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
(multint p) || (p) is set
(multint p) | [:(p),(p):] is Relation-like [:(p),(p):] -defined [:(Segm p),(Segm p):] -defined RAT -valued Segm p -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
multMagma(# (p),(p) #) is non empty strict multMagma
the carrier of (p) is non empty finite set
INT.Ring p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict V181() V182() V183() unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital V238() left_unital V259() V260() V261() V262() V267() doubleLoopStr
addint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
In (1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of Segm p
In (0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),(In (1,(Segm p))),(In (0,(Segm p))) #) is non empty strict doubleLoopStr
the carrier of (INT.Ring p) is non empty non trivial set
power (p) is non empty Relation-like [: the carrier of (p),NAT:] -defined the carrier of (p) -valued Function-like total quasi_total Element of bool [:[: the carrier of (p),NAT:], the carrier of (p):]
[: the carrier of (p),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued natural-valued set
[:[: the carrier of (p),NAT:], the carrier of (p):] is non empty non trivial Relation-like non finite set
bool [:[: the carrier of (p),NAT:], the carrier of (p):] is non empty non trivial non finite set
power (INT.Ring p) is non empty Relation-like [: the carrier of (INT.Ring p),NAT:] -defined the carrier of (INT.Ring p) -valued Function-like total quasi_total Element of bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued natural-valued set
[:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial Relation-like non finite set
bool [:[: the carrier of (INT.Ring p),NAT:], the carrier of (INT.Ring p):] is non empty non trivial non finite set
a is Element of the carrier of (p)
ZP is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(power (p)) . (a,f) is set
[a,f] is set
{a,f} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,f},{a}} is non empty finite V42() set
(power (p)) . [a,f] is set
(power (INT.Ring p)) . (ZP,f) is set
[ZP,f] is set
{ZP,f} is non empty finite set
{ZP} is non empty trivial finite 1 -element set
{{ZP,f},{ZP}} is non empty finite V42() set
(power (INT.Ring p)) . [ZP,f] is set
f + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(power (p)) . (a,(f + 1)) is Element of the carrier of (p)
[a,(f + 1)] is set
{a,(f + 1)} is non empty finite set
{{a,(f + 1)},{a}} is non empty finite V42() set
(power (p)) . [a,(f + 1)] is set
(power (p)) . (a,f) is Element of the carrier of (p)
((power (p)) . (a,f)) * a is Element of the carrier of (p)
the multF of (p) is non empty Relation-like [: the carrier of (p), the carrier of (p):] -defined the carrier of (p) -valued Function-like total quasi_total finite finite-support associative Element of bool [:[: the carrier of (p), the carrier of (p):], the carrier of (p):]
[: the carrier of (p), the carrier of (p):] is non empty Relation-like finite set
[:[: the carrier of (p), the carrier of (p):], the carrier of (p):] is non empty Relation-like finite set
bool [:[: the carrier of (p), the carrier of (p):], the carrier of (p):] is non empty finite V42() set
the multF of (p) . (((power (p)) . (a,f)),a) is Element of the carrier of (p)
[((power (p)) . (a,f)),a] is set
{((power (p)) . (a,f)),a} is non empty finite set
{((power (p)) . (a,f))} is non empty trivial finite 1 -element set
{{((power (p)) . (a,f)),a},{((power (p)) . (a,f))}} is non empty finite V42() set
the multF of (p) . [((power (p)) . (a,f)),a] is set
(power (INT.Ring p)) . (ZP,f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
((power (INT.Ring p)) . (ZP,f)) * ZP is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the multF of (INT.Ring p) is non empty Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like total quasi_total associative Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty Relation-like set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty Relation-like set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty set
the multF of (INT.Ring p) . (((power (INT.Ring p)) . (ZP,f)),ZP) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[((power (INT.Ring p)) . (ZP,f)),ZP] is set
{((power (INT.Ring p)) . (ZP,f)),ZP} is non empty finite set
{((power (INT.Ring p)) . (ZP,f))} is non empty trivial finite 1 -element set
{{((power (INT.Ring p)) . (ZP,f)),ZP},{((power (INT.Ring p)) . (ZP,f))}} is non empty finite V42() set
the multF of (INT.Ring p) . [((power (INT.Ring p)) . (ZP,f)),ZP] is set
(power (INT.Ring p)) . (ZP,(f + 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[ZP,(f + 1)] is set
{ZP,(f + 1)} is non empty finite set
{{ZP,(f + 1)},{ZP}} is non empty finite V42() set
(power (INT.Ring p)) . [ZP,(f + 1)] is set
(power (p)) . (a,(f + 1)) is set
(power (INT.Ring p)) . (ZP,(f + 1)) is set
(power (p)) . (a,0) is Element of the carrier of (p)
[a,0] is set
{a,0} is non empty finite set
{{a,0},{a}} is non empty finite V42() set
(power (p)) . [a,0] is set
1_ (p) is non being_of_order_0 Element of the carrier of (p)
1_ (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
1. (INT.Ring p) is V110( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
(power (INT.Ring p)) . (ZP,0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[ZP,0] is set
{ZP,0} is non empty finite set
{{ZP,0},{ZP}} is non empty finite V42() set
(power (INT.Ring p)) . [ZP,0] is set
(power (p)) . (a,0) is set
(power (INT.Ring p)) . (ZP,0) is set
f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(power (p)) . (a,f) is Element of the carrier of (p)
[a,f] is set
{a,f} is non empty finite set
{{a,f},{a}} is non empty finite V42() set
(power (p)) . [a,f] is set
(power (INT.Ring p)) . (ZP,f) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[ZP,f] is set
{ZP,f} is non empty finite set
{{ZP,f},{ZP}} is non empty finite V42() set
(power (INT.Ring p)) . [ZP,f] is set
p is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
INT.Ring p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict V181() V182() V183() unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital V238() left_unital V259() V260() V261() V262() V267() doubleLoopStr
Segm p is non empty V71() V72() V73() V74() V75() V76() Element of bool NAT
addint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
[:(Segm p),(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
[:[:(Segm p),(Segm p):],(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
multint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
In (1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of Segm p
In (0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),(In (1,(Segm p))),(In (0,(Segm p))) #) is non empty strict doubleLoopStr
(p) is non empty finite unital Group-like associative commutative multMagma
(p) is non empty finite V71() V72() V73() V74() V75() V76() Element of bool NAT
(p) is non empty Relation-like [:(p),(p):] -defined (p) -valued Function-like total quasi_total finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:[:(p),(p):],(p):]
[:(p),(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
[:[:(p),(p):],(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(p),(p):],(p):] is non empty finite V42() set
(multint p) || (p) is set
(multint p) | [:(p),(p):] is Relation-like [:(p),(p):] -defined [:(Segm p),(Segm p):] -defined RAT -valued Segm p -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
multMagma(# (p),(p) #) is non empty strict multMagma
the carrier of (p) is non empty finite set
the carrier of (INT.Ring p) is non empty non trivial set
1_ (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
1. (INT.Ring p) is V110( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
a is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible V181() V182() V183() unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital V238() left_unital V259() V260() V261() V262() V267() doubleLoopStr
the carrier of a is non empty non trivial set
[:NAT, the carrier of a:] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of a:] is non empty non trivial non finite set
ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
1_. a is non empty Relation-like NAT -defined the carrier of a -valued Function-like total quasi_total V249(a) Element of bool [:NAT, the carrier of a:]
0_. a is non empty Relation-like NAT -defined the carrier of a -valued Function-like total quasi_total V249(a) with_roots Element of bool [:NAT, the carrier of a:]
0. a is V110(a) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
the ZeroF of a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
NAT --> (0. a) is non empty V8() Relation-like NAT -defined the carrier of a -valued Function-like total quasi_total Element of bool [:NAT, the carrier of a:]
1. a is V110(a) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
the OneF of a is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
(0_. a) +* (0,(1. a)) is non empty Relation-like NAT -defined the carrier of a -valued Function-like total quasi_total Element of bool [:NAT, the carrier of a:]
<%(0. a),(1. a)%> is non empty Relation-like NAT -defined the carrier of a -valued Function-like total quasi_total V249(a) non-zero Element of bool [:NAT, the carrier of a:]
g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
<%(0. a),(1. a)%> `^ g is non empty Relation-like NAT -defined the carrier of a -valued Function-like total quasi_total V249(a) non-zero Element of bool [:NAT, the carrier of a:]
(<%(0. a),(1. a)%> `^ g) - (1_. a) is non empty Relation-like NAT -defined the carrier of a -valued Function-like total quasi_total V249(a) Element of bool [:NAT, the carrier of a:]
- (1_. a) is non empty Relation-like NAT -defined the carrier of a -valued Function-like total quasi_total V249(a) Element of bool [:NAT, the carrier of a:]
K680(a,(<%(0. a),(1. a)%> `^ g),(- (1_. a))) is non empty Relation-like NAT -defined the carrier of a -valued Function-like total quasi_total V249(a) Element of bool [:NAT, the carrier of a:]
x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
gg is Element of the carrier of (p)
n is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
gg |^ ZP is Element of the carrier of (p)
power (p) is non empty Relation-like [: the carrier of (p),NAT:] -defined the carrier of (p) -valued Function-like total quasi_total Element of bool [:[: the carrier of (p),NAT:], the carrier of (p):]
[: the carrier of (p),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued natural-valued set
[:[: the carrier of (p),NAT:], the carrier of (p):] is non empty non trivial Relation-like non finite set
bool [:[: the carrier of (p),NAT:], the carrier of (p):] is non empty non trivial non finite set
(power (p)) . (gg,ZP) is set
[gg,ZP] is set
{gg,ZP} is non empty finite set
{gg} is non empty trivial finite 1 -element set
{{gg,ZP},{gg}} is non empty finite V42() set
(power (p)) . [gg,ZP] is set
gg |^ g is Element of the carrier of (p)
(power (p)) . (gg,g) is set
[gg,g] is set
{gg,g} is non empty finite set
{{gg,g},{gg}} is non empty finite V42() set
(power (p)) . [gg,g] is set
power a is non empty Relation-like [: the carrier of a,NAT:] -defined the carrier of a -valued Function-like total quasi_total Element of bool [:[: the carrier of a,NAT:], the carrier of a:]
[: the carrier of a,NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued natural-valued set
[:[: the carrier of a,NAT:], the carrier of a:] is non empty non trivial Relation-like non finite set
bool [:[: the carrier of a,NAT:], the carrier of a:] is non empty non trivial non finite set
(power a) . (x,g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
[x,g] is set
{x,g} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,g},{x}} is non empty finite V42() set
(power a) . [x,g] is set
eval (((<%(0. a),(1. a)%> `^ g) - (1_. a)),x) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
eval ((<%(0. a),(1. a)%> `^ g),x) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
eval ((1_. a),x) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
(eval ((<%(0. a),(1. a)%> `^ g),x)) - (eval ((1_. a),x)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
- (eval ((1_. a),x)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
(eval ((<%(0. a),(1. a)%> `^ g),x)) + (- (eval ((1_. a),x))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
the addF of a is non empty Relation-like [: the carrier of a, the carrier of a:] -defined the carrier of a -valued Function-like total quasi_total Element of bool [:[: the carrier of a, the carrier of a:], the carrier of a:]
[: the carrier of a, the carrier of a:] is non empty Relation-like set
[:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty Relation-like set
bool [:[: the carrier of a, the carrier of a:], the carrier of a:] is non empty set
the addF of a . ((eval ((<%(0. a),(1. a)%> `^ g),x)),(- (eval ((1_. a),x)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
[(eval ((<%(0. a),(1. a)%> `^ g),x)),(- (eval ((1_. a),x)))] is set
{(eval ((<%(0. a),(1. a)%> `^ g),x)),(- (eval ((1_. a),x)))} is non empty finite set
{(eval ((<%(0. a),(1. a)%> `^ g),x))} is non empty trivial finite 1 -element set
{{(eval ((<%(0. a),(1. a)%> `^ g),x)),(- (eval ((1_. a),x)))},{(eval ((<%(0. a),(1. a)%> `^ g),x))}} is non empty finite V42() set
the addF of a . [(eval ((<%(0. a),(1. a)%> `^ g),x)),(- (eval ((1_. a),x)))] is set
(eval ((<%(0. a),(1. a)%> `^ g),x)) - (1. a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
- (1. a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
(eval ((<%(0. a),(1. a)%> `^ g),x)) + (- (1. a)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
the addF of a . ((eval ((<%(0. a),(1. a)%> `^ g),x)),(- (1. a))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
[(eval ((<%(0. a),(1. a)%> `^ g),x)),(- (1. a))] is set
{(eval ((<%(0. a),(1. a)%> `^ g),x)),(- (1. a))} is non empty finite set
{{(eval ((<%(0. a),(1. a)%> `^ g),x)),(- (1. a))},{(eval ((<%(0. a),(1. a)%> `^ g),x))}} is non empty finite V42() set
the addF of a . [(eval ((<%(0. a),(1. a)%> `^ g),x)),(- (1. a))] is set
eval (<%(0. a),(1. a)%>,x) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
(power a) . ((eval (<%(0. a),(1. a)%>,x)),g) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
[(eval (<%(0. a),(1. a)%>,x)),g] is set
{(eval (<%(0. a),(1. a)%>,x)),g} is non empty finite set
{(eval (<%(0. a),(1. a)%>,x))} is non empty trivial finite 1 -element set
{{(eval (<%(0. a),(1. a)%>,x)),g},{(eval (<%(0. a),(1. a)%>,x))}} is non empty finite V42() set
(power a) . [(eval (<%(0. a),(1. a)%>,x)),g] is set
((power a) . ((eval (<%(0. a),(1. a)%>,x)),g)) - (1. a) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
((power a) . ((eval (<%(0. a),(1. a)%>,x)),g)) + (- (1. a)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
the addF of a . (((power a) . ((eval (<%(0. a),(1. a)%>,x)),g)),(- (1. a))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of a
[((power a) . ((eval (<%(0. a),(1. a)%>,x)),g)),(- (1. a))] is set
{((power a) . ((eval (<%(0. a),(1. a)%>,x)),g)),(- (1. a))} is non empty finite set
{((power a) . ((eval (<%(0. a),(1. a)%>,x)),g))} is non empty trivial finite 1 -element set
{{((power a) . ((eval (<%(0. a),(1. a)%>,x)),g)),(- (1. a))},{((power a) . ((eval (<%(0. a),(1. a)%>,x)),g))}} is non empty finite V42() set
the addF of a . [((power a) . ((eval (<%(0. a),(1. a)%>,x)),g)),(- (1. a))] is set
n - (1_ (INT.Ring p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- (1_ (INT.Ring p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
n + (- (1_ (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) is non empty Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like total quasi_total Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty Relation-like set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty Relation-like set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty set
the addF of (INT.Ring p) . (n,(- (1_ (INT.Ring p)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[n,(- (1_ (INT.Ring p)))] is set
{n,(- (1_ (INT.Ring p)))} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,(- (1_ (INT.Ring p)))},{n}} is non empty finite V42() set
the addF of (INT.Ring p) . [n,(- (1_ (INT.Ring p)))] is set
len (1_. a) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
len <%(0. a),(1. a)%> is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
len (<%(0. a),(1. a)%> `^ g) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP * 2 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(ZP * 2) - ZP is V11() V12() integer ext-real set
((ZP * 2) - ZP) + 1 is V11() V12() integer ext-real set
ZP + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
0 + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
len (- (1_. a)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
len ((<%(0. a),(1. a)%> `^ g) - (1_. a)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
max ((len (<%(0. a),(1. a)%> `^ g)),(len (- (1_. a)))) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
max ((ZP + 1),1) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
deg ((<%(0. a),(1. a)%> `^ g) - (1_. a)) is V11() V12() integer ext-real set
(len ((<%(0. a),(1. a)%> `^ g) - (1_. a))) - 1 is V11() V12() integer ext-real set
p is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
(p) is non empty finite unital Group-like associative commutative multMagma
(p) is non empty finite V71() V72() V73() V74() V75() V76() Element of bool NAT
(p) is non empty Relation-like [:(p),(p):] -defined (p) -valued Function-like total quasi_total finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:[:(p),(p):],(p):]
[:(p),(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
[:[:(p),(p):],(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(p),(p):],(p):] is non empty finite V42() set
multint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
Segm p is non empty V71() V72() V73() V74() V75() V76() Element of bool NAT
[:(Segm p),(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
[:[:(Segm p),(Segm p):],(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
(multint p) || (p) is set
(multint p) | [:(p),(p):] is Relation-like [:(p),(p):] -defined [:(Segm p),(Segm p):] -defined RAT -valued Segm p -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
multMagma(# (p),(p) #) is non empty strict multMagma
the carrier of (p) is non empty finite set
a is Element of the carrier of (p)
ord a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP is Element of the carrier of (p)
{a} is non empty trivial finite 1 -element Element of bool the carrier of (p)
bool the carrier of (p) is non empty finite V42() set
gr {a} is non empty finite strict unital Group-like associative commutative Subgroup of (p)
the carrier of (gr {a}) is non empty finite set
f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
ZP |^ f is Element of the carrier of (p)
power (p) is non empty Relation-like [: the carrier of (p),NAT:] -defined the carrier of (p) -valued Function-like total quasi_total Element of bool [:[: the carrier of (p),NAT:], the carrier of (p):]
[: the carrier of (p),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued natural-valued set
[:[: the carrier of (p),NAT:], the carrier of (p):] is non empty non trivial Relation-like non finite set
bool [:[: the carrier of (p),NAT:], the carrier of (p):] is non empty non trivial non finite set
(power (p)) . (ZP,f) is set
[ZP,f] is set
{ZP,f} is non empty finite set
{ZP} is non empty trivial finite 1 -element set
{{ZP,f},{ZP}} is non empty finite V42() set
(power (p)) . [ZP,f] is set
card (gr {a}) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
card the carrier of (gr {a}) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
INT.Ring p is non empty non degenerated non trivial left_add-cancelable right_add-cancelable add-cancelable right_complementable almost_left_invertible strict V181() V182() V183() unital associative commutative Euclidian right-distributive left-distributive right_unital well-unital V238() left_unital V259() V260() V261() V262() V267() doubleLoopStr
addint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
In (1,(Segm p)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of Segm p
In (0,(Segm p)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() Element of Segm p
doubleLoopStr(# (Segm p),(addint p),(multint p),(In (1,(Segm p))),(In (0,(Segm p))) #) is non empty strict doubleLoopStr
y is non empty unital doubleLoopStr
the carrier of y is non empty set
[:NAT, the carrier of y:] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of y:] is non empty non trivial non finite set
the carrier of (INT.Ring p) is non empty non trivial set
1_ (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
1. (INT.Ring p) is V110( INT.Ring p) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the OneF of (INT.Ring p) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
x is non empty Relation-like NAT -defined the carrier of y -valued Function-like total quasi_total V249(y) Element of bool [:NAT, the carrier of y:]
deg x is V11() V12() integer ext-real set
len x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(len x) - 1 is V11() V12() integer ext-real set
Roots x is Element of bool the carrier of y
bool the carrier of y is non empty set
card (Roots x) is V4() V5() V6() cardinal set
gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
{ZP} is non empty trivial finite 1 -element Element of bool the carrier of (p)
the carrier of (gr {a}) \/ {ZP} is non empty finite set
card ( the carrier of (gr {a}) \/ {ZP}) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
g is finite set
card g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(card g) + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
gg + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
n is finite set
card n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
card (gg + 1) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
n is Element of the carrier of (p)
n |^ f is Element of the carrier of (p)
(power (p)) . (n,f) is set
[n,f] is set
{n,f} is non empty finite set
{n} is non empty trivial finite 1 -element set
{{n,f},{n}} is non empty finite V42() set
(power (p)) . [n,f] is set
1_ (p) is non being_of_order_0 Element of the carrier of (p)
(Segm p) \ {0} is V71() V72() V73() V74() V75() V76() Element of bool NAT
n0 is Element of the carrier of y
eval (x,n0) is Element of the carrier of y
m0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
m0 - (1_ (INT.Ring p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
- (1_ (INT.Ring p)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
m0 + (- (1_ (INT.Ring p))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
the addF of (INT.Ring p) is non empty Relation-like [: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] -defined the carrier of (INT.Ring p) -valued Function-like total quasi_total Element of bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):]
[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):] is non empty Relation-like set
[:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty Relation-like set
bool [:[: the carrier of (INT.Ring p), the carrier of (INT.Ring p):], the carrier of (INT.Ring p):] is non empty set
the addF of (INT.Ring p) . (m0,(- (1_ (INT.Ring p)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of (INT.Ring p)
[m0,(- (1_ (INT.Ring p)))] is set
{m0,(- (1_ (INT.Ring p)))} is non empty finite set
{m0} is non empty trivial finite 1 -element set
{{m0,(- (1_ (INT.Ring p)))},{m0}} is non empty finite V42() set
the addF of (INT.Ring p) . [m0,(- (1_ (INT.Ring p)))] is set
0. y is V110(y) Element of the carrier of y
the ZeroF of y is Element of the carrier of y
n is set
m0 is Element of the carrier of (p)
n0 is V11() V12() integer ext-real set
a |^ n0 is Element of the carrier of (p)
m0 |^ f is Element of the carrier of (p)
(power (p)) . (m0,f) is set
[m0,f] is set
{m0,f} is non empty finite set
{m0} is non empty trivial finite 1 -element set
{{m0,f},{m0}} is non empty finite V42() set
(power (p)) . [m0,f] is set
n0 * f is V11() V12() integer ext-real set
a |^ (n0 * f) is Element of the carrier of (p)
a |^ f is Element of the carrier of (p)
(power (p)) . (a,f) is set
[a,f] is set
{a,f} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,f},{a}} is non empty finite V42() set
(power (p)) . [a,f] is set
(a |^ f) |^ n0 is Element of the carrier of (p)
1_ (p) is non being_of_order_0 Element of the carrier of (p)
(1_ (p)) |^ n0 is Element of the carrier of (p)
card x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p is non empty unital Group-like associative multMagma
the carrier of p is non empty set
a is Element of the carrier of p
ord a is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
ZP * f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
a |^ ZP is Element of the carrier of p
power p is non empty Relation-like [: the carrier of p,NAT:] -defined the carrier of p -valued Function-like total quasi_total Element of bool [:[: the carrier of p,NAT:], the carrier of p:]
[: the carrier of p,NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued natural-valued set
[:[: the carrier of p,NAT:], the carrier of p:] is non empty non trivial Relation-like non finite set
bool [:[: the carrier of p,NAT:], the carrier of p:] is non empty non trivial non finite set
(power p) . (a,ZP) is set
[a,ZP] is set
{a,ZP} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,ZP},{a}} is non empty finite V42() set
(power p) . [a,ZP] is set
ord (a |^ ZP) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
{a} is non empty trivial finite 1 -element Element of bool the carrier of p
bool the carrier of p is non empty set
gr {a} is non empty strict unital Group-like associative Subgroup of p
y is non empty strict unital Group-like associative Subgroup of p
x is non empty finite strict unital Group-like associative Subgroup of p
the carrier of x is non empty finite set
x is Element of the carrier of x
{x} is non empty trivial finite 1 -element Element of bool the carrier of x
bool the carrier of x is non empty finite V42() set
gr {x} is non empty finite strict unital Group-like associative Subgroup of x
card x is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
card the carrier of x is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
x |^ ZP is Element of the carrier of x
power x is non empty Relation-like [: the carrier of x,NAT:] -defined the carrier of x -valued Function-like total quasi_total Element of bool [:[: the carrier of x,NAT:], the carrier of x:]
[: the carrier of x,NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued natural-valued set
[:[: the carrier of x,NAT:], the carrier of x:] is non empty non trivial Relation-like non finite set
bool [:[: the carrier of x,NAT:], the carrier of x:] is non empty non trivial non finite set
(power x) . (x,ZP) is set
[x,ZP] is set
{x,ZP} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,ZP},{x}} is non empty finite V42() set
(power x) . [x,ZP] is set
ord (x |^ ZP) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
p is non empty V4() V5() V6() V10() V11() V12() integer prime finite cardinal ext-real positive non negative set
(p) is non empty finite unital Group-like associative commutative multMagma
(p) is non empty finite V71() V72() V73() V74() V75() V76() Element of bool NAT
(p) is non empty Relation-like [:(p),(p):] -defined (p) -valued Function-like total quasi_total finite complex-yielding ext-real-valued real-valued natural-valued finite-support Element of bool [:[:(p),(p):],(p):]
[:(p),(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
[:[:(p),(p):],(p):] is non empty Relation-like RAT -valued INT -valued finite complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(p),(p):],(p):] is non empty finite V42() set
multint p is non empty Relation-like [:(Segm p),(Segm p):] -defined Segm p -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:[:(Segm p),(Segm p):],(Segm p):]
Segm p is non empty V71() V72() V73() V74() V75() V76() Element of bool NAT
[:(Segm p),(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
[:[:(Segm p),(Segm p):],(Segm p):] is non empty Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:(Segm p),(Segm p):],(Segm p):] is non empty set
(multint p) || (p) is set
(multint p) | [:(p),(p):] is Relation-like [:(p),(p):] -defined [:(Segm p),(Segm p):] -defined RAT -valued Segm p -valued Function-like finite complex-yielding ext-real-valued real-valued natural-valued finite-support set
multMagma(# (p),(p) #) is non empty strict multMagma
the carrier of (p) is non empty finite set
the Element of the carrier of (p) is Element of the carrier of (p)
card (p) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
card the carrier of (p) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
f is Element of the carrier of (p)
ord f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
f is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
g is Element of the carrier of (p)
ord g is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
{g} is non empty trivial finite 1 -element Element of bool the carrier of (p)
bool the carrier of (p) is non empty finite V42() set
gr {g} is non empty finite strict unital Group-like associative commutative Subgroup of (p)
card (gr {g}) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
the carrier of (gr {g}) is non empty finite set
card the carrier of (gr {g}) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
the carrier of (p) \ the carrier of (gr {g}) is finite Element of bool the carrier of (p)
x is set
x is Element of the carrier of (p)
ord x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(ord x) lcm (ord g) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
m0 is V11() V12() integer ext-real set
(ord x) * m0 is V11() V12() integer ext-real set
x |^ (ord g) is Element of the carrier of (p)
power (p) is non empty Relation-like [: the carrier of (p),NAT:] -defined the carrier of (p) -valued Function-like total quasi_total Element of bool [:[: the carrier of (p),NAT:], the carrier of (p):]
[: the carrier of (p),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued natural-valued set
[:[: the carrier of (p),NAT:], the carrier of (p):] is non empty non trivial Relation-like non finite set
bool [:[: the carrier of (p),NAT:], the carrier of (p):] is non empty non trivial non finite set
(power (p)) . (x,(ord g)) is set
[x,(ord g)] is set
{x,(ord g)} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,(ord g)},{x}} is non empty finite V42() set
(power (p)) . [x,(ord g)] is set
x |^ (ord x) is Element of the carrier of (p)
(power (p)) . (x,(ord x)) is set
[x,(ord x)] is set
{x,(ord x)} is non empty finite set
{{x,(ord x)},{x}} is non empty finite V42() set
(power (p)) . [x,(ord x)] is set
(x |^ (ord x)) |^ m0 is Element of the carrier of (p)
1_ (p) is non being_of_order_0 Element of the carrier of (p)
(1_ (p)) |^ m0 is Element of the carrier of (p)
{x} is non empty trivial finite 1 -element Element of bool the carrier of (p)
gr {x} is non empty finite strict unital Group-like associative commutative Subgroup of (p)
card (gr {x}) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
the carrier of (gr {x}) is non empty finite set
card the carrier of (gr {x}) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative set
n0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
m0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
n0 * m0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
n0 gcd m0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
j is V11() V12() integer ext-real set
n0 * j is V11() V12() integer ext-real set
u is V11() V12() integer ext-real set
m0 * u is V11() V12() integer ext-real set
(ord x) / m0 is V11() V12() ext-real non negative set
((ord x) / m0) * m0 is V11() V12() ext-real non negative set
d2 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
x |^ d2 is Element of the carrier of (p)
power (p) is non empty Relation-like [: the carrier of (p),NAT:] -defined the carrier of (p) -valued Function-like total quasi_total Element of bool [:[: the carrier of (p),NAT:], the carrier of (p):]
[: the carrier of (p),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued non finite complex-yielding ext-real-valued real-valued natural-valued set
[:[: the carrier of (p),NAT:], the carrier of (p):] is non empty non trivial Relation-like non finite set
bool [:[: the carrier of (p),NAT:], the carrier of (p):] is non empty non trivial non finite set
(power (p)) . (x,d2) is set
[x,d2] is set
{x,d2} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,d2},{x}} is non empty finite V42() set
(power (p)) . [x,d2] is set
ord (x |^ d2) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(ord g) / n0 is V11() V12() ext-real non negative set
j is V11() V12() integer ext-real set
(ord g) * j is V11() V12() integer ext-real set
d1 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
g |^ d1 is Element of the carrier of (p)
(power (p)) . (g,d1) is set
[g,d1] is set
{g,d1} is non empty finite set
{g} is non empty trivial finite 1 -element set
{{g,d1},{g}} is non empty finite V42() set
(power (p)) . [g,d1] is set
(g |^ d1) * (x |^ d2) is Element of the carrier of (p)
the multF of (p) is non empty Relation-like [: the carrier of (p), the carrier of (p):] -defined the carrier of (p) -valued Function-like total quasi_total finite finite-support associative Element of bool [:[: the carrier of (p), the carrier of (p):], the carrier of (p):]
[: the carrier of (p), the carrier of (p):] is non empty Relation-like finite set
[:[: the carrier of (p), the carrier of (p):], the carrier of (p):] is non empty Relation-like finite set
bool [:[: the carrier of (p), the carrier of (p):], the carrier of (p):] is non empty finite V42() set
the multF of (p) . ((g |^ d1),(x |^ d2)) is Element of the carrier of (p)
[(g |^ d1),(x |^ d2)] is set
{(g |^ d1),(x |^ d2)} is non empty finite set
{(g |^ d1)} is non empty trivial finite 1 -element set
{{(g |^ d1),(x |^ d2)},{(g |^ d1)}} is non empty finite V42() set
the multF of (p) . [(g |^ d1),(x |^ d2)] is set
((ord g) / n0) * n0 is V11() V12() ext-real non negative set
ord (g |^ d1) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
y is Element of the carrier of (p)
ord y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
m0 * n0 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
((ord x) lcm (ord g)) / (ord g) is V11() V12() ext-real non negative set
(ord g) * 1 is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
n is Element of the carrier of (p)
ord n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
[:NAT, the carrier of (p):] is non empty non trivial Relation-like non finite set
bool [:NAT, the carrier of (p):] is non empty non trivial non finite set
f is non empty Relation-like NAT -defined the carrier of (p) -valued Function-like total quasi_total Element of bool [:NAT, the carrier of (p):]
f . 0 is Element of the carrier of (p)
g is non empty Relation-like NAT -defined NAT -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued natural-valued Element of bool [:NAT,NAT:]
y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
y + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
g . (y + 1) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
f . (y + 1) is Element of the carrier of (p)
ord (f . (y + 1)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
g . y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
f . y is Element of the carrier of (p)
ord (f . y) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
y + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
g . y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(y + 1) + x is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
g . ((y + 1) + x) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
((y + 1) + x) + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
g . (((y + 1) + x) + 1) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
x + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(y + 1) + (x + 1) is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
g . ((y + 1) + (x + 1)) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(y + 1) + 0 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
g . ((y + 1) + 0) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(y + 1) + x is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
g . ((y + 1) + x) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
g . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
g . y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
x - y is V11() V12() integer ext-real set
x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative set
gg + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
y + 1 is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
n is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
(y + 1) + n is non empty V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real positive non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
y is set
x is set
g . y is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
g . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
dom g is non empty V71() V72() V73() V74() V75() V76() Element of bool NAT
rng g is non empty V71() V72() V73() V74() V75() V76() Element of bool NAT
card (dom g) is non empty V4() V5() V6() cardinal set
card (rng g) is non empty V4() V5() V6() cardinal set
card NAT is non empty non trivial V4() V5() V6() non finite cardinal set
Segm (card (p)) is non empty V71() V72() V73() V74() V75() V76() Element of bool NAT
y is set
x is set
g . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
g . x is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
f . x is Element of the carrier of (p)
ord (f . x) is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT
gg is V4() V5() V6() V10() V11() V12() integer finite cardinal ext-real non negative V52() V71() V72() V73() V74() V75() V76() Element of NAT