:: NAT_5 semantic presentation

REAL is non empty non trivial non finite V69() V70() V71() V75() set
NAT is ordinal non empty non trivial non finite cardinal limit_cardinal V69() V70() V71() V72() V73() V74() V75() Element of bool REAL
bool REAL is non empty non trivial non finite V48() set
COMPLEX is non empty non trivial non finite V69() V75() set
RAT is non empty non trivial non finite V69() V70() V71() V72() V75() set
INT is non empty non trivial non finite V69() V70() V71() V72() V73() V75() set
[:COMPLEX,COMPLEX:] is Relation-like non empty non trivial non finite V59() set
bool [:COMPLEX,COMPLEX:] is non empty non trivial non finite V48() set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is Relation-like non empty non trivial non finite V59() set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty non trivial non finite V48() set
[:REAL,REAL:] is Relation-like non empty non trivial non finite V59() V60() V61() set
bool [:REAL,REAL:] is non empty non trivial non finite V48() set
[:[:REAL,REAL:],REAL:] is Relation-like non empty non trivial non finite V59() V60() V61() set
bool [:[:REAL,REAL:],REAL:] is non empty non trivial non finite V48() set
[:RAT,RAT:] is Relation-like RAT -valued non empty non trivial non finite V59() V60() V61() set
bool [:RAT,RAT:] is non empty non trivial non finite V48() set
[:[:RAT,RAT:],RAT:] is Relation-like RAT -valued non empty non trivial non finite V59() V60() V61() set
bool [:[:RAT,RAT:],RAT:] is non empty non trivial non finite V48() set
[:INT,INT:] is Relation-like RAT -valued INT -valued non empty non trivial non finite V59() V60() V61() set
bool [:INT,INT:] is non empty non trivial non finite V48() set
[:[:INT,INT:],INT:] is Relation-like RAT -valued INT -valued non empty non trivial non finite V59() V60() V61() set
bool [:[:INT,INT:],INT:] is non empty non trivial non finite V48() set
[:NAT,NAT:] is Relation-like RAT -valued INT -valued non empty non trivial non finite V59() V60() V61() V62() set
[:[:NAT,NAT:],NAT:] is Relation-like RAT -valued INT -valued non empty non trivial non finite V59() V60() V61() V62() set
bool [:[:NAT,NAT:],NAT:] is non empty non trivial non finite V48() set
omega is ordinal non empty non trivial non finite cardinal limit_cardinal V69() V70() V71() V72() V73() V74() V75() set
bool omega is non empty non trivial non finite V48() set
bool NAT is non empty non trivial non finite V48() set
{} is Relation-like non-empty empty-yielding NAT -defined RAT -valued ordinal natural empty trivial V16() V17() integer Function-like one-to-one constant functional ext-real non positive non negative finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V59() V60() V61() V62() V63() V64() V65() V66() V69() V70() V71() V72() V73() V74() V75() Function-yielding FinSequence-yielding finite-support set
1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
{{},1} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
K420() is set
bool K420() is non empty set
K421() is Element of bool K420()
SetPrimes is non empty non trivial non finite V69() V70() V71() V72() V73() V74() Element of bool NAT
ExtREAL is non empty V70() set
2 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[:NAT,REAL:] is Relation-like non empty non trivial non finite V59() V60() V61() set
bool [:NAT,REAL:] is non empty non trivial non finite V48() set
1 -tuples_on NAT is FinSequenceSet of NAT
3 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[:NAT,{}:] is Relation-like non-empty empty-yielding NAT -defined RAT -valued INT -valued ordinal natural empty trivial V16() V17() integer Function-like one-to-one constant functional ext-real non positive non negative finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V59() V60() V61() V62() V63() V64() V65() V66() V69() V70() V71() V72() V73() V74() V75() Function-yielding FinSequence-yielding finite-support set
0 is Relation-like non-empty empty-yielding NAT -defined RAT -valued ordinal natural empty trivial V16() V17() integer Function-like one-to-one constant functional V32() ext-real non positive non negative finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V59() V60() V61() V62() V63() V64() V65() V66() V69() V70() V71() V72() V73() V74() V75() Function-yielding FinSequence-yielding finite-support Element of NAT
dom {} is Relation-like non-empty empty-yielding NAT -defined RAT -valued ordinal natural empty trivial V16() V17() integer Function-like one-to-one constant functional ext-real non positive non negative finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V59() V60() V61() V62() V63() V64() V65() V66() V69() V70() V71() V72() V73() V74() V75() Function-yielding FinSequence-yielding finite-support set
rng {} is Relation-like non-empty empty-yielding NAT -defined RAT -valued ordinal natural empty trivial V16() V17() integer Function-like one-to-one constant functional ext-real non positive non negative finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V47() V59() V60() V61() V62() V63() V64() V65() V66() V69() V70() V71() V72() V73() V74() V75() Function-yielding FinSequence-yielding finite-support set
4 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
K50(1) is non empty V16() V17() integer ext-real non positive negative set
Sgm {} is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
<*> REAL is Relation-like non-empty empty-yielding NAT -defined REAL -valued RAT -valued ordinal natural empty trivial proper V16() V17() integer Function-like one-to-one constant functional ext-real non positive non negative finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V59() V60() V61() V62() V63() V64() V65() V66() V69() V70() V71() V72() V73() V74() V75() Function-yielding FinSequence-yielding finite-support FinSequence of REAL
Sum (<*> REAL) is V16() V17() ext-real Element of REAL
Product (<*> REAL) is V16() V17() ext-real Element of REAL
card {} is Relation-like non-empty empty-yielding NAT -defined RAT -valued ordinal natural empty trivial V16() V17() integer Function-like one-to-one constant functional ext-real non positive non negative finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V59() V60() V61() V62() V63() V64() V65() V66() V69() V70() V71() V72() V73() V74() V75() Function-yielding FinSequence-yielding finite-support set
NatDivisors 1 is finite V47() V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides 1 ) } is set
{1} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() Element of bool NAT
K776() is non empty V17() ext-real non positive negative Element of ExtREAL
multnat is Relation-like [:NAT,NAT:] -defined NAT -valued RAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:[:NAT,NAT:],NAT:]
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
n0 |-count EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
X is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
EU9 gcd X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 |-count (EU9 gcd X) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 |-count X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
min ((n0 |-count EU9),(n0 |-count X)) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
fp is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
f1 is ordinal natural non empty V16() V17() integer prime ext-real positive non negative finite cardinal set
f1 |-count fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 |-count EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 |-count X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 |^ (f1 |-count EU9) is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
(f1 |-count EU9) |-> f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product ((f1 |-count EU9) |-> f1) is V16() V17() ext-real set
f1 |^ (n0 |-count EU9) is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
(n0 |-count EU9) |-> f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product ((n0 |-count EU9) |-> f1) is V16() V17() ext-real set
f1 |-count (f1 |^ (f1 |-count EU9)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 |^ (f1 |-count X) is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
(f1 |-count X) |-> f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product ((f1 |-count X) |-> f1) is V16() V17() ext-real set
f1 |^ (n0 |-count X) is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
(n0 |-count X) |-> f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product ((n0 |-count X) |-> f1) is V16() V17() ext-real set
f1 |-count (f1 |^ (f1 |-count X)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 + 2 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 |^ (n0 + 2) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 + 2) |-> 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product ((n0 + 2) |-> 2) is V16() V17() ext-real set
(2 |^ (n0 + 2)) - 1 is V16() V17() integer V32() ext-real Element of INT
n0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 |^ (n0 + 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 + 1) |-> 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product ((n0 + 1) |-> 2) is V16() V17() ext-real set
EU9 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 + 2 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 |^ (EU9 + 2) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(EU9 + 2) |-> 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product ((EU9 + 2) |-> 2) is V16() V17() ext-real set
(2 |^ (EU9 + 2)) - 1 is V16() V17() integer V32() ext-real Element of INT
EU9 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 |^ (EU9 + 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(EU9 + 1) |-> 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product ((EU9 + 1) |-> 2) is V16() V17() ext-real set
(EU9 + 1) + 2 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 |^ ((EU9 + 1) + 2) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((EU9 + 1) + 2) |-> 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (((EU9 + 1) + 2) |-> 2) is V16() V17() ext-real set
(2 |^ ((EU9 + 1) + 2)) - 1 is V16() V17() integer V32() ext-real Element of INT
(EU9 + 1) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 |^ ((EU9 + 1) + 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((EU9 + 1) + 1) |-> 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (((EU9 + 1) + 1) |-> 2) is V16() V17() ext-real set
((2 |^ (EU9 + 2)) - 1) * 2 is V16() V17() integer V32() ext-real even Element of INT
(2 |^ (EU9 + 1)) * 2 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() even Element of NAT
(2 |^ (EU9 + 2)) * 2 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() even Element of NAT
1 * 2 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() even Element of NAT
((2 |^ (EU9 + 2)) * 2) - (1 * 2) is V16() V17() integer V32() ext-real Element of INT
(EU9 + 2) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 |^ ((EU9 + 2) + 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((EU9 + 2) + 1) |-> 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (((EU9 + 2) + 1) |-> 2) is V16() V17() ext-real set
(2 |^ ((EU9 + 2) + 1)) - 2 is V16() V17() integer V32() ext-real Element of INT
- 1 is non empty V16() V17() integer V32() ext-real non positive negative Element of INT
(- 1) + (2 |^ ((EU9 + 1) + 2)) is V16() V17() integer V32() ext-real Element of INT
- 2 is non empty V16() V17() integer V32() ext-real non positive negative Element of INT
(- 2) + (2 |^ ((EU9 + 1) + 2)) is V16() V17() integer V32() ext-real Element of INT
2 * 2 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() even Element of NAT
(2 * 2) - 1 is non empty V16() V17() integer V32() ext-real non even Element of INT
2 |^ 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 |-> 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (1 |-> 2) is V16() V17() ext-real set
(2 |^ 1) * 2 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() even Element of NAT
((2 |^ 1) * 2) - 1 is non empty V16() V17() integer V32() ext-real non even Element of INT
1 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 |^ (1 + 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1 + 1) |-> 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product ((1 + 1) |-> 2) is V16() V17() ext-real set
(2 |^ (1 + 1)) - 1 is V16() V17() integer V32() ext-real Element of INT
0 + 2 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 |^ (0 + 2) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(0 + 2) |-> 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product ((0 + 2) |-> 2) is V16() V17() ext-real set
(2 |^ (0 + 2)) - 1 is V16() V17() integer V32() ext-real Element of INT
0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 |^ (0 + 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(0 + 1) |-> 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product ((0 + 1) |-> 2) is V16() V17() ext-real set
n0 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
2 |-count n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 |^ (2 |-count n0) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(2 |-count n0) |-> 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product ((2 |-count n0) |-> 2) is V16() V17() ext-real set
X is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(2 |^ (2 |-count n0)) * X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 |^ (2 |-count n0) is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal Element of REAL
(2 |^ (2 |-count n0)) * X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 * f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() even Element of NAT
(2 |^ (2 |-count n0)) * 2 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() even Element of NAT
((2 |^ (2 |-count n0)) * 2) * f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() even Element of NAT
(2 |-count n0) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 |^ ((2 |-count n0) + 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((2 |-count n0) + 1) |-> 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (((2 |-count n0) + 1) |-> 2) is V16() V17() ext-real set
(2 |^ ((2 |-count n0) + 1)) * f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 * X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
2 |^ EU9 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal Element of REAL
EU9 |-> 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (EU9 |-> 2) is V16() V17() ext-real set
X is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 gcd X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
f29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 |-count fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 |-count 1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 |-count n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 |-count X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
min ((f29 |-count n0),(f29 |-count X)) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
f19 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
f29 * f19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 |-count 2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 * (f29 |-count 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 * 0 is Relation-like non-empty empty-yielding NAT -defined RAT -valued ordinal natural empty trivial V16() V17() integer Function-like one-to-one constant functional V32() ext-real non positive non negative finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V59() V60() V61() V62() V63() V64() V65() V66() V69() V70() V71() V72() V73() V74() V75() Function-yielding FinSequence-yielding finite-support Element of NAT
f1 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
k is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
f1 gcd k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 |-count (f1 gcd k) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 |-count f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 |-count k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
min ((f29 |-count f1),(f29 |-count k)) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
{n0} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
{n0,EU9} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
X is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
{n0,EU9,X} is non empty finite V69() V70() V71() V72() V73() V74() set
{EU9,X} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
{n0} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
f1 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
fp is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
f1 \/ fp is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
X is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
fp is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
{n0,EU9,X,fp} is non empty finite set
{X,fp} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
{n0,EU9} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
k is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
f1 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
k \/ f1 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
Del (EU9,n0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom EU9 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
{n0} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
(dom EU9) \ {n0} is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sgm ((dom EU9) \ {n0}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
(Sgm ((dom EU9) \ {n0})) * EU9 is Relation-like NAT -defined Function-like finite finite-support set
dom EU9 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
len EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Seg (len EU9) is finite len EU9 -element V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( 1 <= b₁ & b₁ <= len EU9 ) } is set
(dom EU9) \ {n0} is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sgm ((dom EU9) \ {n0}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom EU9 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
EU9 . n0 is set
Del (EU9,n0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom EU9 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
{n0} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
(dom EU9) \ {n0} is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sgm ((dom EU9) \ {n0}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
(Sgm ((dom EU9) \ {n0})) * EU9 is Relation-like NAT -defined Function-like finite finite-support set
rng (Del (EU9,n0)) is finite set
X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Del (EU9,X) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
{X} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
(dom EU9) \ {X} is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sgm ((dom EU9) \ {X}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
(Sgm ((dom EU9) \ {X})) * EU9 is Relation-like NAT -defined Function-like finite finite-support set
dom (Del (EU9,X)) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
len EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
len (Del (EU9,n0)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
fp + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
dom (Del (EU9,n0)) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
f1 is set
(Del (EU9,n0)) . f1 is set
Seg fp is finite fp -element V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( 1 <= b₁ & b₁ <= fp ) } is set
k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 . k is set
k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
k + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Seg (fp + 1) is non empty finite fp + 1 -element K204(fp,1) -element V69() V70() V71() V72() V73() V74() Element of bool NAT
K204(fp,1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( 1 <= b₁ & b₁ <= fp + 1 ) } is set
EU9 . (k + 1) is set
k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
rng EU9 is finite set
Del (EU9,n0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom EU9 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
{n0} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
(dom EU9) \ {n0} is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sgm ((dom EU9) \ {n0}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
(Sgm ((dom EU9) \ {n0})) * EU9 is Relation-like NAT -defined Function-like finite finite-support set
rng (Del (EU9,n0)) is finite set
EU9 . n0 is set
X is set
dom EU9 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
f1 is set
EU9 . f1 is set
k is set
card k is ordinal cardinal set
len EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
k is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
k + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Seg (k + 1) is non empty finite k + 1 -element K204(k,1) -element V69() V70() V71() V72() V73() V74() Element of bool NAT
K204(k,1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( 1 <= b₁ & b₁ <= k + 1 ) } is set
len (Del (EU9,n0)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Del (EU9,fp) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
{fp} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
(dom EU9) \ {fp} is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sgm ((dom EU9) \ {fp}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
(Sgm ((dom EU9) \ {fp})) * EU9 is Relation-like NAT -defined Function-like finite finite-support set
(Del (EU9,fp)) . f29 is set
EU9 . f29 is set
dom (Del (EU9,n0)) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Seg k is finite k -element V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 -' 1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 - 1 is V16() V17() integer V32() ext-real Element of INT
(k + 1) - 1 is V16() V17() integer V32() ext-real Element of INT
f19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(fp + 1) - 1 is V16() V17() integer V32() ext-real Element of INT
Seg k is finite k -element V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( 1 <= b₁ & b₁ <= k ) } is set
dom (Del (EU9,n0)) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Del (EU9,fp) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
{fp} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
(dom EU9) \ {fp} is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sgm ((dom EU9) \ {fp}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
(Sgm ((dom EU9) \ {fp})) * EU9 is Relation-like NAT -defined Function-like finite finite-support set
(Del (EU9,fp)) . (f29 -' 1) is set
(f29 -' 1) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 . ((f29 -' 1) + 1) is set
EU9 . f29 is set
(f29 - 1) + 1 is V16() V17() integer V32() ext-real Element of INT
EU9 . ((f29 - 1) + 1) is set
fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is set
EU9 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
rng EU9 is finite V69() V70() V71() V72() V73() V74() Element of bool REAL
X is Relation-like NAT -defined n0 -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of n0
dom X is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
X * EU9 is Relation-like NAT -defined n0 -valued Function-like finite finite-support Element of bool [:NAT,n0:]
[:NAT,n0:] is Relation-like set
bool [:NAT,n0:] is non empty set
dom EU9 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
fp is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
Seg fp is finite fp -element V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( 1 <= b₁ & b₁ <= fp ) } is set
dom (X * EU9) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
rng (X * EU9) is finite Element of bool n0
bool n0 is non empty set
n0 is set
Sgm n0 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
EU9 is set
n0 \/ EU9 is set
Sgm EU9 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
X is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
dom X is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
X * (Sgm n0) is Relation-like NAT -defined REAL -valued Function-like finite V59() V60() V61() finite-support Element of bool [:NAT,REAL:]
X * (Sgm EU9) is Relation-like NAT -defined REAL -valued Function-like finite V59() V60() V61() finite-support Element of bool [:NAT,REAL:]
Sum X is V16() V17() ext-real Element of REAL
fp is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
Sum fp is V16() V17() ext-real Element of REAL
f1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
Sum f1 is V16() V17() ext-real Element of REAL
(Sum fp) + (Sum f1) is V16() V17() ext-real Element of REAL
len X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Seg (len X) is finite len X -element V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( 1 <= b₁ & b₁ <= len X ) } is set
id (dom X) is Relation-like dom X -defined dom X -valued RAT -valued INT -valued Function-like one-to-one total quasi_total finite V59() V60() V61() V62() V63() V65() finite-support Element of bool [:(dom X),(dom X):]
[:(dom X),(dom X):] is Relation-like RAT -valued INT -valued finite V59() V60() V61() V62() set
bool [:(dom X),(dom X):] is non empty finite V40() set
f19 is Relation-like NAT -defined ExtREAL -valued Function-like finite FinSequence-like FinSubsequence-like V60() finite-support FinSequence of ExtREAL
dom f19 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
k is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom k is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
rng (Sgm EU9) is finite V69() V70() V71() V72() V73() V74() Element of bool REAL
f29 is non empty set
(dom X) \ n0 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
rng k is finite set
(rng k) \ n0 is finite Element of bool (rng k)
bool (rng k) is non empty finite V40() set
k " ((rng k) \ n0) is finite set
rng (Sgm n0) is finite V69() V70() V71() V72() V73() V74() Element of bool REAL
k " n0 is finite set
[:(dom f19),(dom f19):] is Relation-like RAT -valued INT -valued finite V59() V60() V61() V62() set
bool [:(dom f19),(dom f19):] is non empty finite V40() set
(Sgm n0) ^ (Sgm EU9) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V97() finite-support M24( REAL , NAT )
h is Relation-like dom f19 -defined dom f19 -valued Function-like one-to-one total quasi_total onto bijective finite V59() V60() V61() V62() finite-support Element of bool [:(dom f19),(dom f19):]
rng h is finite V69() V70() V71() V72() V73() V74() Element of bool REAL
X * h is Relation-like dom f19 -defined REAL -valued Function-like finite V59() V60() V61() finite-support Element of bool [:(dom f19),REAL:]
[:(dom f19),REAL:] is Relation-like V59() V60() V61() set
bool [:(dom f19),REAL:] is non empty set
[:f29,REAL:] is Relation-like non empty non trivial non finite V59() V60() V61() set
bool [:f29,REAL:] is non empty non trivial non finite V48() set
Y is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
-infty is non empty V17() ext-real non positive negative set
rng f19 is finite V70() Element of bool ExtREAL
bool ExtREAL is non empty V48() set
Sum f19 is ext-real Element of ExtREAL
x19 is Relation-like NAT -defined ExtREAL -valued Function-like finite FinSequence-like FinSubsequence-like V60() finite-support FinSequence of ExtREAL
Sum x19 is ext-real Element of ExtREAL
i is Relation-like NAT -defined f29 -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of f29
x2 is Relation-like f29 -defined REAL -valued non empty Function-like total quasi_total V59() V60() V61() Element of bool [:f29,REAL:]
x2 * i is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
x is Relation-like NAT -defined f29 -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of f29
x2 * x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
(x2 * i) ^ (x2 * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
Sum Y is V16() V17() ext-real Element of REAL
Sum (x2 * i) is V16() V17() ext-real Element of REAL
Sum (x2 * x) is V16() V17() ext-real Element of REAL
(Sum (x2 * i)) + (Sum (x2 * x)) is V16() V17() ext-real Element of REAL
{0} is non empty trivial functional finite V40() 1 -element V69() V70() V71() V72() V73() V74() Element of bool NAT
n0 is set
Sgm n0 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
EU9 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
Sum EU9 is V16() V17() ext-real Element of REAL
X is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
X * (Sgm n0) is Relation-like NAT -defined REAL -valued Function-like finite V59() V60() V61() finite-support Element of bool [:NAT,REAL:]
dom X is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
X " {0} is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
(dom X) \ (X " {0}) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sum X is V16() V17() ext-real Element of REAL
(dom X) \ n0 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
n0 \ (dom X) is Element of bool n0
bool n0 is non empty set
len X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Seg (len X) is finite len X -element V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( 1 <= b₁ & b₁ <= len X ) } is set
idseq (len X) is Relation-like NAT -defined RAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() finite-support set
Sgm ((dom X) \ n0) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
X * (Sgm ((dom X) \ n0)) is Relation-like NAT -defined REAL -valued Function-like finite V59() V60() V61() finite-support Element of bool [:NAT,REAL:]
len X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Seg (len X) is finite len X -element V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( 1 <= b₁ & b₁ <= len X ) } is set
rng (Sgm ((dom X) \ n0)) is finite V69() V70() V71() V72() V73() V74() Element of bool REAL
f29 is set
n0 /\ ((dom X) \ n0) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
k is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
rng k is finite V69() V70() V71() Element of bool REAL
f29 is set
f19 is set
dom k is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
x is set
k . x is V16() V17() ext-real set
dom (Sgm ((dom X) \ n0)) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
(Sgm ((dom X) \ n0)) . x is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
X . ((Sgm ((dom X) \ n0)) . x) is V16() V17() ext-real set
x is set
(Sgm ((dom X) \ n0)) . x is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
X . f19 is V16() V17() ext-real set
X . ((Sgm ((dom X) \ n0)) . x) is V16() V17() ext-real set
k . x is V16() V17() ext-real set
dom k is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
len k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Seg (len k) is finite len k -element V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( 1 <= b₁ & b₁ <= len k ) } is set
(Seg (len k)) --> 0 is Relation-like NAT -defined NAT -valued RAT -valued INT -valued Function-like V59() V60() V61() V62() Element of PFuncs (NAT,NAT)
PFuncs (NAT,NAT) is PartFunc-set of NAT , NAT
(len k) |-> 0 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() Function-yielding V97() FinSequence-yielding finite-support Element of (len k) -tuples_on NAT
(len k) -tuples_on NAT is FinSequenceSet of NAT
n0 \/ ((dom X) \ n0) is set
f29 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
Sum f29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(Sum EU9) + (Sum f29) is V16() V17() ext-real Element of REAL
n0 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
Sum n0 is V16() V17() ext-real Element of REAL
EU9 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
EU9 - {0} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom EU9 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
EU9 " {0} is finite set
(dom EU9) \ (EU9 " {0}) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sgm ((dom EU9) \ (EU9 " {0})) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
(Sgm ((dom EU9) \ (EU9 " {0}))) * EU9 is Relation-like NAT -defined REAL -valued Function-like finite V59() V60() V61() finite-support set
Sum EU9 is V16() V17() ext-real Element of REAL
dom EU9 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
EU9 " {0} is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
(dom EU9) \ (EU9 " {0}) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
n0 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
dom n0 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
EU9 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 . EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
NatDivisors n0 is V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides n0 ) } is set
EU9 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
NatDivisors EU9 is V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides EU9 ) } is set
X is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
fp is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
X gcd fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(X gcd fp) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 gcd EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
NatDivisors n0 is V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides n0 ) } is set
EU9 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
NatDivisors EU9 is V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides EU9 ) } is set
X is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
fp is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
X * fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
k is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
f1 * k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 gcd EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
i is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
h is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
h |-count x is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
h |-count i is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Y is ordinal natural non empty V16() V17() integer prime ext-real positive non negative finite cardinal set
Y |-count x is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
Y |-count f29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(Y |-count x) + (Y |-count f29) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x * f29 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Y |-count (x * f29) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Y |-count i is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f19 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
Y |-count f19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(Y |-count i) + (Y |-count f19) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
NatDivisors n0 is finite V47() V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides n0 ) } is set
EU9 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
NatDivisors EU9 is finite V47() V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides EU9 ) } is set
n0 * EU9 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
NatDivisors (n0 * EU9) is finite V47() V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides n0 * EU9 ) } is set
X is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
fp is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
X * fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
k is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
f1 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
x is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x |-count k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x |-count f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
f19 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
f29 * f19 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
i is ordinal natural non empty V16() V17() integer prime ext-real positive non negative finite cardinal set
i |-count (f29 * f19) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
i |-count f29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
i |-count f19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(i |-count f29) + (i |-count f19) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
i |-count (n0 * EU9) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
i |-count n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
i |-count EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(i |-count n0) + (i |-count EU9) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(X * fp) * f29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
n0 gcd EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
X is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
EU9 * X is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 gcd (EU9 * X) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 gcd X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 gcd EU9) * (n0 gcd X) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
abs (EU9 * X) is ordinal natural V16() V17() integer ext-real non negative finite cardinal Element of REAL
abs EU9 is ordinal natural V16() V17() integer ext-real non negative finite cardinal Element of REAL
abs X is ordinal natural V16() V17() integer ext-real non negative finite cardinal Element of REAL
(abs EU9) * (abs X) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 gcd EU9) * (abs X) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
f19 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
x is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x |-count f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x |-count f19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
i is ordinal natural non empty V16() V17() integer prime ext-real positive non negative finite cardinal set
i |-count f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
i |-count fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
i |-count (EU9 * X) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
min ((i |-count fp),(i |-count (EU9 * X))) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
i |-count n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
i |-count EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
i |-count X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(i |-count EU9) + (i |-count X) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
min ((i |-count n0),((i |-count EU9) + (i |-count X))) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 gcd X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
i |-count 1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
min ((i |-count EU9),(i |-count X)) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
i |-count f19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
k is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
i |-count k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
i |-count f29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(i |-count k) + (i |-count f29) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
min ((i |-count fp),(i |-count EU9)) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(min ((i |-count fp),(i |-count EU9))) + (i |-count f29) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
min ((i |-count fp),(i |-count X)) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(min ((i |-count fp),(i |-count EU9))) + (min ((i |-count fp),(i |-count X))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
min ((i |-count n0),(i |-count EU9)) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
min ((i |-count n0),(i |-count X)) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
NatDivisors EU9 is finite V47() V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides EU9 ) } is set
X is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
EU9 * X is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
NatDivisors (EU9 * X) is finite V47() V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides EU9 * X ) } is set
NatDivisors X is finite V47() V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides X ) } is set
n0 gcd X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 gcd EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 gcd EU9) * (n0 gcd X) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 gcd (EU9 * X) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 |^ EU9 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 |-> n0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (EU9 |-> n0) is V16() V17() ext-real set
NatDivisors (n0 |^ EU9) is V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides n0 |^ EU9 ) } is set
{ (n0 |^ b₁) where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : b₁ <= EU9 } is set
X is set
fp is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 |^ f1 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
f1 |-> n0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (f1 |-> n0) is V16() V17() ext-real set
f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 |^ f1 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
f1 |-> n0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (f1 |-> n0) is V16() V17() ext-real set
fp is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 |^ f1 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
f1 |-> n0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (f1 |-> n0) is V16() V17() ext-real set
f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 |^ f1 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
f1 |-> n0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (f1 |-> n0) is V16() V17() ext-real set
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
X is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 * X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 * X) mod EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 * fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 * fp) mod EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 * X) - (n0 * fp) is V16() V17() integer V32() ext-real Element of INT
((n0 * X) - (n0 * fp)) mod EU9 is V16() V17() integer ext-real set
X - fp is V16() V17() integer V32() ext-real Element of INT
n0 * (X - fp) is V16() V17() integer V32() ext-real Element of INT
X -' fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 + fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(X -' fp) + fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(X - fp) + fp is V16() V17() integer V32() ext-real Element of INT
EU9 - EU9 is V16() V17() integer V32() ext-real Element of INT
(EU9 + fp) - EU9 is V16() V17() integer V32() ext-real Element of INT
- (X - fp) is V16() V17() integer V32() ext-real Element of INT
fp - X is V16() V17() integer V32() ext-real Element of INT
fp -' X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 + X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(fp -' X) + X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(fp - X) + X is V16() V17() integer V32() ext-real Element of INT
EU9 - EU9 is V16() V17() integer V32() ext-real Element of INT
(EU9 + X) - EU9 is V16() V17() integer V32() ext-real Element of INT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
X is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
EU9 gcd X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 |-count (EU9 gcd X) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 |-count EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 |-count X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
min ((n0 |-count EU9),(n0 |-count X)) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 - 1 is V16() V17() integer V32() ext-real Element of INT
n0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 - 1 is V16() V17() integer V32() ext-real Element of INT
EU9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom EU9 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
EU9 . n0 is set
<*(EU9 . n0)*> is Relation-like NAT -defined non empty trivial Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support set
[1,(EU9 . n0)] is non empty set
{1,(EU9 . n0)} is non empty finite set
{1} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{{1,(EU9 . n0)},{1}} is non empty finite V40() set
{[1,(EU9 . n0)]} is Relation-like non empty trivial Function-like constant finite 1 -element finite-support set
len EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(len EU9) - n0 is V16() V17() integer V32() ext-real Element of INT
X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 + X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
len f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
k is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
len k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 ^ k is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
f19 is set
<*f19*> is Relation-like NAT -defined non empty trivial Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support set
[1,f19] is non empty set
{1,f19} is non empty finite set
{{1,f19},{1}} is non empty finite V40() set
{[1,f19]} is Relation-like non empty trivial Function-like constant finite 1 -element finite-support set
f29 ^ <*f19*> is Relation-like NAT -defined non empty Function-like finite FinSequence-like FinSubsequence-like finite-support set
len f29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(len f29) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
dom f1 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
f1 . n0 is set
n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 - 1 is V16() V17() integer V32() ext-real Element of INT
EU9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom EU9 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
X is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
fp is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
len X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Del (EU9,n0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom EU9 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
{n0} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
(dom EU9) \ {n0} is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sgm ((dom EU9) \ {n0}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
(Sgm ((dom EU9) \ {n0})) * EU9 is Relation-like NAT -defined Function-like finite finite-support set
X ^ fp is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
f1 is set
<*f1*> is Relation-like NAT -defined non empty trivial Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support set
[1,f1] is non empty set
{1,f1} is non empty finite set
{1} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{{1,f1},{1}} is non empty finite V40() set
{[1,f1]} is Relation-like non empty trivial Function-like constant finite 1 -element finite-support set
X ^ <*f1*> is Relation-like NAT -defined non empty Function-like finite FinSequence-like FinSubsequence-like finite-support set
(X ^ <*f1*>) ^ fp is Relation-like NAT -defined non empty Function-like finite FinSequence-like FinSubsequence-like finite-support set
len (Del (EU9,n0)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(len (Del (EU9,n0))) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
len EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
len (X ^ <*f1*>) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
len fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(len (X ^ <*f1*>)) + (len fp) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(len X) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((len X) + 1) + (len fp) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 + (len fp) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(len fp) + (len X) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
len (X ^ fp) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
len <*f1*> is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
<*f1*> ^ fp is Relation-like NAT -defined non empty Function-like finite FinSequence-like FinSubsequence-like finite-support set
X ^ (<*f1*> ^ fp) is Relation-like NAT -defined non empty Function-like finite FinSequence-like FinSubsequence-like finite-support set
len (<*f1*> ^ fp) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 - 1) + (len (<*f1*> ^ fp)) is V16() V17() integer V32() ext-real Element of INT
(len EU9) - (n0 - 1) is V16() V17() integer V32() ext-real Element of INT
k is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
dom X is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
(X ^ fp) . k is set
X . k is set
EU9 . k is set
(Del (EU9,n0)) . k is set
k + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(k + 1) - n0 is V16() V17() integer V32() ext-real Element of INT
((k + 1) - n0) + 1 is V16() V17() integer V32() ext-real Element of INT
0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(k + 1) - (n0 - 1) is V16() V17() integer V32() ext-real Element of INT
(X ^ fp) . k is set
k - (len X) is V16() V17() integer V32() ext-real Element of INT
fp . (k - (len X)) is set
f29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 - 1 is V16() V17() integer V32() ext-real Element of INT
fp . (f29 - 1) is set
(<*f1*> ^ fp) . f29 is set
(X ^ (<*f1*> ^ fp)) . (k + 1) is set
(Del (EU9,n0)) . k is set
(X ^ fp) . k is set
(Del (EU9,n0)) . k is set
(X ^ fp) . k is set
(Del (EU9,n0)) . k is set
n0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
len n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 . 1 is set
<*(n0 . 1)*> is Relation-like NAT -defined non empty trivial Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support set
[1,(n0 . 1)] is non empty set
{1,(n0 . 1)} is non empty finite set
{1} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{{1,(n0 . 1)},{1}} is non empty finite V40() set
{[1,(n0 . 1)]} is Relation-like non empty trivial Function-like constant finite 1 -element finite-support set
Del (n0,1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom n0 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
(dom n0) \ {1} is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sgm ((dom n0) \ {1}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
(Sgm ((dom n0) \ {1})) * n0 is Relation-like NAT -defined Function-like finite finite-support set
<*(n0 . 1)*> ^ (Del (n0,1)) is Relation-like NAT -defined non empty Function-like finite FinSequence-like FinSubsequence-like finite-support set
Del (n0,(len n0)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
{(len n0)} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
(dom n0) \ {(len n0)} is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sgm ((dom n0) \ {(len n0)}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
(Sgm ((dom n0) \ {(len n0)})) * n0 is Relation-like NAT -defined Function-like finite finite-support set
n0 . (len n0) is set
<*(n0 . (len n0))*> is Relation-like NAT -defined non empty trivial Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support set
[1,(n0 . (len n0))] is non empty set
{1,(n0 . (len n0))} is non empty finite set
{{1,(n0 . (len n0))},{1}} is non empty finite V40() set
{[1,(n0 . (len n0))]} is Relation-like non empty trivial Function-like constant finite 1 -element finite-support set
(Del (n0,(len n0))) ^ <*(n0 . (len n0))*> is Relation-like NAT -defined non empty Function-like finite FinSequence-like FinSubsequence-like finite-support set
len <*(n0 . 1)*> is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
dom n0 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
len (Del (n0,1)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(len <*(n0 . 1)*>) + (len (Del (n0,1))) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
len (<*(n0 . 1)*> ^ (Del (n0,1))) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 . fp is set
(<*(n0 . 1)*> ^ (Del (n0,1))) . fp is set
dom <*(n0 . 1)*> is non empty trivial finite 1 -element V69() V70() V71() V72() V73() V74() Element of bool NAT
<*(n0 . 1)*> . 1 is set
fp - 1 is V16() V17() integer V32() ext-real Element of INT
f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(Del (n0,1)) . f1 is set
f1 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 . (f1 + 1) is set
len <*(n0 . (len n0))*> is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
len (Del (n0,(len n0))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(len <*(n0 . (len n0))*>) + (len (Del (n0,(len n0)))) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
len ((Del (n0,(len n0))) ^ <*(n0 . (len n0))*>) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(len (Del (n0,(len n0)))) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(len n0) - 1 is V16() V17() integer V32() ext-real Element of INT
fp is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 . fp is set
((Del (n0,(len n0))) ^ <*(n0 . (len n0))*>) . fp is set
fp - 1 is V16() V17() integer V32() ext-real Element of INT
fp - (fp - 1) is V16() V17() integer V32() ext-real Element of INT
f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
<*(n0 . (len n0))*> . f1 is set
fp + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
dom (Del (n0,(len n0))) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
(Del (n0,(len n0))) . fp is set
n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
dom EU9 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Del (EU9,n0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
dom EU9 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
{n0} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
(dom EU9) \ {n0} is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sgm ((dom EU9) \ {n0}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
(Sgm ((dom EU9) \ {n0})) * EU9 is Relation-like NAT -defined REAL -valued Function-like finite V59() V60() V61() finite-support set
Product (Del (EU9,n0)) is V16() V17() ext-real Element of REAL
EU9 . n0 is V16() V17() ext-real set
(Product (Del (EU9,n0))) * (EU9 . n0) is V16() V17() ext-real Element of REAL
Product EU9 is V16() V17() ext-real Element of REAL
X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 . X is V16() V17() ext-real set
Del (EU9,X) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
{X} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
(dom EU9) \ {X} is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sgm ((dom EU9) \ {X}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
(Sgm ((dom EU9) \ {X})) * EU9 is Relation-like NAT -defined REAL -valued Function-like finite V59() V60() V61() finite-support set
Product (Del (EU9,X)) is V16() V17() ext-real Element of REAL
(EU9 . X) * (Product (Del (EU9,X))) is V16() V17() ext-real Element of REAL
X + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 . (X + 1) is V16() V17() ext-real set
Del (EU9,(X + 1)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
{(X + 1)} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
(dom EU9) \ {(X + 1)} is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sgm ((dom EU9) \ {(X + 1)}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
(Sgm ((dom EU9) \ {(X + 1)})) * EU9 is Relation-like NAT -defined REAL -valued Function-like finite V59() V60() V61() finite-support set
Product (Del (EU9,(X + 1))) is V16() V17() ext-real Element of REAL
(EU9 . (X + 1)) * (Product (Del (EU9,(X + 1)))) is V16() V17() ext-real Element of REAL
len EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 . 1 is V16() V17() ext-real set
<*(EU9 . 1)*> is Relation-like NAT -defined non empty trivial Function-like one-to-one constant finite 1 -element FinSequence-like FinSubsequence-like V59() V60() V61() V63() V64() V65() V66() finite-support set
[1,(EU9 . 1)] is non empty set
{1,(EU9 . 1)} is non empty finite V69() V70() V71() set
{1} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{{1,(EU9 . 1)},{1}} is non empty finite V40() set
{[1,(EU9 . 1)]} is Relation-like non empty trivial Function-like constant finite 1 -element finite-support set
Del (EU9,1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
(dom EU9) \ {1} is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sgm ((dom EU9) \ {1}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
(Sgm ((dom EU9) \ {1})) * EU9 is Relation-like NAT -defined REAL -valued Function-like finite V59() V60() V61() finite-support set
<*(EU9 . 1)*> ^ (Del (EU9,1)) is Relation-like NAT -defined non empty Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product <*(EU9 . 1)*> is V16() V17() ext-real set
Product (Del (EU9,1)) is V16() V17() ext-real Element of REAL
(Product <*(EU9 . 1)*>) * (Product (Del (EU9,1))) is V16() V17() ext-real Element of REAL
(EU9 . 1) * (Product (Del (EU9,1))) is V16() V17() ext-real Element of REAL
len EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
<*(EU9 . (X + 1))*> is Relation-like NAT -defined non empty trivial Function-like one-to-one constant finite 1 -element FinSequence-like FinSubsequence-like V59() V60() V61() V63() V64() V65() V66() finite-support set
[1,(EU9 . (X + 1))] is non empty set
{1,(EU9 . (X + 1))} is non empty finite V69() V70() V71() set
{1} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{{1,(EU9 . (X + 1))},{1}} is non empty finite V40() set
{[1,(EU9 . (X + 1))]} is Relation-like non empty trivial Function-like constant finite 1 -element finite-support set
(X + 1) - 1 is V16() V17() integer V32() ext-real Element of INT
(len EU9) - (X + 1) is V16() V17() integer V32() ext-real Element of INT
fp is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
fp ^ <*(EU9 . (X + 1))*> is Relation-like NAT -defined non empty Function-like finite FinSequence-like FinSubsequence-like finite-support set
f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
(fp ^ <*(EU9 . (X + 1))*>) ^ f1 is Relation-like NAT -defined non empty Function-like finite FinSequence-like FinSubsequence-like finite-support set
len fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
len f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp ^ f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
f29 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
f29 ^ <*(EU9 . (X + 1))*> is Relation-like NAT -defined non empty Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (f29 ^ <*(EU9 . (X + 1))*>) is V16() V17() ext-real set
k is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
Product k is V16() V17() ext-real Element of REAL
(Product (f29 ^ <*(EU9 . (X + 1))*>)) * (Product k) is V16() V17() ext-real Element of REAL
Product f29 is V16() V17() ext-real Element of REAL
Product <*(EU9 . (X + 1))*> is V16() V17() ext-real set
(Product f29) * (Product <*(EU9 . (X + 1))*>) is V16() V17() ext-real Element of REAL
((Product f29) * (Product <*(EU9 . (X + 1))*>)) * (Product k) is V16() V17() ext-real Element of REAL
(EU9 . (X + 1)) * (Product f29) is V16() V17() ext-real Element of REAL
((EU9 . (X + 1)) * (Product f29)) * (Product k) is V16() V17() ext-real Element of REAL
(Product f29) * (Product k) is V16() V17() ext-real Element of REAL
(EU9 . (X + 1)) * ((Product f29) * (Product k)) is V16() V17() ext-real Element of REAL
len EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
len EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 . 0 is V16() V17() ext-real set
Del (EU9,0) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
{0} is non empty trivial functional finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
(dom EU9) \ {0} is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sgm ((dom EU9) \ {0}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
(Sgm ((dom EU9) \ {0})) * EU9 is Relation-like NAT -defined REAL -valued Function-like finite V59() V60() V61() finite-support set
Product (Del (EU9,0)) is V16() V17() ext-real Element of REAL
(EU9 . 0) * (Product (Del (EU9,0))) is V16() V17() ext-real Element of REAL
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 + 2 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Seg n0 is finite n0 -element V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( 1 <= b₁ & b₁ <= n0 ) } is set
EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 + 2 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
X is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 + n0 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 + n0 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 * fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(f1 * fp) mod (EU9 + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
X * f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(X * f1) mod (n0 + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 - 1 is V16() V17() integer V32() ext-real Element of INT
X - 1 is V16() V17() integer V32() ext-real Element of INT
(n0 + 1) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
X + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 + 1) * X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((n0 + 1) * X) mod (n0 + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 mod (n0 + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 + 2) * X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((n0 + 2) * X) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((n0 + 2) * X) + 1) mod (n0 + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((n0 + 2) * X) + 1) - ((n0 + 1) * X) is V16() V17() integer V32() ext-real Element of INT
((((n0 + 2) * X) + 1) - ((n0 + 1) * X)) mod (n0 + 2) is V16() V17() integer ext-real set
(n0 + 2) - 1 is V16() V17() integer V32() ext-real Element of INT
X -' 1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 * X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1 * X) mod (n0 + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 mod (n0 + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(X - 1) mod (n0 + 2) is V16() V17() integer ext-real set
(X -' 1) mod (n0 + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
X * X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(X * X) mod (n0 + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 mod (n0 + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(X * X) - 1 is V16() V17() integer V32() ext-real Element of INT
((X * X) - 1) mod (n0 + 2) is V16() V17() integer ext-real set
(X + 1) * (X - 1) is V16() V17() integer V32() ext-real Element of INT
(X + 1) - 1 is V16() V17() integer V32() ext-real Element of INT
(n0 + 2) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(X - 1) + 1 is V16() V17() integer V32() ext-real Element of INT
n0 + 3 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 + 3) - n0 is V16() V17() integer V32() ext-real Element of INT
n0 - n0 is V16() V17() integer V32() ext-real Element of INT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 + 2 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Seg n0 is finite n0 -element V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( 1 <= b₁ & b₁ <= n0 ) } is set
EU9 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
rng EU9 is finite V69() V70() V71() V72() V73() V74() Element of bool REAL
Product EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(Product EU9) mod (n0 + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
len EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
f1 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
len f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
rng f1 is finite V69() V70() V71() V72() V73() V74() Element of bool REAL
Product f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(Product f1) mod (n0 + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 + 1) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
<*> NAT is Relation-like non-empty empty-yielding NAT -defined NAT -valued RAT -valued ordinal natural empty trivial V16() V17() integer Function-like one-to-one constant functional ext-real non positive non negative finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V59() V60() V61() V62() V63() V64() V65() V66() V69() V70() V71() V72() V73() V74() V75() Function-yielding V97() FinSequence-yielding finite-support Element of NAT *
NAT * is non empty functional FinSequence-membered FinSequenceSet of NAT
dom f1 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
f29 is set
f19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Del (f1,f19) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V97() finite-support M24( REAL , NAT )
dom f1 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
{f19} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
(dom f1) \ {f19} is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sgm ((dom f1) \ {f19}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
(Sgm ((dom f1) \ {f19})) * f1 is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite V59() V60() V61() V62() finite-support set
len (Del (f1,f19)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
k is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
Del (k,f19) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
dom k is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
(dom k) \ {f19} is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sgm ((dom k) \ {f19}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
(Sgm ((dom k) \ {f19})) * k is Relation-like NAT -defined REAL -valued Function-like finite V59() V60() V61() finite-support set
Product (Del (k,f19)) is V16() V17() ext-real Element of REAL
k . f19 is V16() V17() ext-real set
(Product (Del (k,f19))) * (k . f19) is V16() V17() ext-real Element of REAL
rng (Del (f1,f19)) is finite V69() V70() V71() Element of bool REAL
1 + (len (Del (f1,f19))) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
0 + (len (Del (f1,f19))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
i is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
h is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
i * h is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(i * h) mod (n0 + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
i is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
i + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 . f19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Y is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(f1 . f19) * Y is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((f1 . f19) * Y) mod (n0 + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
dom (Del (f1,f19)) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
x2 is set
(Del (f1,f19)) . x2 is V16() V17() ext-real set
x19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Del ((Del (f1,f19)),x19) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V97() finite-support M24( REAL , NAT )
dom (Del (f1,f19)) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
{x19} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
(dom (Del (f1,f19))) \ {x19} is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sgm ((dom (Del (f1,f19))) \ {x19}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
(Sgm ((dom (Del (f1,f19))) \ {x19})) * (Del (f1,f19)) is Relation-like NAT -defined REAL -valued Function-like finite V59() V60() V61() finite-support set
rng (Del ((Del (f1,f19)),x19)) is finite V69() V70() V71() Element of bool REAL
rng (Del (k,f19)) is finite V69() V70() V71() Element of bool REAL
2 + n0 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
0 + n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x29 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
x is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
x29 * x is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(x29 * x) mod (n0 + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Y * (f1 . f19) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(Y * (f1 . f19)) mod (n0 + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Y * x29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(Y * x29) mod (n0 + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(f1 . f19) * x29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((f1 . f19) * x29) mod (n0 + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(Del (f1,f19)) . x19 is V16() V17() ext-real set
len (Del ((Del (f1,f19)),x19)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 + (len (Del ((Del (f1,f19)),x19))) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
0 + (len (Del ((Del (f1,f19)),x19))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
len (Del (k,f19)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
x + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
l is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
l + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Product (Del ((Del (f1,f19)),x19)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(Del (f1,f19)) . x19 is V16() V17() ext-real set
(Product (Del ((Del (f1,f19)),x19))) * ((Del (f1,f19)) . x19) is V16() V17() ext-real Element of REAL
Product (Del (f1,f19)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Y * (f1 . f19) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(Product (Del ((Del (f1,f19)),x19))) * (Y * (f1 . f19)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(Y * (f1 . f19)) mod (n0 + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(Product (Del ((Del (f1,f19)),x19))) * ((Y * (f1 . f19)) mod (n0 + 2)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((Product (Del ((Del (f1,f19)),x19))) * ((Y * (f1 . f19)) mod (n0 + 2))) mod (n0 + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
len fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
rng fp is finite V69() V70() V71() V72() V73() V74() Element of bool REAL
Product fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(Product fp) mod (n0 + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 -' 1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 -' 1) ! is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
idseq (n0 -' 1) is Relation-like NAT -defined RAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() finite-support set
Product (idseq (n0 -' 1)) is V16() V17() ext-real set
((n0 -' 1) !) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((n0 -' 1) !) + 1) mod n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 - 2 is V16() V17() integer V32() ext-real Element of INT
n0 - 2 is V16() V17() integer V32() ext-real Element of INT
0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 - 2) + 1 is V16() V17() integer V32() ext-real Element of INT
n0 -' 2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 + (n0 -' 2) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 + (n0 -' 2) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Seg (n0 -' 2) is finite n0 -' 2 -element V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( 1 <= b₁ & b₁ <= n0 -' 2 ) } is set
Sgm (Seg (n0 -' 2)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
n0 * 1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 * 1) mod n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 -' 2) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 - 1 is V16() V17() integer V32() ext-real Element of INT
rng (Sgm (Seg (n0 -' 2))) is finite V69() V70() V71() V72() V73() V74() Element of bool REAL
(n0 -' 2) + 2 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
f1 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
fp * f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(fp * f1) mod ((n0 -' 2) + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 -' 2) ! is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
idseq (n0 -' 2) is Relation-like NAT -defined RAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() finite-support set
Product (idseq (n0 -' 2)) is V16() V17() ext-real set
Product (Sgm (Seg (n0 -' 2))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((n0 -' 2) !) mod ((n0 -' 2) + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((n0 -' 2) + 1) ! is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
idseq ((n0 -' 2) + 1) is Relation-like NAT -defined RAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() finite-support set
Product (idseq ((n0 -' 2) + 1)) is V16() V17() ext-real set
(((n0 -' 2) + 1) !) mod ((n0 -' 2) + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((n0 -' 2) + 1) * ((n0 -' 2) !) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((n0 -' 2) + 1) * ((n0 -' 2) !)) mod ((n0 -' 2) + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((n0 -' 2) + 1) * 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((n0 -' 2) + 1) * 1) mod ((n0 -' 2) + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((((n0 -' 2) + 1) !) mod ((n0 -' 2) + 2)) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((((n0 -' 2) + 1) !) mod ((n0 -' 2) + 2)) + 1) mod ((n0 -' 2) + 2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
X is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 * X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((n0 -' 1) !) + 1) mod EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 - 1 is V16() V17() integer V32() ext-real Element of INT
EU9 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 - 1) + 1 is V16() V17() integer V32() ext-real Element of INT
(EU9 * X) / EU9 is V16() V17() V32() ext-real non negative Element of RAT
EU9 / EU9 is V16() V17() V32() ext-real non negative Element of RAT
X * (EU9 / EU9) is V16() V17() ext-real non negative Element of REAL
X * 1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 mod 4 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
sqrt n0 is V16() V17() ext-real set
[\(sqrt n0)/] is V16() V17() integer ext-real set
EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Segm X is finite V69() V70() V71() V72() V73() V74() Element of bool omega
card (Segm X) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
card X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
1 + [\(sqrt n0)/] is V16() V17() integer V32() ext-real Element of INT
(card (Segm X)) * (card (Segm X)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(sqrt n0) * (card (Segm X)) is V16() V17() ext-real Element of REAL
n0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 ^2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 ^2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 * f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 * n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 * n0) / n0 is V16() V17() ext-real non negative Element of REAL
n0 / n0 is V16() V17() ext-real non negative Element of REAL
n0 * (n0 / n0) is V16() V17() ext-real non negative Element of REAL
n0 * 1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(sqrt n0) ^2 is V16() V17() ext-real set
- 1 is non empty V16() V17() integer V32() ext-real non positive negative Element of INT
f1 is V16() V17() integer ext-real set
f1 ^2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(f1 ^2) - (- 1) is non empty V16() V17() integer V32() ext-real positive non negative Element of INT
((f1 ^2) - (- 1)) mod n0 is V16() V17() integer ext-real set
(card (Segm X)) * (sqrt n0) is V16() V17() ext-real Element of REAL
(sqrt n0) * (sqrt n0) is V16() V17() ext-real Element of REAL
n0 * n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
sqrt (n0 * n0) is V16() V17() ext-real Element of REAL
n0 ^2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
sqrt (n0 ^2) is V16() V17() ext-real set
[:(Segm X),(Segm X):] is Relation-like omega -defined RAT -valued INT -valued omega -valued finite V59() V60() V61() V62() Element of bool [:omega,omega:]
[:omega,omega:] is Relation-like RAT -valued INT -valued non empty non trivial non finite V59() V60() V61() V62() set
bool [:omega,omega:] is non empty non trivial non finite V48() set
card [:(Segm X),(Segm X):] is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
f19 is V16() V17() integer ext-real set
f29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Segm f29 is finite V69() V70() V71() V72() V73() V74() Element of bool omega
card (Segm f29) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
card f29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
i is set
h is set
Y is set
[h,Y] is non empty set
{h,Y} is non empty finite set
{h} is non empty trivial finite 1 -element set
{{h,Y},{h}} is non empty finite V40() set
x2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f19 * x19 is V16() V17() integer V32() ext-real Element of INT
x2 - (f19 * x19) is V16() V17() integer V32() ext-real Element of INT
(x2 - (f19 * x19)) mod n0 is V16() V17() integer ext-real set
x is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[:[:(Segm X),(Segm X):],(Segm f29):] is Relation-like RAT -valued INT -valued finite V59() V60() V61() V62() set
bool [:[:(Segm X),(Segm X):],(Segm f29):] is non empty finite V40() set
i is Relation-like [:(Segm X),(Segm X):] -defined Segm f29 -valued Function-like quasi_total finite V59() V60() V61() V62() finite-support Element of bool [:[:(Segm X),(Segm X):],(Segm f29):]
h is set
Y is set
i . h is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
i . Y is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x2 is set
x19 is set
[x2,x19] is non empty set
{x2,x19} is non empty finite set
{x2} is non empty trivial finite 1 -element set
{{x2,x19},{x2}} is non empty finite V40() set
l is set
m19 is set
[l,m19] is non empty set
{l,m19} is non empty finite set
{l} is non empty trivial finite 1 -element set
{{l,m19},{l}} is non empty finite V40() set
x29 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n1 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
x is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
[x29,x] is non empty set
{x29,x} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
{x29} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{{x29,x},{x29}} is non empty finite V40() set
f19 * x is V16() V17() integer V32() ext-real Element of INT
x29 - (f19 * x) is V16() V17() integer V32() ext-real Element of INT
(x29 - (f19 * x)) mod n0 is V16() V17() integer ext-real set
m1 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
[n1,m1] is non empty set
{n1,m1} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
{n1} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{{n1,m1},{n1}} is non empty finite V40() set
f19 * m1 is V16() V17() integer V32() ext-real Element of INT
n1 - (f19 * m1) is V16() V17() integer V32() ext-real Element of INT
(n1 - (f19 * m1)) mod n0 is V16() V17() integer ext-real set
x is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fn1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[x,fn1] is non empty Element of [:NAT,NAT:]
{x,fn1} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
{x} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{{x,fn1},{x}} is non empty finite V40() set
fm1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f19 * fn1 is V16() V17() integer V32() ext-real Element of INT
x - (f19 * fn1) is V16() V17() integer V32() ext-real Element of INT
(x - (f19 * fn1)) mod n0 is V16() V17() integer ext-real set
n21 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n22 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[n21,n22] is non empty Element of [:NAT,NAT:]
{n21,n22} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
{n21} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{{n21,n22},{n21}} is non empty finite V40() set
n23 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f19 * n22 is V16() V17() integer V32() ext-real Element of INT
n21 - (f19 * n22) is V16() V17() integer V32() ext-real Element of INT
(n21 - (f19 * n22)) mod n0 is V16() V17() integer ext-real set
k is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
f29 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
f19 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
x is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
[k,f19] is non empty set
{k,f19} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
{k} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{{k,f19},{k}} is non empty finite V40() set
[f29,x] is non empty set
{f29,x} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
{f29} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{{f29,x},{f29}} is non empty finite V40() set
f1 * f19 is V16() V17() integer V32() ext-real Element of INT
k - (f1 * f19) is V16() V17() integer V32() ext-real Element of INT
(k - (f1 * f19)) mod n0 is V16() V17() integer ext-real set
f1 * x is V16() V17() integer V32() ext-real Element of INT
f29 - (f1 * x) is V16() V17() integer V32() ext-real Element of INT
(f29 - (f1 * x)) mod n0 is V16() V17() integer ext-real set
f19 - x is V16() V17() integer V32() ext-real Element of INT
(f1 ^2) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((f1 ^2) + 1) mod n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(f19 - x) ^2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((f19 - x) ^2) mod n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((f1 ^2) + 1) mod n0) * (((f19 - x) ^2) mod n0) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((((f1 ^2) + 1) mod n0) * (((f19 - x) ^2) mod n0)) mod n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((f1 ^2) + 1) * ((f19 - x) ^2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((f1 ^2) + 1) * ((f19 - x) ^2)) mod n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(f1 ^2) * ((f19 - x) ^2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((f1 ^2) * ((f19 - x) ^2)) + ((f19 - x) ^2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((f1 ^2) * ((f19 - x) ^2)) + ((f19 - x) ^2)) mod n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 * (f19 - x) is V16() V17() integer V32() ext-real Element of INT
(f1 * (f19 - x)) ^2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((f1 * (f19 - x)) ^2) + ((f19 - x) ^2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((f1 * (f19 - x)) ^2) + ((f19 - x) ^2)) mod n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
k - f29 is V16() V17() integer V32() ext-real Element of INT
(k - f29) + (f1 * (f19 - x)) is V16() V17() integer V32() ext-real Element of INT
(k - f29) - (f1 * (f19 - x)) is V16() V17() integer V32() ext-real Element of INT
((k - f29) + (f1 * (f19 - x))) * ((k - f29) - (f1 * (f19 - x))) is V16() V17() integer V32() ext-real Element of INT
(k - f29) to_power 2 is V16() V17() ext-real set
(f1 * (f19 - x)) to_power 2 is V16() V17() ext-real set
((k - f29) to_power 2) - ((f1 * (f19 - x)) to_power 2) is V16() V17() ext-real Element of REAL
(k - f29) ^2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((k - f29) ^2) - ((f1 * (f19 - x)) to_power 2) is V16() V17() ext-real Element of REAL
((k - f29) ^2) - ((f1 * (f19 - x)) ^2) is V16() V17() integer V32() ext-real Element of INT
((k - (f1 * f19)) mod n0) - ((f29 - (f1 * x)) mod n0) is V16() V17() integer V32() ext-real Element of INT
(k - (f1 * f19)) - (f29 - (f1 * x)) is V16() V17() integer V32() ext-real Element of INT
((k - (f1 * f19)) - (f29 - (f1 * x))) mod n0 is V16() V17() integer ext-real set
0 mod n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((k - f29) - (f1 * (f19 - x))) mod n0 is V16() V17() integer ext-real set
((k - f29) + (f1 * (f19 - x))) mod n0 is V16() V17() integer ext-real set
(((k - f29) + (f1 * (f19 - x))) mod n0) * (((k - f29) - (f1 * (f19 - x))) mod n0) is V16() V17() integer V32() ext-real Element of INT
((((k - f29) + (f1 * (f19 - x))) mod n0) * (((k - f29) - (f1 * (f19 - x))) mod n0)) mod n0 is V16() V17() integer ext-real set
(((k - f29) ^2) - ((f1 * (f19 - x)) ^2)) mod n0 is V16() V17() integer ext-real set
((((k - f29) ^2) - ((f1 * (f19 - x)) ^2)) mod n0) + ((((f1 * (f19 - x)) ^2) + ((f19 - x) ^2)) mod n0) is V16() V17() integer V32() ext-real Element of INT
(((((k - f29) ^2) - ((f1 * (f19 - x)) ^2)) mod n0) + ((((f1 * (f19 - x)) ^2) + ((f19 - x) ^2)) mod n0)) mod n0 is V16() V17() integer ext-real set
(((k - f29) ^2) - ((f1 * (f19 - x)) ^2)) + (((f1 * (f19 - x)) ^2) + ((f19 - x) ^2)) is V16() V17() integer V32() ext-real Element of INT
((((k - f29) ^2) - ((f1 * (f19 - x)) ^2)) + (((f1 * (f19 - x)) ^2) + ((f19 - x) ^2))) mod n0 is V16() V17() integer ext-real set
((k - f29) ^2) + ((f19 - x) ^2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((k - f29) ^2) + ((f19 - x) ^2)) mod n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Y is V16() V17() integer ext-real set
n0 * Y is V16() V17() integer V32() ext-real Element of INT
|.(k - f29).| is ordinal natural V16() V17() integer ext-real non negative finite cardinal Element of REAL
|.(k - f29).| ^2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(|.(k - f29).| ^2) + ((f19 - x) ^2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
abs (k - f29) is ordinal natural V16() V17() integer ext-real non negative finite cardinal Element of REAL
(abs (k - f29)) ^2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
abs (f19 - x) is ordinal natural V16() V17() integer ext-real non negative finite cardinal Element of REAL
(abs (f19 - x)) ^2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((abs (k - f29)) ^2) + ((abs (f19 - x)) ^2) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
l is V16() V17() ext-real Element of REAL
m19 is V16() V17() ext-real Element of REAL
l - m19 is V16() V17() ext-real Element of REAL
abs (l - m19) is V16() V17() ext-real Element of REAL
EU9 - 0 is V16() V17() integer V32() ext-real non negative Element of INT
x29 is V16() V17() ext-real Element of REAL
x is V16() V17() ext-real Element of REAL
x29 - x is V16() V17() ext-real Element of REAL
abs (x29 - x) is V16() V17() ext-real Element of REAL
n0 + n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 * n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() even Element of NAT
(2 * n0) / n0 is V16() V17() ext-real non negative Element of REAL
Y * n0 is V16() V17() integer V32() ext-real Element of INT
(Y * n0) / n0 is V16() V17() ext-real Element of REAL
n0 / n0 is V16() V17() ext-real non negative Element of REAL
2 * (n0 / n0) is V16() V17() ext-real non negative Element of REAL
Y * (n0 / n0) is V16() V17() ext-real Element of REAL
2 * 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() even Element of NAT
Y * 1 is V16() V17() integer V32() ext-real Element of INT
Y + 1 is V16() V17() integer V32() ext-real Element of INT
(Y + 1) - 1 is V16() V17() integer V32() ext-real Element of INT
2 - 1 is V16() V17() integer V32() ext-real Element of INT
(abs (f19 - x)) * (abs (f19 - x)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(abs (k - f29)) * (abs (k - f29)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is set
[:n0,NAT:] is Relation-like RAT -valued INT -valued V59() V60() V61() V62() set
bool [:n0,NAT:] is non empty set
bool n0 is non empty set
EU9 is Relation-like n0 -defined NAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:n0,NAT:]
X is finite Element of bool n0
EU9 | X is Relation-like n0 -defined X -defined n0 -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
n0 is set
[:n0,NAT:] is Relation-like RAT -valued INT -valued V59() V60() V61() V62() set
bool [:n0,NAT:] is non empty set
bool n0 is non empty set
X is finite Element of bool n0
EU9 is Relation-like n0 -defined NAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:n0,NAT:]
(n0,EU9,X) is Relation-like n0 -defined X -defined n0 -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (n0,EU9,X) is V16() V17() ext-real set
support (n0,EU9,X) is finite set
canFS (support (n0,EU9,X)) is Relation-like NAT -defined support (n0,EU9,X) -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like finite-support FinSequence of support (n0,EU9,X)
(canFS (support (n0,EU9,X))) * (n0,EU9,X) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite V59() V60() V61() V62() finite-support set
f1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
Sum f1 is V16() V17() ext-real Element of REAL
rng f1 is finite V69() V70() V71() Element of bool REAL
k is set
k is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
Sum k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 is set
bool [:NAT,NAT:] is non empty non trivial non finite V48() set
n0 is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
EU9 is Relation-like NAT -defined REAL -valued non empty Function-like total quasi_total V59() V60() V61() Element of bool [:NAT,REAL:]
X is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
(NAT,n0,X) is Relation-like NAT -defined X -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,n0,X) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
Sgm X is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
Func_Seq (EU9,(Sgm X)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
Sum (Func_Seq (EU9,(Sgm X))) is V16() V17() ext-real Element of REAL
bool X is non empty finite V40() set
fp is finite V69() V70() V71() V72() V73() V74() Element of bool X
n0 | fp is Relation-like NAT -defined fp -defined NAT -defined NAT -valued RAT -valued Function-like finite V59() V60() V61() V62() finite-support Element of bool [:NAT,NAT:]
dom n0 is non empty V69() V70() V71() V72() V73() V74() Element of bool NAT
dom (n0 | fp) is finite V69() V70() V71() V72() V73() V74() Element of bool fp
bool fp is non empty finite V40() set
f1 is Relation-like X -defined RAT -valued Function-like total V59() V60() V61() V62() finite-support set
support f1 is finite set
canFS fp is Relation-like NAT -defined fp -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() finite-support FinSequence of fp
(canFS fp) * f1 is Relation-like NAT -defined RAT -valued Function-like finite V59() V60() V61() V62() finite-support set
Sum f1 is V16() V17() ext-real set
k is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
Sum k is V16() V17() ext-real Element of REAL
canFS X is Relation-like NAT -defined X -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() finite-support FinSequence of X
rng (canFS X) is finite V69() V70() V71() V72() V73() V74() Element of bool REAL
dom f1 is finite V69() V70() V71() V72() V73() V74() Element of bool X
dom (canFS X) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
dom k is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
f29 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
Seg f29 is finite f29 -element V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( 1 <= b₁ & b₁ <= f29 ) } is set
rng (Sgm X) is finite V69() V70() V71() V72() V73() V74() Element of bool REAL
f29 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
Seg f29 is finite f29 -element V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( 1 <= b₁ & b₁ <= f29 ) } is set
n0 * (Sgm X) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
X |` (Sgm X) is Relation-like NAT -defined NAT -valued X -valued NAT -valued Function-like finite FinSubsequence-like V59() V60() V61() V62() finite-support Element of bool [:NAT,NAT:]
n0 * (X |` (Sgm X)) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite V59() V60() V61() V62() finite-support Element of bool [:NAT,NAT:]
(Sgm X) * (NAT,n0,X) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite V59() V60() V61() V62() finite-support set
dom (NAT,n0,X) is finite V69() V70() V71() V72() V73() V74() Element of bool X
f29 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
Seg f29 is finite f29 -element V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( 1 <= b₁ & b₁ <= f29 ) } is set
dom (Sgm X) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
dom ((Sgm X) * (NAT,n0,X)) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
n0 is non empty set
[:n0,REAL:] is Relation-like non empty non trivial non finite V59() V60() V61() set
bool [:n0,REAL:] is non empty non trivial non finite V48() set
[:n0,NAT:] is Relation-like RAT -valued INT -valued non empty non trivial non finite V59() V60() V61() V62() set
bool [:n0,NAT:] is non empty non trivial non finite V48() set
bool n0 is non empty V48() set
EU9 is Relation-like n0 -defined REAL -valued Function-like V59() V60() V61() Element of bool [:n0,REAL:]
X is Relation-like n0 -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:n0,NAT:]
fp is finite Element of bool n0
(n0,X,fp) is Relation-like n0 -defined fp -defined n0 -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (n0,X,fp) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
Sum (EU9,fp) is V16() V17() ext-real Element of REAL
bool fp is non empty finite V40() set
f1 is finite Element of bool fp
X | f1 is Relation-like n0 -defined f1 -defined n0 -defined NAT -valued RAT -valued Function-like finite V59() V60() V61() V62() finite-support Element of bool [:n0,NAT:]
EU9 | fp is Relation-like n0 -defined fp -defined n0 -defined REAL -valued Function-like finite V59() V60() V61() finite-support Element of bool [:n0,REAL:]
dom (EU9 | fp) is finite Element of bool n0
FinS (EU9,fp) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V66() finite-support FinSequence of REAL
dom X is non empty Element of bool n0
dom (X | f1) is finite Element of bool n0
k is Relation-like fp -defined RAT -valued Function-like total V59() V60() V61() V62() finite-support set
support k is finite set
canFS f1 is Relation-like NAT -defined f1 -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like finite-support FinSequence of f1
(canFS f1) * k is Relation-like NAT -defined RAT -valued Function-like finite V59() V60() V61() V62() finite-support set
Sum k is V16() V17() ext-real set
f29 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
Sum f29 is V16() V17() ext-real Element of REAL
canFS fp is Relation-like NAT -defined fp -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like finite-support FinSequence of fp
rng (canFS fp) is finite Element of bool fp
dom k is finite Element of bool fp
dom (canFS fp) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
dom f29 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sum (FinS (EU9,fp)) is V16() V17() ext-real Element of REAL
n0 is set
[:n0,NAT:] is Relation-like RAT -valued INT -valued V59() V60() V61() V62() set
bool [:n0,NAT:] is non empty set
bool n0 is non empty set
EU9 is Relation-like n0 -defined NAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:n0,NAT:]
X is finite Element of bool n0
(n0,EU9,X) is Relation-like n0 -defined X -defined n0 -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (n0,EU9,X) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
fp is finite Element of bool n0
X \/ fp is finite Element of bool n0
(n0,EU9,(X \/ fp)) is Relation-like n0 -defined X \/ fp -defined n0 -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (n0,EU9,(X \/ fp)) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(n0,EU9,fp) is Relation-like n0 -defined fp -defined n0 -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (n0,EU9,fp) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(Sum (n0,EU9,X)) + (Sum (n0,EU9,fp)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EmptyBag {} is Relation-like non-empty empty-yielding {} -defined RAT -valued ordinal natural empty trivial V16() V17() integer Function-like one-to-one constant functional total ext-real non positive non negative finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V59() V60() V61() V62() V63() V64() V65() V66() V69() V70() V71() V72() V73() V74() V75() Function-yielding FinSequence-yielding finite-support Element of Bags {}
Bags {} is non empty set
Bags {} is non empty functional Element of bool (Bags {})
bool (Bags {}) is non empty V48() set
Sum (EmptyBag {}) is V16() V17() ext-real set
f1 is non empty set
[:f1,NAT:] is Relation-like RAT -valued INT -valued non empty non trivial non finite V59() V60() V61() V62() set
[:f1,REAL:] is Relation-like non empty non trivial non finite V59() V60() V61() set
bool [:f1,REAL:] is non empty non trivial non finite V48() set
k is Relation-like f1 -defined REAL -valued Function-like V59() V60() V61() Element of bool [:f1,REAL:]
k | (X \/ fp) is Relation-like X \/ fp -defined f1 -defined REAL -valued Function-like finite V59() V60() V61() finite-support Element of bool [:f1,REAL:]
dom (k | (X \/ fp)) is finite Element of bool f1
bool f1 is non empty V48() set
Sum (k,(X \/ fp)) is V16() V17() ext-real Element of REAL
Sum (k,X) is V16() V17() ext-real Element of REAL
Sum (k,fp) is V16() V17() ext-real Element of REAL
(Sum (k,X)) + (Sum (k,fp)) is V16() V17() ext-real Element of REAL
(Sum (n0,EU9,X)) + (Sum (k,fp)) is V16() V17() ext-real Element of REAL
n0 is set
[:n0,NAT:] is Relation-like RAT -valued INT -valued V59() V60() V61() V62() set
bool [:n0,NAT:] is non empty set
bool n0 is non empty set
EU9 is set
{EU9} is non empty trivial finite 1 -element set
X is Relation-like n0 -defined NAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:n0,NAT:]
X . EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp is finite Element of bool n0
(n0,X,fp) is Relation-like n0 -defined fp -defined n0 -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (n0,X,fp) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
support (n0,X,fp) is finite set
canFS (support (n0,X,fp)) is Relation-like NAT -defined support (n0,X,fp) -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like finite-support FinSequence of support (n0,X,fp)
(canFS (support (n0,X,fp))) * (n0,X,fp) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite V59() V60() V61() V62() finite-support set
f1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
Sum f1 is V16() V17() ext-real Element of REAL
dom X is Element of bool n0
dom (n0,X,fp) is finite Element of bool fp
bool fp is non empty finite V40() set
(n0,X,fp) . EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
<*EU9*> is Relation-like NAT -defined non empty trivial Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support set
[1,EU9] is non empty set
{1,EU9} is non empty finite set
{1} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{{1,EU9},{1}} is non empty finite V40() set
{[1,EU9]} is Relation-like non empty trivial Function-like constant finite 1 -element finite-support set
(n0,X,fp) . EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
<*((n0,X,fp) . EU9)*> is Relation-like NAT -defined NAT -valued non empty trivial Function-like one-to-one constant finite 1 -element FinSequence-like FinSubsequence-like V59() V60() V61() V62() V63() V64() V65() V66() V97() finite-support Element of NAT *
NAT * is non empty functional FinSequence-membered FinSequenceSet of NAT
[1,((n0,X,fp) . EU9)] is non empty set
{1,((n0,X,fp) . EU9)} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
{{1,((n0,X,fp) . EU9)},{1}} is non empty finite V40() set
{[1,((n0,X,fp) . EU9)]} is Relation-like non empty trivial Function-like constant finite 1 -element finite-support set
<*(X . EU9)*> is Relation-like NAT -defined NAT -valued non empty trivial Function-like one-to-one constant finite 1 -element FinSequence-like FinSubsequence-like V59() V60() V61() V62() V63() V64() V65() V66() V97() finite-support Element of NAT *
[1,(X . EU9)] is non empty set
{1,(X . EU9)} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
{{1,(X . EU9)},{1}} is non empty finite V40() set
{[1,(X . EU9)]} is Relation-like non empty trivial Function-like constant finite 1 -element finite-support set
n0 is set
[:n0,NAT:] is Relation-like RAT -valued INT -valued V59() V60() V61() V62() set
bool [:n0,NAT:] is non empty set
bool n0 is non empty set
[:n0,n0:] is Relation-like set
EU9 is set
{EU9} is non empty trivial finite 1 -element set
X is Relation-like n0 -defined NAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:n0,NAT:]
X . EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp is Relation-like n0 -defined NAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:n0,NAT:]
[:X,fp:] is Relation-like [:n0,n0:] -defined [:NAT,NAT:] -valued Function-like total quasi_total Element of bool [:[:n0,n0:],[:NAT,NAT:]:]
[:[:n0,n0:],[:NAT,NAT:]:] is Relation-like set
bool [:[:n0,n0:],[:NAT,NAT:]:] is non empty set
multnat * [:X,fp:] is Relation-like [:n0,n0:] -defined NAT -valued RAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:[:n0,n0:],NAT:]
[:[:n0,n0:],NAT:] is Relation-like RAT -valued INT -valued V59() V60() V61() V62() set
bool [:[:n0,n0:],NAT:] is non empty set
f1 is finite Element of bool n0
k is finite Element of bool n0
[:f1,k:] is Relation-like n0 -defined n0 -valued finite Element of bool [:n0,n0:]
bool [:n0,n0:] is non empty set
([:n0,n0:],(multnat * [:X,fp:]),[:f1,k:]) is Relation-like [:n0,n0:] -defined [:f1,k:] -defined [:n0,n0:] -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum ([:n0,n0:],(multnat * [:X,fp:]),[:f1,k:]) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(n0,fp,k) is Relation-like n0 -defined k -defined n0 -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (n0,fp,k) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(X . EU9) * (Sum (n0,fp,k)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
f29 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f19 is set
[:f19,NAT:] is Relation-like RAT -valued INT -valued V59() V60() V61() V62() set
bool [:f19,NAT:] is non empty set
bool f19 is non empty set
x is set
{x} is non empty trivial finite 1 -element set
[:f19,f19:] is Relation-like set
i is Relation-like f19 -defined NAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:f19,NAT:]
h is Relation-like f19 -defined NAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:f19,NAT:]
[:i,h:] is Relation-like [:f19,f19:] -defined [:NAT,NAT:] -valued Function-like total quasi_total Element of bool [:[:f19,f19:],[:NAT,NAT:]:]
[:[:f19,f19:],[:NAT,NAT:]:] is Relation-like set
bool [:[:f19,f19:],[:NAT,NAT:]:] is non empty set
multnat * [:i,h:] is Relation-like [:f19,f19:] -defined NAT -valued RAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:[:f19,f19:],NAT:]
[:[:f19,f19:],NAT:] is Relation-like RAT -valued INT -valued V59() V60() V61() V62() set
bool [:[:f19,f19:],NAT:] is non empty set
i . x is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Y is finite Element of bool f19
x2 is finite Element of bool f19
card x2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
[:Y,x2:] is Relation-like f19 -defined f19 -valued finite Element of bool [:f19,f19:]
bool [:f19,f19:] is non empty set
([:f19,f19:],(multnat * [:i,h:]),[:Y,x2:]) is Relation-like [:f19,f19:] -defined [:Y,x2:] -defined [:f19,f19:] -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum ([:f19,f19:],(multnat * [:i,h:]),[:Y,x2:]) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(f19,h,x2) is Relation-like f19 -defined x2 -defined f19 -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (f19,h,x2) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(i . x) * (Sum (f19,h,x2)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EmptyBag {} is Relation-like non-empty empty-yielding {} -defined RAT -valued ordinal natural empty trivial V16() V17() integer Function-like one-to-one constant functional total ext-real non positive non negative finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V59() V60() V61() V62() V63() V64() V65() V66() V69() V70() V71() V72() V73() V74() V75() Function-yielding FinSequence-yielding finite-support Element of Bags {}
Bags {} is non empty set
Bags {} is non empty functional Element of bool (Bags {})
bool (Bags {}) is non empty V48() set
Sum (EmptyBag {}) is V16() V17() ext-real set
the set is set
{ the set } is non empty trivial finite 1 -element set
card { the set } is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
x29 is set
{x29} is non empty trivial finite 1 -element set
support ([:f19,f19:],(multnat * [:i,h:]),[:Y,x2:]) is finite set
canFS (support ([:f19,f19:],(multnat * [:i,h:]),[:Y,x2:])) is Relation-like NAT -defined support ([:f19,f19:],(multnat * [:i,h:]),[:Y,x2:]) -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like finite-support FinSequence of support ([:f19,f19:],(multnat * [:i,h:]),[:Y,x2:])
(canFS (support ([:f19,f19:],(multnat * [:i,h:]),[:Y,x2:]))) * ([:f19,f19:],(multnat * [:i,h:]),[:Y,x2:]) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite V59() V60() V61() V62() finite-support set
l is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
Sum l is V16() V17() ext-real Element of REAL
[x,x29] is non empty set
{x,x29} is non empty finite set
{{x,x29},{x}} is non empty finite V40() set
{[x,x29]} is Relation-like non empty trivial Function-like constant finite 1 -element finite-support set
dom (multnat * [:i,h:]) is Relation-like f19 -defined f19 -valued Element of bool [:f19,f19:]
dom ([:f19,f19:],(multnat * [:i,h:]),[:Y,x2:]) is Relation-like f19 -defined f19 -valued finite Element of bool [:Y,x2:]
bool [:Y,x2:] is non empty finite V40() set
h . x29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(i . x) * (h . x29) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
m19 is non empty set
multnat . ((i . x),(h . x29)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n1 is Element of m19
i . n1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
m1 is Element of m19
h . m1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[(i . n1),(h . m1)] is non empty Element of [:NAT,NAT:]
{(i . n1),(h . m1)} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
{(i . n1)} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{{(i . n1),(h . m1)},{(i . n1)}} is non empty finite V40() set
multnat . [(i . n1),(h . m1)] is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[:i,h:] . (n1,m1) is set
multnat . ([:i,h:] . (n1,m1)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[:i,h:] . [x,x29] is set
multnat . ([:i,h:] . [x,x29]) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(multnat * [:i,h:]) . [x,x29] is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
([:f19,f19:],(multnat * [:i,h:]),[:Y,x2:]) . [x,x29] is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
<*[x,x29]*> is Relation-like NAT -defined non empty trivial Function-like constant finite 1 -element FinSequence-like FinSubsequence-like finite-support set
[1,[x,x29]] is non empty set
{1,[x,x29]} is non empty finite set
{1} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{{1,[x,x29]},{1}} is non empty finite V40() set
{[1,[x,x29]]} is Relation-like non empty trivial Function-like constant finite 1 -element finite-support set
<*(([:f19,f19:],(multnat * [:i,h:]),[:Y,x2:]) . [x,x29])*> is Relation-like NAT -defined NAT -valued non empty trivial Function-like one-to-one constant finite 1 -element FinSequence-like FinSubsequence-like V59() V60() V61() V62() V63() V64() V65() V66() V97() finite-support Element of NAT *
NAT * is non empty functional FinSequence-membered FinSequenceSet of NAT
[1,(([:f19,f19:],(multnat * [:i,h:]),[:Y,x2:]) . [x,x29])] is non empty set
{1,(([:f19,f19:],(multnat * [:i,h:]),[:Y,x2:]) . [x,x29])} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
{{1,(([:f19,f19:],(multnat * [:i,h:]),[:Y,x2:]) . [x,x29])},{1}} is non empty finite V40() set
{[1,(([:f19,f19:],(multnat * [:i,h:]),[:Y,x2:]) . [x,x29])]} is Relation-like non empty trivial Function-like constant finite 1 -element finite-support set
x19 is set
{x19} is non empty trivial finite 1 -element set
x2 \ {x19} is finite Element of bool f19
l is finite Element of bool f19
card l is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
0 + f29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
- 1 is non empty V16() V17() integer V32() ext-real non positive negative Element of INT
(- 1) + f29 is V16() V17() integer V32() ext-real Element of INT
[:Y,l:] is Relation-like f19 -defined f19 -valued finite Element of bool [:f19,f19:]
([:f19,f19:],(multnat * [:i,h:]),[:Y,l:]) is Relation-like [:f19,f19:] -defined [:Y,l:] -defined [:f19,f19:] -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum ([:f19,f19:],(multnat * [:i,h:]),[:Y,l:]) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(f19,h,l) is Relation-like f19 -defined l -defined f19 -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (f19,h,l) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(i . x) * (Sum (f19,h,l)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[:Y,(x2 \ {x19}):] is Relation-like f19 -defined f19 -valued finite Element of bool [:f19,f19:]
(x2 \ {x19}) \/ l is finite Element of bool f19
card ((x2 \ {x19}) \/ l) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
card (x2 \ {x19}) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
(card (x2 \ {x19})) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x2 \/ {x19} is non empty finite set
[:Y,(x2 \ {x19}):] \/ [:Y,l:] is Relation-like f19 -defined f19 -valued finite Element of bool [:f19,f19:]
([:f19,f19:],(multnat * [:i,h:]),[:Y,(x2 \ {x19}):]) is Relation-like [:f19,f19:] -defined [:Y,(x2 \ {x19}):] -defined [:f19,f19:] -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum ([:f19,f19:],(multnat * [:i,h:]),[:Y,(x2 \ {x19}):]) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(Sum ([:f19,f19:],(multnat * [:i,h:]),[:Y,(x2 \ {x19}):])) + (Sum ([:f19,f19:],(multnat * [:i,h:]),[:Y,l:])) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(f19,h,(x2 \ {x19})) is Relation-like f19 -defined x2 \ {x19} -defined f19 -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (f19,h,(x2 \ {x19})) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(i . x) * (Sum (f19,h,(x2 \ {x19}))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((i . x) * (Sum (f19,h,(x2 \ {x19})))) + ((i . x) * (Sum (f19,h,l))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(Sum (f19,h,(x2 \ {x19}))) + (Sum (f19,h,l)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(i . x) * ((Sum (f19,h,(x2 \ {x19}))) + (Sum (f19,h,l))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
card k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
f29 is set
[:f29,NAT:] is Relation-like RAT -valued INT -valued V59() V60() V61() V62() set
bool [:f29,NAT:] is non empty set
bool f29 is non empty set
h is finite Element of bool f29
f19 is set
{f19} is non empty trivial finite 1 -element set
Y is finite Element of bool f29
card Y is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
[:h,Y:] is Relation-like f29 -defined f29 -valued finite Element of bool [:f29,f29:]
[:f29,f29:] is Relation-like set
bool [:f29,f29:] is non empty set
x is Relation-like f29 -defined NAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:f29,NAT:]
i is Relation-like f29 -defined NAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:f29,NAT:]
[:x,i:] is Relation-like [:f29,f29:] -defined [:NAT,NAT:] -valued Function-like total quasi_total Element of bool [:[:f29,f29:],[:NAT,NAT:]:]
[:[:f29,f29:],[:NAT,NAT:]:] is Relation-like set
bool [:[:f29,f29:],[:NAT,NAT:]:] is non empty set
multnat * [:x,i:] is Relation-like [:f29,f29:] -defined NAT -valued RAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:[:f29,f29:],NAT:]
[:[:f29,f29:],NAT:] is Relation-like RAT -valued INT -valued V59() V60() V61() V62() set
bool [:[:f29,f29:],NAT:] is non empty set
([:f29,f29:],(multnat * [:x,i:]),[:h,Y:]) is Relation-like [:h,Y:] -defined [:f29,f29:] -defined [:h,Y:] -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum ([:f29,f29:],(multnat * [:x,i:]),[:h,Y:]) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
x . f19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(f29,i,Y) is Relation-like f29 -defined Y -defined f29 -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (f29,i,Y) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(x . f19) * (Sum (f29,i,Y)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is set
[:n0,NAT:] is Relation-like RAT -valued INT -valued V59() V60() V61() V62() set
bool [:n0,NAT:] is non empty set
bool n0 is non empty set
[:n0,n0:] is Relation-like set
EU9 is Relation-like n0 -defined NAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:n0,NAT:]
X is Relation-like n0 -defined NAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:n0,NAT:]
[:EU9,X:] is Relation-like [:n0,n0:] -defined [:NAT,NAT:] -valued Function-like total quasi_total Element of bool [:[:n0,n0:],[:NAT,NAT:]:]
[:[:n0,n0:],[:NAT,NAT:]:] is Relation-like set
bool [:[:n0,n0:],[:NAT,NAT:]:] is non empty set
multnat * [:EU9,X:] is Relation-like [:n0,n0:] -defined NAT -valued RAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:[:n0,n0:],NAT:]
[:[:n0,n0:],NAT:] is Relation-like RAT -valued INT -valued V59() V60() V61() V62() set
bool [:[:n0,n0:],NAT:] is non empty set
fp is finite Element of bool n0
(n0,EU9,fp) is Relation-like n0 -defined fp -defined n0 -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (n0,EU9,fp) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
f1 is finite Element of bool n0
[:fp,f1:] is Relation-like n0 -defined n0 -valued finite Element of bool [:n0,n0:]
bool [:n0,n0:] is non empty set
([:n0,n0:],(multnat * [:EU9,X:]),[:fp,f1:]) is Relation-like [:n0,n0:] -defined [:fp,f1:] -defined [:n0,n0:] -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum ([:n0,n0:],(multnat * [:EU9,X:]),[:fp,f1:]) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(n0,X,f1) is Relation-like n0 -defined f1 -defined n0 -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (n0,X,f1) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(Sum (n0,EU9,fp)) * (Sum (n0,X,f1)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
k is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
k + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 is set
[:f29,NAT:] is Relation-like RAT -valued INT -valued V59() V60() V61() V62() set
bool [:f29,NAT:] is non empty set
bool f29 is non empty set
[:f29,f29:] is Relation-like set
f19 is Relation-like f29 -defined NAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:f29,NAT:]
x is Relation-like f29 -defined NAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:f29,NAT:]
[:f19,x:] is Relation-like [:f29,f29:] -defined [:NAT,NAT:] -valued Function-like total quasi_total Element of bool [:[:f29,f29:],[:NAT,NAT:]:]
[:[:f29,f29:],[:NAT,NAT:]:] is Relation-like set
bool [:[:f29,f29:],[:NAT,NAT:]:] is non empty set
multnat * [:f19,x:] is Relation-like [:f29,f29:] -defined NAT -valued RAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:[:f29,f29:],NAT:]
[:[:f29,f29:],NAT:] is Relation-like RAT -valued INT -valued V59() V60() V61() V62() set
bool [:[:f29,f29:],NAT:] is non empty set
i is finite Element of bool f29
card i is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
h is finite Element of bool f29
[:i,h:] is Relation-like f29 -defined f29 -valued finite Element of bool [:f29,f29:]
bool [:f29,f29:] is non empty set
([:f29,f29:],(multnat * [:f19,x:]),[:i,h:]) is Relation-like [:f29,f29:] -defined [:i,h:] -defined [:f29,f29:] -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum ([:f29,f29:],(multnat * [:f19,x:]),[:i,h:]) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(f29,f19,i) is Relation-like f29 -defined i -defined f29 -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (f29,f19,i) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(f29,x,h) is Relation-like f29 -defined h -defined f29 -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (f29,x,h) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(Sum (f29,f19,i)) * (Sum (f29,x,h)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EmptyBag {} is Relation-like non-empty empty-yielding {} -defined RAT -valued ordinal natural empty trivial V16() V17() integer Function-like one-to-one constant functional total ext-real non positive non negative finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V59() V60() V61() V62() V63() V64() V65() V66() V69() V70() V71() V72() V73() V74() V75() Function-yielding FinSequence-yielding finite-support Element of Bags {}
Bags {} is non empty set
Bags {} is non empty functional Element of bool (Bags {})
bool (Bags {}) is non empty V48() set
{} --> 0 is Relation-like non-empty empty-yielding {} -defined NAT -valued RAT -valued INT -valued ordinal T-Sequence-like natural empty trivial non proper V16() V17() integer Function-like one-to-one constant functional total quasi_total ext-real non positive non negative finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V59() V60() V61() V62() V63() V64() V65() V66() V69() V70() V71() V72() V73() V74() V75() Function-yielding FinSequence-yielding finite-support Element of bool [:{},NAT:]
[:{},NAT:] is Relation-like non-empty empty-yielding NAT -defined RAT -valued INT -valued ordinal natural empty trivial V16() V17() integer Function-like one-to-one constant functional ext-real non positive non negative finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered V59() V60() V61() V62() V63() V64() V65() V66() V69() V70() V71() V72() V73() V74() V75() Function-yielding FinSequence-yielding finite-support set
bool [:{},NAT:] is non empty finite V40() set
the set is set
{ the set } is non empty trivial finite 1 -element set
card { the set } is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
x2 is set
{x2} is non empty trivial finite 1 -element set
f19 . x2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(f19 . x2) * (Sum (f29,x,h)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Y is set
{Y} is non empty trivial finite 1 -element set
i \ {Y} is finite Element of bool f29
x29 is finite Element of bool f29
(i \ {Y}) \/ x29 is finite Element of bool f29
i \/ {Y} is non empty finite set
(f29,f19,(i \ {Y})) is Relation-like f29 -defined i \ {Y} -defined f29 -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (f29,f19,(i \ {Y})) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(f29,f19,x29) is Relation-like f29 -defined x29 -defined f29 -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (f29,f19,x29) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(Sum (f29,f19,(i \ {Y}))) + (Sum (f29,f19,x29)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
card x29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
0 + k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
- 1 is non empty V16() V17() integer V32() ext-real non positive negative Element of INT
(- 1) + k is V16() V17() integer V32() ext-real Element of INT
[:x29,h:] is Relation-like f29 -defined f29 -valued finite Element of bool [:f29,f29:]
([:f29,f29:],(multnat * [:f19,x:]),[:x29,h:]) is Relation-like [:f29,f29:] -defined [:x29,h:] -defined [:f29,f29:] -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum ([:f29,f29:],(multnat * [:f19,x:]),[:x29,h:]) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(Sum (f29,f19,x29)) * (Sum (f29,x,h)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[:(i \ {Y}),h:] is Relation-like f29 -defined f29 -valued finite Element of bool [:f29,f29:]
card ((i \ {Y}) \/ x29) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
card (i \ {Y}) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
(card (i \ {Y})) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[:(i \ {Y}),h:] \/ [:x29,h:] is Relation-like f29 -defined f29 -valued finite Element of bool [:f29,f29:]
([:f29,f29:],(multnat * [:f19,x:]),[:(i \ {Y}),h:]) is Relation-like [:f29,f29:] -defined [:(i \ {Y}),h:] -defined [:f29,f29:] -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum ([:f29,f29:],(multnat * [:f19,x:]),[:(i \ {Y}),h:]) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(Sum ([:f29,f29:],(multnat * [:f19,x:]),[:(i \ {Y}),h:])) + (Sum ([:f29,f29:],(multnat * [:f19,x:]),[:x29,h:])) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(Sum (f29,f19,(i \ {Y}))) * (Sum (f29,x,h)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((Sum (f29,f19,(i \ {Y}))) * (Sum (f29,x,h))) + ((Sum (f29,f19,x29)) * (Sum (f29,x,h))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
card fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
k is set
[:k,NAT:] is Relation-like RAT -valued INT -valued V59() V60() V61() V62() set
bool [:k,NAT:] is non empty set
bool k is non empty set
x is finite Element of bool k
card x is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
i is finite Element of bool k
[:x,i:] is Relation-like k -defined k -valued finite Element of bool [:k,k:]
[:k,k:] is Relation-like set
bool [:k,k:] is non empty set
f29 is Relation-like k -defined NAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:k,NAT:]
f19 is Relation-like k -defined NAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:k,NAT:]
[:f29,f19:] is Relation-like [:k,k:] -defined [:NAT,NAT:] -valued Function-like total quasi_total Element of bool [:[:k,k:],[:NAT,NAT:]:]
[:[:k,k:],[:NAT,NAT:]:] is Relation-like set
bool [:[:k,k:],[:NAT,NAT:]:] is non empty set
multnat * [:f29,f19:] is Relation-like [:k,k:] -defined NAT -valued RAT -valued Function-like total quasi_total V59() V60() V61() V62() Element of bool [:[:k,k:],NAT:]
[:[:k,k:],NAT:] is Relation-like RAT -valued INT -valued V59() V60() V61() V62() set
bool [:[:k,k:],NAT:] is non empty set
([:k,k:],(multnat * [:f29,f19:]),[:x,i:]) is Relation-like [:x,i:] -defined [:k,k:] -defined [:x,i:] -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum ([:k,k:],(multnat * [:f29,f19:]),[:x,i:]) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(k,f29,x) is Relation-like k -defined x -defined k -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (k,f29,x) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(k,f19,i) is Relation-like k -defined i -defined k -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (k,f19,i) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(Sum (k,f29,x)) * (Sum (k,f19,i)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
X is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
fp is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
X . fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp |^ n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 |-> fp is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (n0 |-> fp) is V16() V17() ext-real set
f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
X . f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 |^ EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 |-> f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (EU9 |-> f1) is V16() V17() ext-real set
fp is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
X . fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp |^ n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 |-> fp is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (n0 |-> fp) is V16() V17() ext-real set
EU9 is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
X is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
fp is set
EU9 . fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
X . fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 . f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 |^ n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 |-> f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (n0 |-> f1) is V16() V17() ext-real set
X . f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(n0) is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
NatDivisors f1 is finite V47() V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides f1 ) } is set
(NAT,(n0),(NatDivisors f1)) is Relation-like NAT -defined NatDivisors f1 -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(n0),(NatDivisors f1)) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
X is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
NatDivisors X is finite V47() V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides X ) } is set
(NAT,(n0),(NatDivisors X)) is Relation-like NAT -defined NatDivisors X -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(n0),(NatDivisors X)) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
NatDivisors f1 is finite V47() V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides f1 ) } is set
(NAT,(n0),(NatDivisors f1)) is Relation-like NAT -defined NatDivisors f1 -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(n0),(NatDivisors f1)) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
X is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 . X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0,X) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 . fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
X is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
fp is set
EU9 . fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
X . fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(n0,f1) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(1,n0) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(n0,1) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0) is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
(NAT,(n0),(NatDivisors 1)) is Relation-like NAT -defined NatDivisors 1 -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(n0),(NatDivisors 1)) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
support (NAT,(n0),(NatDivisors 1)) is finite set
canFS (support (NAT,(n0),(NatDivisors 1))) is Relation-like NAT -defined support (NAT,(n0),(NatDivisors 1)) -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like finite-support FinSequence of support (NAT,(n0),(NatDivisors 1))
(canFS (support (NAT,(n0),(NatDivisors 1)))) * (NAT,(n0),(NatDivisors 1)) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite V59() V60() V61() V62() finite-support set
X is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
Sum X is V16() V17() ext-real Element of REAL
dom (n0) is non empty V69() V70() V71() V72() V73() V74() Element of bool NAT
dom (NAT,(n0),(NatDivisors 1)) is finite V69() V70() V71() V72() V73() V74() Element of bool (NatDivisors 1)
bool (NatDivisors 1) is non empty finite V40() set
(NAT,(n0),(NatDivisors 1)) . 1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0) . 1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 |^ n0 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal Element of REAL
n0 |-> 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (n0 |-> 1) is V16() V17() ext-real set
fp is set
<*1*> is Relation-like NAT -defined NAT -valued non empty trivial Function-like one-to-one constant finite 1 -element FinSequence-like FinSubsequence-like V59() V60() V61() V62() V63() V64() V65() V66() V97() finite-support Element of NAT *
NAT * is non empty functional FinSequence-membered FinSequenceSet of NAT
[1,1] is non empty set
{1,1} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
{1} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{{1,1},{1}} is non empty finite V40() set
{[1,1]} is Relation-like non empty trivial Function-like constant finite 1 -element finite-support set
<*1*> * (NAT,(n0),(NatDivisors 1)) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite V59() V60() V61() V62() finite-support set
<*((NAT,(n0),(NatDivisors 1)) . 1)*> is Relation-like NAT -defined NAT -valued non empty trivial Function-like one-to-one constant finite 1 -element FinSequence-like FinSubsequence-like V59() V60() V61() V62() V63() V64() V65() V66() V97() finite-support Element of NAT *
[1,((NAT,(n0),(NatDivisors 1)) . 1)] is non empty set
{1,((NAT,(n0),(NatDivisors 1)) . 1)} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
{{1,((NAT,(n0),(NatDivisors 1)) . 1)},{1}} is non empty finite V40() set
{[1,((NAT,(n0),(NatDivisors 1)) . 1)]} is Relation-like non empty trivial Function-like constant finite 1 -element finite-support set
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 - 1 is V16() V17() integer V32() ext-real Element of INT
EU9 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 |^ EU9 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 |-> n0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (EU9 |-> n0) is V16() V17() ext-real set
((n0 |^ EU9)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1,(n0 |^ EU9)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 |^ (EU9 + 1) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(EU9 + 1) |-> n0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product ((EU9 + 1) |-> n0) is V16() V17() ext-real set
(n0 |^ (EU9 + 1)) - 1 is V16() V17() integer V32() ext-real Element of INT
((n0 |^ (EU9 + 1)) - 1) / (n0 - 1) is V16() V17() V32() ext-real Element of RAT
X is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
X + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(X + 1) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
fp |^ (X + 1) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(X + 1) |-> fp is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product ((X + 1) |-> fp) is V16() V17() ext-real set
((fp |^ (X + 1))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1,(fp |^ (X + 1))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp |^ ((X + 1) + 1) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
((X + 1) + 1) |-> fp is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (((X + 1) + 1) |-> fp) is V16() V17() ext-real set
(fp |^ ((X + 1) + 1)) - 1 is V16() V17() integer V32() ext-real Element of INT
fp - 1 is V16() V17() integer V32() ext-real Element of INT
((fp |^ ((X + 1) + 1)) - 1) / (fp - 1) is V16() V17() V32() ext-real Element of RAT
fp |^ X is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
X |-> fp is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (X |-> fp) is V16() V17() ext-real set
NatDivisors (fp |^ X) is V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides fp |^ X ) } is set
f29 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
(1) is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
(NAT,(1),f29) is Relation-like NAT -defined f29 -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(1),f29) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
f19 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
(1,f19) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((fp |^ X)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1,(fp |^ X)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(fp |^ (X + 1)) - 1 is V16() V17() integer V32() ext-real Element of INT
((fp |^ (X + 1)) - 1) / (fp - 1) is V16() V17() V32() ext-real Element of RAT
k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
k |^ f1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 |-> k is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (f1 |-> k) is V16() V17() ext-real set
{(fp |^ (X + 1))} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
1 - 1 is V16() V17() integer V32() ext-real Element of INT
i is set
x is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
f29 /\ x is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
{ (fp |^ b₁) where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : b₁ <= X } is set
h is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp |^ h is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
h |-> fp is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (h |-> fp) is V16() V17() ext-real set
fp |-count (fp |^ (X + 1)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(X + 1) - X is V16() V17() integer V32() ext-real Element of INT
X - X is V16() V17() integer V32() ext-real Element of INT
(1) . (fp |^ (X + 1)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(fp |^ (X + 1)) |^ 1 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
1 |-> (fp |^ (X + 1)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (1 |-> (fp |^ (X + 1))) is V16() V17() ext-real set
(X + 1) * 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp |^ ((X + 1) * 1) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
((X + 1) * 1) |-> fp is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (((X + 1) * 1) |-> fp) is V16() V17() ext-real set
NatDivisors (fp |^ (X + 1)) is V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides fp |^ (X + 1) ) } is set
(NatDivisors (fp |^ X)) \/ {(fp |^ (X + 1))} is non empty V69() V70() V71() V72() V73() V74() set
h is set
{ (fp |^ b₁) where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : b₁ <= X + 1 } is set
Y is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp |^ Y is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
Y |-> fp is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (Y |-> fp) is V16() V17() ext-real set
Y is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp |^ Y is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
Y |-> fp is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (Y |-> fp) is V16() V17() ext-real set
0 + X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 + X is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp |^ f1 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
f1 |-> fp is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (f1 |-> fp) is V16() V17() ext-real set
i is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
(1,i) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 \/ x is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
(NAT,(1),(f29 \/ x)) is Relation-like NAT -defined f29 \/ x -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(1),(f29 \/ x)) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(NAT,(1),x) is Relation-like NAT -defined x -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(1),x) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(Sum (NAT,(1),f29)) + (Sum (NAT,(1),x)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(Sum (NAT,(1),f29)) + ((1) . (fp |^ (X + 1))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(fp |^ (X + 1)) * (fp - 1) is V16() V17() integer V32() ext-real Element of INT
((fp |^ (X + 1)) * (fp - 1)) / (fp - 1) is V16() V17() V32() ext-real Element of RAT
(((fp |^ (X + 1)) - 1) / (fp - 1)) + (((fp |^ (X + 1)) * (fp - 1)) / (fp - 1)) is V16() V17() V32() ext-real Element of RAT
((fp |^ (X + 1)) - 1) + ((fp |^ (X + 1)) * (fp - 1)) is V16() V17() integer V32() ext-real Element of INT
(((fp |^ (X + 1)) - 1) + ((fp |^ (X + 1)) * (fp - 1))) / (fp - 1) is V16() V17() V32() ext-real Element of RAT
(fp |^ (X + 1)) * fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((fp |^ (X + 1)) * fp) - 1 is V16() V17() integer V32() ext-real Element of INT
(((fp |^ (X + 1)) * fp) - 1) / (fp - 1) is V16() V17() V32() ext-real Element of RAT
0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
X is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
X |^ 0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
0 |-> X is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (0 |-> X) is V16() V17() ext-real set
((X |^ 0)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1,(X |^ 0)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
X |^ (0 + 1) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(0 + 1) |-> X is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product ((0 + 1) |-> X) is V16() V17() ext-real set
(X |^ (0 + 1)) - 1 is V16() V17() integer V32() ext-real Element of INT
X - 1 is V16() V17() integer V32() ext-real Element of INT
((X |^ (0 + 1)) - 1) / (X - 1) is V16() V17() V32() ext-real Element of RAT
1 - 1 is V16() V17() integer V32() ext-real Element of INT
(1) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1,1) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(X - 1) / (X - 1) is V16() V17() V32() ext-real Element of RAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
1 + n0 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
(1 + n0) + EU9 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(EU9) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1,EU9) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
{n0,EU9} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
f1 is set
X is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
{1} /\ X is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
{EU9} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{n0} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{1,n0,EU9} is non empty finite V69() V70() V71() V72() V73() V74() set
NatDivisors EU9 is finite V47() V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides EU9 ) } is set
f29 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
(NatDivisors EU9) \ f29 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
(1) is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
(NAT,(1),f29) is Relation-like NAT -defined f29 -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(1),f29) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
0 + (Sum (NAT,(1),f29)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(NAT,(1),((NatDivisors EU9) \ f29)) is Relation-like NAT -defined (NatDivisors EU9) \ f29 -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(1),((NatDivisors EU9) \ f29)) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(Sum (NAT,(1),((NatDivisors EU9) \ f29))) + (Sum (NAT,(1),f29)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x is set
i is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f29 \/ ((NatDivisors EU9) \ f29) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
(NAT,(1),(f29 \/ ((NatDivisors EU9) \ f29))) is Relation-like NAT -defined f29 \/ ((NatDivisors EU9) \ f29) -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(1),(f29 \/ ((NatDivisors EU9) \ f29))) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(Sum (NAT,(1),f29)) + (Sum (NAT,(1),((NatDivisors EU9) \ f29))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x is set
k is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
f1 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
k /\ f1 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
k \/ f1 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
{1} \/ X is non empty finite V69() V70() V71() V72() V73() V74() Element of bool NAT
(NAT,(1),{1}) is Relation-like NAT -defined {1} -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(1),{1}) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(NAT,(1),X) is Relation-like NAT -defined X -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(1),X) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(Sum (NAT,(1),{1})) + (Sum (NAT,(1),X)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1) . 1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1) . 1) + (Sum (NAT,(1),X)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(NAT,(1),k) is Relation-like NAT -defined k -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(1),k) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(NAT,(1),f1) is Relation-like NAT -defined f1 -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(1),f1) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(Sum (NAT,(1),k)) + (Sum (NAT,(1),f1)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1) . 1) + ((Sum (NAT,(1),k)) + (Sum (NAT,(1),f1))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1) . n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1) . n0) + (Sum (NAT,(1),f1)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1) . 1) + (((1) . n0) + (Sum (NAT,(1),f1))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1) . 1) + ((1) . n0) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((1) . 1) + ((1) . n0)) + (Sum (NAT,(1),f1)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1) . EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((1) . 1) + ((1) . n0)) + ((1) . EU9) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 |^ 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 |-> 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (1 |-> 1) is V16() V17() ext-real set
(1 |^ 1) + ((1) . n0) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1 |^ 1) + ((1) . n0)) + ((1) . EU9) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 |^ 1 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
1 |-> n0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (1 |-> n0) is V16() V17() ext-real set
(1 |^ 1) + (n0 |^ 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1 |^ 1) + (n0 |^ 1)) + ((1) . EU9) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 |^ 1 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
1 |-> EU9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (1 |-> EU9) is V16() V17() ext-real set
((1 |^ 1) + (n0 |^ 1)) + (EU9 |^ 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 + (n0 |^ 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1 + (n0 |^ 1)) + (EU9 |^ 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1 + n0) + (EU9 |^ 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
1 + n0 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(1 + n0) + EU9 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
X is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
((1 + n0) + EU9) + X is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(X) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1,X) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
{n0,EU9,X} is non empty finite V69() V70() V71() V72() V73() V74() set
k is set
fp is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
{1} /\ fp is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
{n0} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{X} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{EU9} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{n0,EU9} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
{1,n0,EU9,X} is non empty finite set
NatDivisors X is finite V47() V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides X ) } is set
i is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
(NatDivisors X) \ i is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
(1) is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
(NAT,(1),i) is Relation-like NAT -defined i -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(1),i) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
0 + (Sum (NAT,(1),i)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(NAT,(1),((NatDivisors X) \ i)) is Relation-like NAT -defined (NatDivisors X) \ i -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(1),((NatDivisors X) \ i)) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(Sum (NAT,(1),((NatDivisors X) \ i))) + (Sum (NAT,(1),i)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Y is set
k is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
f19 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
k /\ f19 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
x is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
k \/ f19 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Y is set
x2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
i \/ ((NatDivisors X) \ i) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
(NAT,(1),(i \/ ((NatDivisors X) \ i))) is Relation-like NAT -defined i \/ ((NatDivisors X) \ i) -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(1),(i \/ ((NatDivisors X) \ i))) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(Sum (NAT,(1),i)) + (Sum (NAT,(1),((NatDivisors X) \ i))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Y is set
f29 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
x /\ f29 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
x \/ f29 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
{1} \/ fp is non empty finite V69() V70() V71() V72() V73() V74() Element of bool NAT
(NAT,(1),{1}) is Relation-like NAT -defined {1} -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(1),{1}) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(NAT,(1),fp) is Relation-like NAT -defined fp -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(1),fp) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(Sum (NAT,(1),{1})) + (Sum (NAT,(1),fp)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1) . 1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1) . 1) + (Sum (NAT,(1),fp)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(NAT,(1),x) is Relation-like NAT -defined x -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(1),x) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(NAT,(1),f29) is Relation-like NAT -defined f29 -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(1),f29) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(Sum (NAT,(1),x)) + (Sum (NAT,(1),f29)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1) . 1) + ((Sum (NAT,(1),x)) + (Sum (NAT,(1),f29))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(NAT,(1),k) is Relation-like NAT -defined k -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(1),k) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(NAT,(1),f19) is Relation-like NAT -defined f19 -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(1),f19) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(Sum (NAT,(1),k)) + (Sum (NAT,(1),f19)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((Sum (NAT,(1),k)) + (Sum (NAT,(1),f19))) + (Sum (NAT,(1),f29)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1) . 1) + (((Sum (NAT,(1),k)) + (Sum (NAT,(1),f19))) + (Sum (NAT,(1),f29))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1) . n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1) . n0) + (Sum (NAT,(1),f19)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((1) . n0) + (Sum (NAT,(1),f19))) + (Sum (NAT,(1),f29)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1) . 1) + ((((1) . n0) + (Sum (NAT,(1),f19))) + (Sum (NAT,(1),f29))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1) . 1) + ((1) . n0) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(Sum (NAT,(1),f19)) + (Sum (NAT,(1),f29)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((1) . 1) + ((1) . n0)) + ((Sum (NAT,(1),f19)) + (Sum (NAT,(1),f29))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1) . EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1) . EU9) + (Sum (NAT,(1),f29)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((1) . 1) + ((1) . n0)) + (((1) . EU9) + (Sum (NAT,(1),f29))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((1) . 1) + ((1) . n0)) + ((1) . EU9) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((((1) . 1) + ((1) . n0)) + ((1) . EU9)) + (Sum (NAT,(1),f29)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1) . X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((((1) . 1) + ((1) . n0)) + ((1) . EU9)) + ((1) . X) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 |^ 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 |-> 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (1 |-> 1) is V16() V17() ext-real set
(1 |^ 1) + ((1) . n0) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1 |^ 1) + ((1) . n0)) + ((1) . EU9) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((1 |^ 1) + ((1) . n0)) + ((1) . EU9)) + ((1) . X) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 |^ 1 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
1 |-> n0 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (1 |-> n0) is V16() V17() ext-real set
(1 |^ 1) + (n0 |^ 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1 |^ 1) + (n0 |^ 1)) + ((1) . EU9) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((1 |^ 1) + (n0 |^ 1)) + ((1) . EU9)) + ((1) . X) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 |^ 1 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
1 |-> EU9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (1 |-> EU9) is V16() V17() ext-real set
((1 |^ 1) + (n0 |^ 1)) + (EU9 |^ 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((1 |^ 1) + (n0 |^ 1)) + (EU9 |^ 1)) + ((1) . X) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
X |^ 1 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
1 |-> X is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (1 |-> X) is V16() V17() ext-real set
(((1 |^ 1) + (n0 |^ 1)) + (EU9 |^ 1)) + (X |^ 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 + (n0 |^ 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1 + (n0 |^ 1)) + (EU9 |^ 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1 + (n0 |^ 1)) + (EU9 |^ 1)) + (X |^ 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1 + n0) + (EU9 |^ 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1 + n0) + (EU9 |^ 1)) + (X |^ 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1 + n0) + EU9) + (X |^ 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
(EU9) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1,EU9) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 + n0 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 + n0 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
X is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 * X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 + n0 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1 + n0) + EU9 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 + EU9 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1 + n0) + EU9) - (n0 + EU9) is V16() V17() integer V32() ext-real Element of INT
(EU9 + n0) - (n0 + EU9) is V16() V17() integer V32() ext-real Element of INT
1 + n0 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1 + n0) + X is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1 + n0) + X) + EU9 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 + EU9 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((1 + n0) + X) + EU9) - (n0 + EU9) is V16() V17() integer V32() ext-real Element of INT
(EU9 + n0) - (n0 + EU9) is V16() V17() integer V32() ext-real Element of INT
1 + X is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 / EU9 is non empty V16() V17() ext-real positive non negative Element of REAL
fp is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
1 + fp is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1 + fp) + EU9 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 + EU9 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1 + fp) + EU9) - (1 + EU9) is V16() V17() integer V32() ext-real Element of INT
(EU9 + 1) - (1 + EU9) is V16() V17() integer V32() ext-real Element of INT
n0 is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
EU9 is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
X is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
fp is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
X * fp is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 . (X * fp) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 . X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 . fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(EU9 . X) * (EU9 . fp) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
NatDivisors (X * fp) is finite V47() V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides X * fp ) } is set
(NAT,n0,(NatDivisors (X * fp))) is Relation-like NAT -defined NatDivisors (X * fp) -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
[:n0,n0:] is Relation-like [:NAT,NAT:] -defined [:NAT,NAT:] -valued non empty Function-like total quasi_total Element of bool [:[:NAT,NAT:],[:NAT,NAT:]:]
[:[:NAT,NAT:],[:NAT,NAT:]:] is Relation-like non empty non trivial non finite set
bool [:[:NAT,NAT:],[:NAT,NAT:]:] is non empty non trivial non finite V48() set
multnat * [:n0,n0:] is Relation-like [:NAT,NAT:] -defined NAT -valued RAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:[:NAT,NAT:],NAT:]
NatDivisors X is finite V47() V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides X ) } is set
NatDivisors fp is finite V47() V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides fp ) } is set
[:(NatDivisors X),(NatDivisors fp):] is Relation-like NAT -defined NAT -valued RAT -valued INT -valued finite V59() V60() V61() V62() Element of bool [:NAT,NAT:]
([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]) is Relation-like [:NAT,NAT:] -defined [:(NatDivisors X),(NatDivisors fp):] -defined [:NAT,NAT:] -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,n0,(NatDivisors (X * fp))) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
support (NAT,n0,(NatDivisors (X * fp))) is finite set
canFS (support (NAT,n0,(NatDivisors (X * fp)))) is Relation-like NAT -defined support (NAT,n0,(NatDivisors (X * fp))) -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like finite-support FinSequence of support (NAT,n0,(NatDivisors (X * fp)))
(canFS (support (NAT,n0,(NatDivisors (X * fp))))) * (NAT,n0,(NatDivisors (X * fp))) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite V59() V60() V61() V62() finite-support set
f29 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
Sum f29 is V16() V17() ext-real Element of REAL
([:NAT,NAT:],multnat,[:(NatDivisors X),(NatDivisors fp):]) is Relation-like [:NAT,NAT:] -defined [:(NatDivisors X),(NatDivisors fp):] -defined [:NAT,NAT:] -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]) is finite set
canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):])) is Relation-like NAT -defined support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]) -valued Function-like one-to-one onto bijective finite FinSequence-like FinSubsequence-like finite-support FinSequence of support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):])
Sum ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) * ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite V59() V60() V61() V62() finite-support set
h is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
Sum h is V16() V17() ext-real Element of REAL
dom multnat is Relation-like NAT -defined NAT -valued RAT -valued non empty V59() V60() V61() V62() Element of bool [:NAT,NAT:]
[:NAT,NAT:] is Relation-like REAL -defined REAL -valued RAT -valued INT -valued non empty non trivial non finite V59() V60() V61() V62() Element of bool [:REAL,REAL:]
dom ([:NAT,NAT:],multnat,[:(NatDivisors X),(NatDivisors fp):]) is Relation-like NAT -defined NAT -valued finite V59() V60() V61() V62() Element of bool [:(NatDivisors X),(NatDivisors fp):]
bool [:(NatDivisors X),(NatDivisors fp):] is non empty finite V40() set
Y is set
x2 is set
([:NAT,NAT:],multnat,[:(NatDivisors X),(NatDivisors fp):]) . Y is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
([:NAT,NAT:],multnat,[:(NatDivisors X),(NatDivisors fp):]) . x2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x19 is set
x29 is set
[x19,x29] is non empty set
{x19,x29} is non empty finite set
{x19} is non empty trivial finite 1 -element set
{{x19,x29},{x19}} is non empty finite V40() set
multnat . Y is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
l is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
multnat . (x,l) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x * l is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
m19 is set
n1 is set
[m19,n1] is non empty set
{m19,n1} is non empty finite set
{m19} is non empty trivial finite 1 -element set
{{m19,n1},{m19}} is non empty finite V40() set
multnat . x2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
m1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
multnat . (m1,x) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
m1 * x is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Y is Relation-like Function-like one-to-one set
(canFS (support (NAT,n0,(NatDivisors (X * fp))))) " is Relation-like Function-like one-to-one set
Y * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) ") is Relation-like Function-like one-to-one set
(canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) * (Y * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) ")) is Relation-like NAT -defined Function-like one-to-one finite finite-support set
dom ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]) is Relation-like NAT -defined NAT -valued finite V59() V60() V61() V62() Element of bool [:(NatDivisors X),(NatDivisors fp):]
dom (multnat * [:n0,n0:]) is Relation-like NAT -defined NAT -valued RAT -valued non empty V59() V60() V61() V62() Element of bool [:NAT,NAT:]
dom [:n0,n0:] is Relation-like NAT -defined NAT -valued RAT -valued non empty V59() V60() V61() V62() Element of bool [:NAT,NAT:]
dom (Y * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) ")) is set
x19 is set
rng (canFS (support (NAT,n0,(NatDivisors (X * fp))))) is finite Element of bool (support (NAT,n0,(NatDivisors (X * fp))))
bool (support (NAT,n0,(NatDivisors (X * fp)))) is non empty finite V40() set
([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]) . x19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x29 is set
x is set
[x29,x] is non empty set
{x29,x} is non empty finite set
{x29} is non empty trivial finite 1 -element set
{{x29,x},{x29}} is non empty finite V40() set
l is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
m19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
l * m19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((canFS (support (NAT,n0,(NatDivisors (X * fp))))) ") . (l * m19) is set
n0 . l is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 . m19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(multnat * [:n0,n0:]) . x19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[:n0,n0:] . x19 is set
multnat . ([:n0,n0:] . x19) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[:n0,n0:] . (l,m19) is Element of [:NAT,NAT:]
multnat . ([:n0,n0:] . (l,m19)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[(n0 . l),(n0 . m19)] is non empty Element of [:NAT,NAT:]
{(n0 . l),(n0 . m19)} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
{(n0 . l)} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{{(n0 . l),(n0 . m19)},{(n0 . l)}} is non empty finite V40() set
multnat . [(n0 . l),(n0 . m19)] is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
multnat . ((n0 . l),(n0 . m19)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 . l) * (n0 . m19) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n1 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
m1 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
n1 * m1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 . (n1 * m1) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(NAT,n0,(NatDivisors (X * fp))) . (l * m19) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
dom ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) ") is set
rng ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) ") is set
dom (canFS (support (NAT,n0,(NatDivisors (X * fp))))) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
(canFS (support (NAT,n0,(NatDivisors (X * fp))))) . (((canFS (support (NAT,n0,(NatDivisors (X * fp))))) ") . (l * m19)) is set
multnat . (l,m19) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[l,m19] is non empty Element of [:NAT,NAT:]
{l,m19} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
{l} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{{l,m19},{l}} is non empty finite V40() set
multnat . [l,m19] is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Y . x19 is set
rng (canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) is finite Element of bool (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))
bool (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):])) is non empty finite V40() set
dom ((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) * (Y * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) "))) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
dom (canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
dom h is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
x19 is set
h . x19 is V16() V17() ext-real set
((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) * (Y * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) "))) . x19 is set
f29 . (((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) * (Y * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) "))) . x19) is V16() V17() ext-real set
(canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) . x19 is set
(Y * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) ")) * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) * (NAT,n0,(NatDivisors (X * fp)))) is Relation-like NAT -valued RAT -valued Function-like V59() V60() V61() V62() set
((canFS (support (NAT,n0,(NatDivisors (X * fp))))) ") * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) * (NAT,n0,(NatDivisors (X * fp)))) is Relation-like NAT -valued RAT -valued Function-like V59() V60() V61() V62() set
Y * (((canFS (support (NAT,n0,(NatDivisors (X * fp))))) ") * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) * (NAT,n0,(NatDivisors (X * fp))))) is Relation-like NAT -valued RAT -valued Function-like V59() V60() V61() V62() set
((canFS (support (NAT,n0,(NatDivisors (X * fp))))) ") * (canFS (support (NAT,n0,(NatDivisors (X * fp))))) is Relation-like support (NAT,n0,(NatDivisors (X * fp))) -valued Function-like one-to-one set
(((canFS (support (NAT,n0,(NatDivisors (X * fp))))) ") * (canFS (support (NAT,n0,(NatDivisors (X * fp)))))) * (NAT,n0,(NatDivisors (X * fp))) is Relation-like NAT -valued RAT -valued Function-like V59() V60() V61() V62() set
Y * ((((canFS (support (NAT,n0,(NatDivisors (X * fp))))) ") * (canFS (support (NAT,n0,(NatDivisors (X * fp)))))) * (NAT,n0,(NatDivisors (X * fp)))) is Relation-like NAT -valued RAT -valued Function-like V59() V60() V61() V62() set
rng (canFS (support (NAT,n0,(NatDivisors (X * fp))))) is finite Element of bool (support (NAT,n0,(NatDivisors (X * fp))))
bool (support (NAT,n0,(NatDivisors (X * fp)))) is non empty finite V40() set
id (rng (canFS (support (NAT,n0,(NatDivisors (X * fp)))))) is Relation-like rng (canFS (support (NAT,n0,(NatDivisors (X * fp))))) -defined rng (canFS (support (NAT,n0,(NatDivisors (X * fp))))) -valued Function-like one-to-one total quasi_total finite finite-support Element of bool [:(rng (canFS (support (NAT,n0,(NatDivisors (X * fp)))))),(rng (canFS (support (NAT,n0,(NatDivisors (X * fp)))))):]
[:(rng (canFS (support (NAT,n0,(NatDivisors (X * fp)))))),(rng (canFS (support (NAT,n0,(NatDivisors (X * fp)))))):] is Relation-like finite set
bool [:(rng (canFS (support (NAT,n0,(NatDivisors (X * fp)))))),(rng (canFS (support (NAT,n0,(NatDivisors (X * fp)))))):] is non empty finite V40() set
(id (rng (canFS (support (NAT,n0,(NatDivisors (X * fp))))))) * (NAT,n0,(NatDivisors (X * fp))) is Relation-like rng (canFS (support (NAT,n0,(NatDivisors (X * fp))))) -defined NAT -valued RAT -valued Function-like finite V59() V60() V61() V62() finite-support set
Y * ((id (rng (canFS (support (NAT,n0,(NatDivisors (X * fp))))))) * (NAT,n0,(NatDivisors (X * fp)))) is Relation-like NAT -valued RAT -valued Function-like V59() V60() V61() V62() set
id (support (NAT,n0,(NatDivisors (X * fp)))) is Relation-like support (NAT,n0,(NatDivisors (X * fp))) -defined support (NAT,n0,(NatDivisors (X * fp))) -valued Function-like one-to-one total quasi_total finite finite-support Element of bool [:(support (NAT,n0,(NatDivisors (X * fp)))),(support (NAT,n0,(NatDivisors (X * fp)))):]
[:(support (NAT,n0,(NatDivisors (X * fp)))),(support (NAT,n0,(NatDivisors (X * fp)))):] is Relation-like finite set
bool [:(support (NAT,n0,(NatDivisors (X * fp)))),(support (NAT,n0,(NatDivisors (X * fp)))):] is non empty finite V40() set
(id (support (NAT,n0,(NatDivisors (X * fp))))) * (NAT,n0,(NatDivisors (X * fp))) is Relation-like support (NAT,n0,(NatDivisors (X * fp))) -defined NAT -valued RAT -valued Function-like finite V59() V60() V61() V62() finite-support set
Y * ((id (support (NAT,n0,(NatDivisors (X * fp))))) * (NAT,n0,(NatDivisors (X * fp)))) is Relation-like NAT -valued RAT -valued Function-like V59() V60() V61() V62() set
x is set
l is set
[x,l] is non empty set
{x,l} is non empty finite set
{x} is non empty trivial finite 1 -element set
{{x,l},{x}} is non empty finite V40() set
m19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 . m19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 . n1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]) . ((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) . x19) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(multnat * [:n0,n0:]) . ((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) . x19) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[:n0,n0:] . ((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) . x19) is set
multnat . ([:n0,n0:] . ((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) . x19)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[:n0,n0:] . (m19,n1) is Element of [:NAT,NAT:]
multnat . ([:n0,n0:] . (m19,n1)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[(n0 . m19),(n0 . n1)] is non empty Element of [:NAT,NAT:]
{(n0 . m19),(n0 . n1)} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
{(n0 . m19)} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{{(n0 . m19),(n0 . n1)},{(n0 . m19)}} is non empty finite V40() set
multnat . [(n0 . m19),(n0 . n1)] is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
multnat . ((n0 . m19),(n0 . n1)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 . m19) * (n0 . n1) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
m1 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
x is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
m1 * x is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 . (m1 * x) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
m19 * n1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(NAT,n0,(NatDivisors (X * fp))) . (m19 * n1) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
dom (id (support (NAT,n0,(NatDivisors (X * fp))))) is finite Element of bool (support (NAT,n0,(NatDivisors (X * fp))))
Y . ((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) . x19) is set
multnat . ((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) . x19) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
multnat . (m19,n1) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((canFS (support (NAT,n0,(NatDivisors (X * fp))))) * (NAT,n0,(NatDivisors (X * fp)))) . (((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) * (Y * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) "))) . x19) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) * (Y * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) "))) * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) * (NAT,n0,(NatDivisors (X * fp)))) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite V59() V60() V61() V62() finite-support set
(((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) * (Y * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) "))) * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) * (NAT,n0,(NatDivisors (X * fp))))) . x19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) * ((Y * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) ")) * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) * (NAT,n0,(NatDivisors (X * fp))))) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite V59() V60() V61() V62() finite-support set
((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) * ((Y * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) ")) * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) * (NAT,n0,(NatDivisors (X * fp)))))) . x19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((Y * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) ")) * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) * (NAT,n0,(NatDivisors (X * fp))))) . ((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) . x19) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(Y * ((id (support (NAT,n0,(NatDivisors (X * fp))))) * (NAT,n0,(NatDivisors (X * fp))))) . ((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) . x19) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((id (support (NAT,n0,(NatDivisors (X * fp))))) * (NAT,n0,(NatDivisors (X * fp)))) . (Y . ((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) . x19)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(id (support (NAT,n0,(NatDivisors (X * fp))))) . (m19 * n1) is set
(NAT,n0,(NatDivisors (X * fp))) . ((id (support (NAT,n0,(NatDivisors (X * fp))))) . (m19 * n1)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
dom n0 is non empty V69() V70() V71() V72() V73() V74() Element of bool NAT
dom (NAT,n0,(NatDivisors (X * fp))) is finite V69() V70() V71() V72() V73() V74() Element of bool (NatDivisors (X * fp))
bool (NatDivisors (X * fp)) is non empty finite V40() set
rng (canFS (support (NAT,n0,(NatDivisors (X * fp))))) is finite Element of bool (support (NAT,n0,(NatDivisors (X * fp))))
bool (support (NAT,n0,(NatDivisors (X * fp)))) is non empty finite V40() set
(canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) * Y is Relation-like NAT -defined Function-like one-to-one finite finite-support set
rng ((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) * Y) is finite set
x19 is set
x29 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
x is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
x29 * x is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
m1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(NAT,n0,(NatDivisors (X * fp))) . x19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[n1,m1] is non empty Element of [:NAT,NAT:]
{n1,m1} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
{n1} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{{n1,m1},{n1}} is non empty finite V40() set
(canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) " is Relation-like Function-like one-to-one set
((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) ") . [n1,m1] is set
n0 . x19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
l is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
n0 . l is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
m19 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
n0 . m19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 . l) * (n0 . m19) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 . n1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 . m1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
multnat . ((n0 . n1),(n0 . m1)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[(n0 . n1),(n0 . m1)] is non empty Element of [:NAT,NAT:]
{(n0 . n1),(n0 . m1)} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
{(n0 . n1)} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{{(n0 . n1),(n0 . m1)},{(n0 . n1)}} is non empty finite V40() set
multnat . [(n0 . n1),(n0 . m1)] is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[:n0,n0:] . (n1,m1) is Element of [:NAT,NAT:]
multnat . ([:n0,n0:] . (n1,m1)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
[:n0,n0:] . [n1,m1] is Element of [:NAT,NAT:]
multnat . ([:n0,n0:] . [n1,m1]) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(multnat * [:n0,n0:]) . [n1,m1] is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]) . [n1,m1] is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
dom ((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) ") is set
rng ((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) ") is set
multnat . (n1,m1) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
multnat . [n1,m1] is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
([:NAT,NAT:],multnat,[:(NatDivisors X),(NatDivisors fp):]) . [n1,m1] is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) . (((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) ") . [n1,m1]) is set
Y . ((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) . (((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) ") . [n1,m1])) is set
((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) * Y) . (((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) ") . [n1,m1]) is set
dom ((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) * Y) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
dom ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) ") is set
((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) * Y) * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) ") is Relation-like NAT -defined Function-like one-to-one finite finite-support set
rng (((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) * Y) * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) ")) is finite set
rng ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) ") is set
dom (canFS (support (NAT,n0,(NatDivisors (X * fp))))) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
dom ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) * (NAT,n0,(NatDivisors (X * fp)))) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
rng ((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) * (Y * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) "))) is finite set
dom f29 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
x19 is set
((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) * (Y * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) "))) . x19 is set
x29 is set
((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) * (Y * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) "))) . x29 is set
((canFS (support ([:NAT,NAT:],(multnat * [:n0,n0:]),[:(NatDivisors X),(NatDivisors fp):]))) * (Y * ((canFS (support (NAT,n0,(NatDivisors (X * fp))))) "))) * f29 is Relation-like NAT -defined REAL -valued Function-like finite V59() V60() V61() finite-support set
(NAT,n0,(NatDivisors X)) is Relation-like NAT -defined NatDivisors X -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,n0,(NatDivisors X)) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(NAT,n0,(NatDivisors fp)) is Relation-like NAT -defined NatDivisors fp -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,n0,(NatDivisors fp)) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(Sum (NAT,n0,(NatDivisors X))) * (Sum (NAT,n0,(NatDivisors fp))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(Sum (NAT,n0,(NatDivisors X))) * (EU9 . fp) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(n0) is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
EU9 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
X is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
EU9 * X is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0) . (EU9 * X) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0) . EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0) . X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((n0) . EU9) * ((n0) . X) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(EU9 * X) |^ n0 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal Element of REAL
n0 |-> (EU9 * X) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (n0 |-> (EU9 * X)) is V16() V17() ext-real set
EU9 |^ n0 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
n0 |-> EU9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (n0 |-> EU9) is V16() V17() ext-real set
X |^ n0 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
n0 |-> X is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (n0 |-> X) is V16() V17() ext-real set
(EU9 |^ n0) * (X |^ n0) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((n0) . EU9) * (X |^ n0) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(n0) is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
(n0) is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
EU9 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
(n0) . EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
NatDivisors EU9 is finite V47() V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides EU9 ) } is set
(NAT,(n0),(NatDivisors EU9)) is Relation-like NAT -defined NatDivisors EU9 -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(n0),(NatDivisors EU9)) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(n0,EU9) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
(n0) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1,n0) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
n0 * EU9 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((n0 * EU9)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1,(n0 * EU9)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(EU9) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1,EU9) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0) * (EU9) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1) is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
(1) . (n0 * EU9) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1) . n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1) . EU9 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((1) . n0) * ((1) . EU9) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1,n0) * ((1) . EU9) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
2 |^ n0 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal Element of REAL
n0 |-> 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (n0 |-> 2) is V16() V17() ext-real set
(2 |^ n0) -' 1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 -' 1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 |^ (n0 -' 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 -' 1) |-> 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product ((n0 -' 1) |-> 2) is V16() V17() ext-real set
(2 |^ (n0 -' 1)) * ((2 |^ n0) -' 1) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
n0 -' 2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(2 |^ n0) - 1 is V16() V17() integer V32() ext-real Element of INT
((2 |^ n0) - 1) |^ 2 is V16() V17() ext-real set
2 |-> ((2 |^ n0) - 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (2 |-> ((2 |^ n0) - 1)) is V16() V17() ext-real set
1 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((2 |^ n0) - 1) |^ (1 + 1) is V16() V17() ext-real set
(1 + 1) |-> ((2 |^ n0) - 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product ((1 + 1) |-> ((2 |^ n0) - 1)) is V16() V17() ext-real set
((2 |^ n0) - 1) |^ 1 is V16() V17() ext-real set
1 |-> ((2 |^ n0) - 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (1 |-> ((2 |^ n0) - 1)) is V16() V17() ext-real set
(((2 |^ n0) - 1) |^ 1) * ((2 |^ n0) - 1) is V16() V17() ext-real Element of REAL
((2 |^ n0) - 1) * ((2 |^ n0) - 1) is V16() V17() integer V32() ext-real Element of INT
((2 |^ n0) - 1) ^2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(2 |^ n0) ^2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 * (2 |^ n0) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() even Element of NAT
(2 * (2 |^ n0)) * 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() even Element of NAT
((2 |^ n0) ^2) - ((2 * (2 |^ n0)) * 1) is V16() V17() integer V32() ext-real Element of INT
1 ^2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((2 |^ n0) ^2) - ((2 * (2 |^ n0)) * 1)) + (1 ^2) is V16() V17() integer V32() ext-real Element of INT
(2 |^ n0) * (2 |^ n0) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((2 |^ n0) * (2 |^ n0)) - (2 * (2 |^ n0)) is V16() V17() integer V32() ext-real Element of INT
(((2 |^ n0) * (2 |^ n0)) - (2 * (2 |^ n0))) + (1 ^2) is V16() V17() integer V32() ext-real Element of INT
1 * 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((2 |^ n0) * (2 |^ n0)) - (2 * (2 |^ n0))) + (1 * 1) is V16() V17() integer V32() ext-real Element of INT
(2 |^ n0) - 2 is V16() V17() integer V32() ext-real Element of INT
(2 |^ n0) * ((2 |^ n0) - 2) is V16() V17() integer V32() ext-real Element of INT
((2 |^ n0) * ((2 |^ n0) - 2)) + 1 is V16() V17() integer V32() ext-real Element of INT
n0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 + 1) - 2 is V16() V17() integer V32() ext-real Element of INT
1 -' 1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 - 1 is V16() V17() integer V32() ext-real Element of INT
2 -' 1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 - 1 is V16() V17() integer V32() ext-real Element of INT
n0 - 1 is V16() V17() integer V32() ext-real Element of INT
1 - 1 is V16() V17() integer V32() ext-real Element of INT
2 - 2 is V16() V17() integer V32() ext-real Element of INT
n0 - 2 is V16() V17() integer V32() ext-real Element of INT
(n0 -' 2) + 2 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 -' 2) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
(EU9) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1,EU9) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((2 |^ (n0 -' 1))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1,(2 |^ (n0 -' 1))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(f1) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1,f1) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((2 |^ (n0 -' 1))) * (f1) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(n0 -' 1) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 |^ ((n0 -' 1) + 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((n0 -' 1) + 1) |-> 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (((n0 -' 1) + 1) |-> 2) is V16() V17() ext-real set
(2 |^ ((n0 -' 1) + 1)) - 1 is V16() V17() integer V32() ext-real Element of INT
2 - 1 is V16() V17() integer V32() ext-real Element of INT
((2 |^ ((n0 -' 1) + 1)) - 1) / (2 - 1) is V16() V17() V32() ext-real Element of RAT
(((2 |^ ((n0 -' 1) + 1)) - 1) / (2 - 1)) * (f1) is V16() V17() V32() ext-real Element of RAT
f1 |^ 1 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
1 |-> f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (1 |-> f1) is V16() V17() ext-real set
((f1 |^ 1)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1,(f1 |^ 1)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((f1 |^ 1)) * ((2 |^ n0) -' 1) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f1 |^ (1 + 1) is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
(1 + 1) |-> f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product ((1 + 1) |-> f1) is V16() V17() ext-real set
(f1 |^ (1 + 1)) - 1 is V16() V17() integer V32() ext-real Element of INT
f1 - 1 is V16() V17() integer V32() ext-real Element of INT
((f1 |^ (1 + 1)) - 1) / (f1 - 1) is V16() V17() V32() ext-real Element of RAT
(((f1 |^ (1 + 1)) - 1) / (f1 - 1)) * ((2 |^ n0) -' 1) is V16() V17() V32() ext-real Element of RAT
(2 |^ ((n0 -' 1) + 1)) * ((2 |^ n0) -' 1) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(2 |^ (n0 -' 1)) * 2 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() even Element of NAT
((2 |^ (n0 -' 1)) * 2) * ((2 |^ n0) -' 1) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() even Element of NAT
2 * EU9 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() even Element of NAT
n0 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
X is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
EU9 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
2 |^ EU9 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal Element of REAL
EU9 |-> 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (EU9 |-> 2) is V16() V17() ext-real set
(2 |^ EU9) * X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
EU9 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(EU9 + 1) - 1 is V16() V17() integer V32() ext-real Element of INT
(EU9 + 1) -' 1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 |^ (EU9 + 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(EU9 + 1) |-> 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product ((EU9 + 1) |-> 2) is V16() V17() ext-real set
(2 |^ (EU9 + 1)) - 1 is V16() V17() integer V32() ext-real Element of INT
((EU9 + 1) -' 1) + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 |^ (((EU9 + 1) -' 1) + 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(((EU9 + 1) -' 1) + 1) |-> 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product ((((EU9 + 1) -' 1) + 1) |-> 2) is V16() V17() ext-real set
(2 |^ (((EU9 + 1) -' 1) + 1)) - 2 is V16() V17() integer V32() ext-real Element of INT
((2 |^ (((EU9 + 1) -' 1) + 1)) - 2) + 1 is V16() V17() integer V32() ext-real Element of INT
2 |^ ((EU9 + 1) -' 1) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((EU9 + 1) -' 1) |-> 2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support set
Product (((EU9 + 1) -' 1) |-> 2) is V16() V17() ext-real set
(2 |^ ((EU9 + 1) -' 1)) * 2 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() even Element of NAT
((2 |^ ((EU9 + 1) -' 1)) * 2) - 2 is V16() V17() integer V32() ext-real Element of INT
(((2 |^ ((EU9 + 1) -' 1)) * 2) - 2) + 1 is V16() V17() integer V32() ext-real Element of INT
(2 |^ ((EU9 + 1) -' 1)) - 1 is V16() V17() integer V32() ext-real Element of INT
2 * ((2 |^ ((EU9 + 1) -' 1)) - 1) is V16() V17() integer V32() ext-real even Element of INT
(2 * ((2 |^ ((EU9 + 1) -' 1)) - 1)) + 1 is non empty V16() V17() integer V32() ext-real non even Element of INT
(n0) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1,n0) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
2 * n0 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() even Element of NAT
2 |^ (EU9 + 1) is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal Element of REAL
(2 |^ (EU9 + 1)) -' 1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(2 |^ ((EU9 + 1) -' 1)) * ((2 |^ (EU9 + 1)) -' 1) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(2 |^ (EU9 + 1)) -' 1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((2 |^ ((EU9 + 1) -' 1))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1,(2 |^ ((EU9 + 1) -' 1))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(2 |^ (((EU9 + 1) -' 1) + 1)) - 1 is V16() V17() integer V32() ext-real Element of INT
2 - 1 is V16() V17() integer V32() ext-real Element of INT
((2 |^ (((EU9 + 1) -' 1) + 1)) - 1) / (2 - 1) is V16() V17() V32() ext-real Element of RAT
(X) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1,X) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((2 |^ (EU9 + 1)) - 1) * (X) is V16() V17() integer V32() ext-real Element of INT
2 * (2 |^ ((EU9 + 1) -' 1)) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() even Element of NAT
(2 * (2 |^ ((EU9 + 1) -' 1))) * X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() even Element of NAT
(2 |^ (EU9 + 1)) * X is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
(2 |^ (EU9 + 1)) * fp is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
k is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
((2 |^ (EU9 + 1)) -' 1) * k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(X) * ((2 |^ (EU9 + 1)) - 1) is V16() V17() integer V32() ext-real Element of INT
(2 |^ (EU9 + 1)) * k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((2 |^ (EU9 + 1)) * k) * ((2 |^ (EU9 + 1)) - 1) is V16() V17() integer V32() ext-real Element of INT
(fp) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(1,fp) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((2 |^ (EU9 + 1)) - 1) * k is V16() V17() integer V32() ext-real Element of INT
(((2 |^ (EU9 + 1)) - 1) * k) + k is V16() V17() integer V32() ext-real Element of INT
X + k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((2 |^ (EU9 + 1)) -' 1) * fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 * fp is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(2 |^ ((EU9 + 1) -' 1)) * ((2 |^ (EU9 + 1)) -' 1) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
n0 is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
EU9 is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
() is Relation-like NAT -defined NAT -valued non empty Function-like total quasi_total V59() V60() V61() V62() Element of bool [:NAT,NAT:]
n0 is ordinal natural non empty V16() V17() integer ext-real positive non negative finite cardinal set
NatDivisors n0 is finite V47() V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( not b₁ = 0 & b₁ divides n0 ) } is set
(NAT,(),(NatDivisors n0)) is Relation-like NAT -defined NatDivisors n0 -defined NAT -defined NAT -valued RAT -valued Function-like total finite V59() V60() V61() V62() finite-support set
Sum (NAT,(),(NatDivisors n0)) is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
dom () is non empty V69() V70() V71() V72() V73() V74() Element of bool NAT
rng () is non empty V69() V70() V71() V72() V73() V74() Element of bool REAL
Seg n0 is non empty finite n0 -element V69() V70() V71() V72() V73() V74() Element of bool NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( 1 <= b₁ & b₁ <= n0 ) } is set
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ex b₂ being ordinal natural V16() V17() integer ext-real non negative finite cardinal set st
( b₁ in Seg n0 & a₁ in NatDivisors n0 & b₂ = a₁ & b₁ gcd n0 = n0 / b₂ ) } is set
bool (Seg n0) is non empty finite V40() V48() set
bool (Seg n0) is non empty finite V40() V48() Element of bool (bool (Seg n0))
bool (bool (Seg n0)) is non empty finite V40() V48() set
fp is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ex b₂ being ordinal natural V16() V17() integer ext-real non negative finite cardinal set st
( b₁ in Seg n0 & fp in NatDivisors n0 & b₂ = fp & b₁ gcd n0 = n0 / b₂ ) } is set
k is set
f29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
f19 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
f29 gcd n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 / f19 is V16() V17() ext-real non negative Element of REAL
k is finite V69() V70() V71() V72() V73() V74() Element of bool (Seg n0)
fp is Relation-like NAT -defined bool (Seg n0) -valued Function-like finite FinSequence-like FinSubsequence-like finite-support FinSequence of bool (Seg n0)
dom fp is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sgm (NatDivisors n0) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
rng (Sgm (NatDivisors n0)) is finite V69() V70() V71() V72() V73() V74() Element of bool REAL
Card fp is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
dom (Card fp) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
(Card fp) * (Sgm (NatDivisors n0)) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite V59() V60() V61() V62() finite-support Element of bool [:NAT,NAT:]
dom ((Card fp) * (Sgm (NatDivisors n0))) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
dom (Sgm (NatDivisors n0)) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
() * (Sgm (NatDivisors n0)) is Relation-like NAT -defined NAT -valued RAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
dom (() * (Sgm (NatDivisors n0))) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((Card fp) * (Sgm (NatDivisors n0))) . k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(() * (Sgm (NatDivisors n0))) . k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(Sgm (NatDivisors n0)) . k is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( (Sgm (NatDivisors n0)) . k,b₁ are_relative_prime & 1 <= b₁ & b₁ <= (Sgm (NatDivisors n0)) . k ) } is set
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ex b₂ being ordinal natural V16() V17() integer ext-real non negative finite cardinal set st
( b₁ in Seg n0 & (Sgm (NatDivisors n0)) . k in NatDivisors n0 & b₂ = (Sgm (NatDivisors n0)) . k & b₁ gcd n0 = n0 / b₂ ) } is set
i is set
h is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
i is non empty V69() V70() V71() V72() V73() V74() Element of bool NAT
h is Relation-like Function-like set
dom h is set
rng h is set
Y is set
x2 is set
h . x2 is set
x29 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
((Sgm (NatDivisors n0)) . k) * x29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal Element of i
x19 * n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(x19 * n0) / ((Sgm (NatDivisors n0)) . k) is V16() V17() V32() ext-real non negative Element of RAT
n0 / ((Sgm (NatDivisors n0)) . k) is V16() V17() ext-real non negative Element of REAL
x19 * (n0 / ((Sgm (NatDivisors n0)) . k)) is V16() V17() ext-real non negative Element of REAL
((Sgm (NatDivisors n0)) . k) / ((Sgm (NatDivisors n0)) . k) is V16() V17() V32() ext-real non negative Element of RAT
x29 / (((Sgm (NatDivisors n0)) . k) / ((Sgm (NatDivisors n0)) . k)) is V16() V17() ext-real non negative Element of REAL
x19 * (x29 / (((Sgm (NatDivisors n0)) . k) / ((Sgm (NatDivisors n0)) . k))) is V16() V17() ext-real non negative Element of REAL
x29 / 1 is V16() V17() ext-real non negative Element of REAL
x19 * (x29 / 1) is V16() V17() ext-real non negative Element of REAL
x19 * x29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
l is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x29 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
1 * 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
((Sgm (NatDivisors n0)) . k) gcd l is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x gcd n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x2 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x2 gcd n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x19 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(x2 gcd n0) * x19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x19 * n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(x19 * n0) / ((Sgm (NatDivisors n0)) . k) is V16() V17() V32() ext-real non negative Element of RAT
x29 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 / x29 is V16() V17() ext-real non negative Element of REAL
x is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 / x is V16() V17() ext-real non negative Element of REAL
((Sgm (NatDivisors n0)) . k) * (x2 gcd n0) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 / (((Sgm (NatDivisors n0)) . k) / ((Sgm (NatDivisors n0)) . k)) is V16() V17() ext-real non negative Element of REAL
n0 / 1 is non empty V16() V17() ext-real positive non negative Element of REAL
x is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 / x is V16() V17() ext-real non negative Element of REAL
x29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 / x is V16() V17() ext-real non negative Element of REAL
x is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 / x is V16() V17() ext-real non negative Element of REAL
x29 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 / x is V16() V17() ext-real non negative Element of REAL
x is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
n0 / x is V16() V17() ext-real non negative Element of REAL
x is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal Element of i
h . x is set
Y is set
x2 is set
h . Y is set
h . x2 is set
x19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal Element of i
x19 * n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(x19 * n0) / ((Sgm (NatDivisors n0)) . k) is V16() V17() V32() ext-real non negative Element of RAT
h . x19 is set
x29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal Element of i
x29 * n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
(x29 * n0) / ((Sgm (NatDivisors n0)) . k) is V16() V17() V32() ext-real non negative Element of RAT
n0 / ((Sgm (NatDivisors n0)) . k) is V16() V17() ext-real non negative Element of REAL
x19 * (n0 / ((Sgm (NatDivisors n0)) . k)) is V16() V17() ext-real non negative Element of REAL
x29 * (n0 / ((Sgm (NatDivisors n0)) . k)) is V16() V17() ext-real non negative Element of REAL
fp . ((Sgm (NatDivisors n0)) . k) is set
card (fp . ((Sgm (NatDivisors n0)) . k)) is ordinal cardinal set
card i is ordinal non empty cardinal set
(Card fp) . ((Sgm (NatDivisors n0)) . k) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Euler ((Sgm (NatDivisors n0)) . k) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( (Sgm (NatDivisors n0)) . k,b₁ are_relative_prime & 1 <= b₁ & b₁ <= (Sgm (NatDivisors n0)) . k ) } is set
card { b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ( (Sgm (NatDivisors n0)) . k,b₁ are_relative_prime & 1 <= b₁ & b₁ <= (Sgm (NatDivisors n0)) . k ) } is ordinal cardinal set
() . ((Sgm (NatDivisors n0)) . k) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
len fp is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Func_Seq ((),(Sgm (NatDivisors n0))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
EU9 is Relation-like NAT -defined REAL -valued non empty Function-like total quasi_total V59() V60() V61() Element of bool [:NAT,REAL:]
Func_Seq (EU9,(Sgm (NatDivisors n0))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
(Card fp) " {0} is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
f19 is set
f29 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
i is set
[f19,i] is non empty set
{f19,i} is non empty finite set
{f19} is non empty trivial finite 1 -element set
{{f19,i},{f19}} is non empty finite V40() set
(Card fp) . f19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp . f19 is set
card (fp . f19) is ordinal cardinal set
x is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
h is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
x * h is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
h + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
h gcd n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x * (h gcd n0) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 / x is V16() V17() ext-real non negative Element of REAL
x / x is V16() V17() V32() ext-real non negative Element of RAT
(h gcd n0) * (x / x) is V16() V17() V32() ext-real non negative Element of RAT
(h gcd n0) * 1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ex b₂ being ordinal natural V16() V17() integer ext-real non negative finite cardinal set st
( b₁ in Seg n0 & x in NatDivisors n0 & b₂ = x & b₁ gcd n0 = n0 / b₂ ) } is set
x is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp . x is set
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ex b₂ being ordinal natural V16() V17() integer ext-real non negative finite cardinal set st
( b₁ in Seg n0 & x in NatDivisors n0 & b₂ = x & b₁ gcd n0 = n0 / b₂ ) } is set
i is set
h is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
Y is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
h gcd n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 / Y is V16() V17() ext-real non negative Element of REAL
[x,f29] is non empty Element of [:NAT,NAT:]
{x,f29} is non empty finite V40() V69() V70() V71() V72() V73() V74() set
{x} is non empty trivial finite V40() 1 -element V69() V70() V71() V72() V73() V74() set
{{x,f29},{x}} is non empty finite V40() set
f1 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
f19 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
f29 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() finite-support FinSequence of REAL
f29 - {0} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like finite-support set
dom f29 is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
f29 " {0} is finite set
(dom f29) \ (f29 " {0}) is finite V69() V70() V71() V72() V73() V74() Element of bool NAT
Sgm ((dom f29) \ (f29 " {0})) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like V59() V60() V61() V62() V97() finite-support FinSequence of NAT
(Sgm ((dom f29) \ (f29 " {0}))) * f29 is Relation-like NAT -defined REAL -valued Function-like finite V59() V60() V61() finite-support set
Sum f19 is V16() V17() ext-real Element of REAL
Sum f29 is V16() V17() ext-real Element of REAL
x is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
i is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
fp . x is set
fp . i is set
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ex b₂ being ordinal natural V16() V17() integer ext-real non negative finite cardinal set st
( b₁ in Seg n0 & x in NatDivisors n0 & b₂ = x & b₁ gcd n0 = n0 / b₂ ) } is set
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ex b₂ being ordinal natural V16() V17() integer ext-real non negative finite cardinal set st
( b₁ in Seg n0 & i in NatDivisors n0 & b₂ = i & b₁ gcd n0 = n0 / b₂ ) } is set
(fp . x) /\ (fp . i) is set
h is set
n0 / i is V16() V17() ext-real non negative Element of REAL
n0 / (n0 / i) is V16() V17() ext-real non negative Element of REAL
Y is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x2 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
Y gcd n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 / x2 is V16() V17() ext-real non negative Element of REAL
x19 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
x29 is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
x19 gcd n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
n0 / x29 is V16() V17() ext-real non negative Element of REAL
rng fp is finite V40() Element of bool (bool (Seg n0))
bool (bool (Seg n0)) is non empty finite V40() V48() set
union (rng fp) is finite V69() V70() V71() V72() V73() V74() Element of bool (Seg n0)
x is set
i is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
i gcd n0 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
h is ordinal natural V16() V17() integer ext-real non negative finite cardinal set
(i gcd n0) * h is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
h + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
0 + 1 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
fp . h is set
{ b₁ where b₁ is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT : ex b₂ being ordinal natural V16() V17() integer ext-real non negative finite cardinal set st
( b₁ in Seg n0 & h in NatDivisors n0 & b₂ = h & b₁ gcd n0 = n0 / b₂ ) } is set
n0 / h is V16() V17() ext-real non negative Element of REAL
h / h is V16() V17() ext-real non negative Element of REAL
(i gcd n0) * (h / h) is V16() V17() ext-real non negative Element of REAL
(i gcd n0) * 1 is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
card (union (rng fp)) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
Sum (Card fp) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT
card (Seg n0) is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
card n0 is ordinal natural non empty V16() V17() integer V32() ext-real positive non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of omega
Sum (Func_Seq ((),(Sgm (NatDivisors n0)))) is ordinal natural V16() V17() integer V32() ext-real non negative finite cardinal V69() V70() V71() V72() V73() V74() Element of NAT