:: FINSEQ_3 semantic presentation

REAL is set
NAT is non empty non trivial V15() V16() V17() V18() non finite cardinal limit_cardinal countable denumerable Element of K27(REAL)
K27(REAL) is non empty set
NAT is non empty non trivial V15() V16() V17() V18() non finite cardinal limit_cardinal countable denumerable set
K27(NAT) is non empty non trivial non finite set
K27(NAT) is non empty non trivial non finite set
{} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable set
the Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable set is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable set
1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
{{},1} is non empty finite V40() countable set
K28(1,1) is Relation-like non empty finite countable set
K27(K28(1,1)) is non empty finite V40() countable set
K28(K28(1,1),1) is Relation-like non empty finite countable set
K27(K28(K28(1,1),1)) is non empty finite V40() countable set
2 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
3 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
0 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable Element of NAT
card {} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable set
Seg 1 is non empty trivial finite 1 -element countable Element of K27(NAT)
{1} is non empty trivial finite V40() 1 -element countable set
Seg 2 is non empty finite 2 -element countable Element of K27(NAT)
{1,2} is non empty finite V40() countable set
dom {} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable set
rng {} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable with_non-empty_elements set
INT is set
product {} is functional non empty finite with_common_domain product-like countable set
{{}} is functional non empty trivial finite V40() 1 -element with_common_domain countable set
SubFuncs {} is set
Seg 3 is non empty finite 3 -element countable Element of K27(NAT)
{1,2,3} is non empty finite countable set
2 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
{(2 + 1)} is non empty trivial finite V40() 1 -element countable set
{1,2} \/ {(2 + 1)} is non empty finite V40() countable set
4 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg 4 is non empty finite 4 -element countable Element of K27(NAT)
{1,2,3,4} is non empty finite countable set
3 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
{(3 + 1)} is non empty trivial finite V40() 1 -element countable set
{1,2,3} \/ {(3 + 1)} is non empty finite countable set
5 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg 5 is non empty finite 5 -element countable Element of K27(NAT)
{1,2,3,4,5} is non empty finite countable set
4 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
{(4 + 1)} is non empty trivial finite V40() 1 -element countable set
{1,2,3,4} \/ {(4 + 1)} is non empty finite countable set
6 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg 6 is non empty finite 6 -element countable Element of K27(NAT)
{1,2,3,4,5,6} is non empty finite countable set
5 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
{(5 + 1)} is non empty trivial finite V40() 1 -element countable set
{1,2,3,4,5} \/ {(5 + 1)} is non empty finite countable set
7 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg 7 is non empty finite 7 -element countable Element of K27(NAT)
{1,2,3,4,5,6,7} is non empty finite countable set
6 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
{(6 + 1)} is non empty trivial finite V40() 1 -element countable set
{1,2,3,4,5,6} \/ {(6 + 1)} is non empty finite countable set
8 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg 8 is non empty finite 8 -element countable Element of K27(NAT)
{1,2,3,4,5,6,7,8} is non empty finite countable set
7 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
{(7 + 1)} is non empty trivial finite V40() 1 -element countable set
{1,2,3,4,5,6,7} \/ {(7 + 1)} is non empty finite countable set
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg i is finite i -element countable Element of K27(NAT)
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg i is finite i -element countable Element of K27(NAT)
i + 0 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i + D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg (i + D) is finite i + D -element countable Element of K27(NAT)
0 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg i is finite i -element countable Element of K27(NAT)
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i + D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i + 0 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg D is finite D -element countable Element of K27(NAT)
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg D is finite D -element countable Element of K27(NAT)
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i - x is ext-real V25() V26() V33() set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
x + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg i is finite i -element countable Element of K27(NAT)
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i - D is ext-real V25() V26() V33() set
D - D is ext-real V25() V26() V33() set
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg i is finite i -element countable Element of K27(NAT)
i + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
{(i + 1)} is non empty trivial finite V40() 1 -element countable set
(Seg i) /\ {(i + 1)} is finite countable Element of K27(NAT)
the Element of (Seg i) /\ {(i + 1)} is Element of (Seg i) /\ {(i + 1)}
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (i + 1) is non empty finite i + 1 -element countable Element of K27(NAT)
Seg i is finite i -element countable Element of K27(NAT)
(Seg (i + 1)) \ (Seg i) is finite countable Element of K27(NAT)
{(i + 1)} is non empty trivial finite V40() 1 -element countable set
(Seg i) \/ {(i + 1)} is non empty finite countable set
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg i is finite i -element countable Element of K27(NAT)
i + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (i + 1) is non empty finite i + 1 -element countable Element of K27(NAT)
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg i is finite i -element countable Element of K27(NAT)
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i + D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg (i + D) is finite i + D -element countable Element of K27(NAT)
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg i is finite i -element countable Element of K27(NAT)
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i + D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg (i + D) is finite i + D -element countable Element of K27(NAT)
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg i is finite i -element countable Element of K27(NAT)
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg D is finite D -element countable Element of K27(NAT)
i is set
{i} is non empty trivial finite 1 -element countable set
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg D is finite D -element countable Element of K27(NAT)
i is set
D is set
{i,D} is non empty finite countable set
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg x is finite x -element countable Element of K27(NAT)
1 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i ^ D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom (i ^ D) is finite countable Element of K27(NAT)
x is set
D is set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
D is set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len i) is finite len i -element countable Element of K27(NAT)
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg (len i) is finite len i -element countable Element of K27(NAT)
Seg (len i) is finite len i -element countable Element of K27(NAT)
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D - 1 is ext-real V25() V26() V33() set
(len i) - D is ext-real V25() V26() V33() set
0 + D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
0 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom i is finite countable Element of K27(NAT)
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom D is finite countable Element of K27(NAT)
Seg (len i) is finite len i -element countable Element of K27(NAT)
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom i is finite countable Element of K27(NAT)
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom D is finite countable Element of K27(NAT)
Seg (len D) is finite len D -element countable Element of K27(NAT)
Seg (len i) is finite len i -element countable Element of K27(NAT)
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
rng i is finite countable set
dom i is finite countable Element of K27(NAT)
D is set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len i) is finite len i -element countable Element of K27(NAT)
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
rng i is finite countable set
dom i is finite countable Element of K27(NAT)
the Element of rng i is Element of rng i
i is set
D is set
<*i,D*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
i is set
D is set
x is set
<*i,D,x*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like countable set
i is set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
D is set
x is set
<*D,x*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
len <*i*> is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
i is set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
D is set
x is set
n is set
<*D,x,n*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like countable set
len <*i*> is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
i is set
D is set
<*i,D*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
x is set
n is set
m9 is set
<*x,n,m9*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like countable set
len <*i,D*> is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom D is finite countable Element of K27(NAT)
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len D) + (len x) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom x is finite countable Element of K27(NAT)
D ^ x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
Seg ((len D) + (len x)) is finite (len D) + (len x) -element countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len D) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i . ((len D) + n) is set
x . n is set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i . n is set
D . n is set
i is set
Sgm i is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg D is finite D -element countable Element of K27(NAT)
rng (Sgm i) is finite countable Element of K27(NAT)
x is set
dom (Sgm i) is finite countable set
(Sgm i) . x is set
n is set
(Sgm i) . n is set
dom (Sgm i) is finite countable Element of K27(NAT)
len (Sgm i) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len (Sgm i)) is finite len (Sgm i) -element countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg i is finite i -element countable Element of K27(NAT)
D is finite countable set
Sgm D is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
len (Sgm D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom (Sgm D) is finite countable Element of K27(NAT)
Seg (len (Sgm D)) is finite len (Sgm D) -element countable Element of K27(NAT)
card (Seg (len (Sgm D))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
rng (Sgm D) is finite countable Element of K27(NAT)
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg i is finite i -element countable Element of K27(NAT)
D is finite countable set
Sgm D is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
dom (Sgm D) is finite countable Element of K27(NAT)
card D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (card D) is finite card D -element countable Element of K27(NAT)
len (Sgm D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i is set
Sgm i is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
len (Sgm i) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg D is finite D -element countable Element of K27(NAT)
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(Sgm i) . m9 is set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(Sgm i) . n is set
i is set
Sgm i is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
D is set
i \/ D is set
Sgm (i \/ D) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
Sgm D is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm i) ^ (Sgm D) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg x is finite x -element countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg n is finite n -element countable Element of K27(NAT)
dom (Sgm i) is finite countable Element of K27(NAT)
i /\ D is set
the Element of i /\ D is Element of i /\ D
rng (Sgm i) is finite countable Element of K27(NAT)
a is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len (Sgm (i \/ D)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is finite countable set
t is finite countable set
n \/ t is finite countable set
card (n \/ t) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card t is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(card n) + (card t) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len (Sgm i) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len (Sgm i)) + (card t) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len (Sgm D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len (Sgm i)) + (len (Sgm D)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
g is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(Sgm (i \/ D)) . g is set
(Sgm i) . g is set
g + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(Sgm (i \/ D)) . (g + 1) is set
(Sgm i) . (g + 1) is set
rng (Sgm i) is finite countable Element of K27(NAT)
a is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len (Sgm i)) is finite len (Sgm i) -element countable Element of K27(NAT)
Seg (len (Sgm (i \/ D))) is finite len (Sgm (i \/ D)) -element countable Element of K27(NAT)
dom (Sgm (i \/ D)) is finite countable Element of K27(NAT)
rng (Sgm (i \/ D)) is finite countable Element of K27(NAT)
f is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
x is set
(Sgm i) . x is set
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
w is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
x is set
(Sgm (i \/ D)) . x is set
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
s is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
w is set
(Sgm i) . w is set
s is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
w is set
(Sgm (i \/ D)) . w is set
s is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(Sgm (i \/ D)) . 0 is set
(Sgm i) . 0 is set
dom (Sgm D) is finite countable Element of K27(NAT)
g is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len (Sgm i)) + g is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(Sgm (i \/ D)) . ((len (Sgm i)) + g) is set
(Sgm D) . g is set
g + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(len (Sgm i)) + (g + 1) is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(Sgm (i \/ D)) . ((len (Sgm i)) + (g + 1)) is set
(Sgm D) . (g + 1) is set
dom (Sgm (i \/ D)) is finite countable Element of K27(NAT)
rng (Sgm (i \/ D)) is finite countable Element of K27(NAT)
f is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
rng (Sgm i) is finite countable Element of K27(NAT)
w is set
(Sgm i) . w is set
s is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(Sgm (i \/ D)) . s is set
(len (Sgm i)) + 0 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
rng (Sgm D) is finite countable Element of K27(NAT)
w is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
x is set
(Sgm D) . x is set
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
((len (Sgm i)) + g) + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
s is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
x is set
(Sgm (i \/ D)) . x is set
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
((len (Sgm i)) + g) + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
s is set
(Sgm D) . s is set
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len (Sgm i)) + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
s is set
(Sgm (i \/ D)) . s is set
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(Sgm i) . x is set
(len (Sgm i)) + 0 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(Sgm (i \/ D)) . ((len (Sgm i)) + 0) is set
(Sgm D) . 0 is set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
t is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
rng (Sgm D) is finite countable Element of K27(NAT)
dom (Sgm D) is finite countable Element of K27(NAT)
g is set
(Sgm D) . g is set
len (Sgm i) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
a is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len (Sgm i)) + a is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(Sgm (i \/ D)) . ((len (Sgm i)) + a) is set
len (Sgm D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len (Sgm i)) + (len (Sgm D)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len (Sgm (i \/ D)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
rng (Sgm i) is finite countable Element of K27(NAT)
dom (Sgm i) is finite countable Element of K27(NAT)
f is set
(Sgm i) . f is set
w is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len (Sgm i)) is finite len (Sgm i) -element countable Element of K27(NAT)
(Sgm (i \/ D)) . w is set
Sgm {} is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
Seg 0 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty proper V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal 0 -element {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable Element of K27(NAT)
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
{i} is non empty trivial finite V40() 1 -element countable set
Sgm {i} is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
Seg i is finite i -element countable Element of K27(NAT)
len (Sgm {i}) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card {i} is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
rng (Sgm {i}) is finite countable Element of K27(NAT)
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
{i,D} is non empty finite V40() countable set
Sgm {i,D} is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
<*i,D*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
Seg D is finite D -element countable Element of K27(NAT)
Seg i is finite i -element countable Element of K27(NAT)
len (Sgm {i,D}) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card {i,D} is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
dom (Sgm {i,D}) is finite countable Element of K27(NAT)
rng (Sgm {i,D}) is finite countable Element of K27(NAT)
(Sgm {i,D}) . 2 is set
(Sgm {i,D}) . 1 is set
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg i is finite i -element countable Element of K27(NAT)
Sgm (Seg i) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
len (Sgm (Seg i)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card (Seg i) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i + 0 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (i + 0) is finite i + 0 -element countable Element of K27(NAT)
Sgm (Seg (i + 0)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
Seg i is finite i -element countable Element of K27(NAT)
(Sgm (Seg (i + 0))) | (Seg i) is Relation-like NAT -defined Seg i -defined NAT -defined NAT -valued Function-like finite FinSubsequence-like countable Element of K27(K28(NAT,NAT))
K28(NAT,NAT) is Relation-like non empty non trivial non finite set
K27(K28(NAT,NAT)) is non empty non trivial non finite set
Sgm (Seg i) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
card (Seg i) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len (Sgm (Seg i)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom (Sgm (Seg i)) is finite countable Element of K27(NAT)
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
D + (i + 1) is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (D + (i + 1)) is non empty finite D + (i + 1) -element countable Element of K27(NAT)
Sgm (Seg (D + (i + 1))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
D + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (D + 1) is non empty finite D + 1 -element countable Element of K27(NAT)
Sgm (Seg (D + 1)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
Seg D is finite D -element countable Element of K27(NAT)
(Sgm (Seg (D + 1))) | (Seg D) is Relation-like NAT -defined Seg D -defined NAT -defined NAT -valued Function-like finite FinSubsequence-like countable Element of K27(K28(NAT,NAT))
K28(NAT,NAT) is Relation-like non empty non trivial non finite set
K27(K28(NAT,NAT)) is non empty non trivial non finite set
Sgm (Seg D) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
len (Sgm (Seg (D + 1))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom (Sgm (Seg (D + 1))) is finite countable Element of K27(NAT)
m9 is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
dom m9 is finite countable Element of K27(NAT)
rng (Sgm (Seg (D + 1))) is finite countable Element of K27(NAT)
(Sgm (Seg (D + 1))) . (D + 1) is set
n is set
(Sgm (Seg (D + 1))) . n is set
{(D + 1)} is non empty trivial finite V40() 1 -element countable set
(Seg (D + 1)) \ {(D + 1)} is finite countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
rng m9 is finite countable Element of K27(NAT)
{((Sgm (Seg (D + 1))) . (D + 1))} is non empty trivial finite 1 -element countable set
(rng (Sgm (Seg (D + 1)))) \ {((Sgm (Seg (D + 1))) . (D + 1))} is finite countable Element of K27(NAT)
n is set
{(D + 1)} is non empty trivial finite V40() 1 -element countable set
n is set
m9 . n is set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(Sgm (Seg (D + 1))) . n is set
m9 . n is set
n is set
n is set
(Sgm (Seg (D + 1))) . n is set
{(D + 1)} is non empty trivial finite V40() 1 -element countable set
(Seg (D + 1)) \ {(D + 1)} is finite countable Element of K27(NAT)
m9 . n is set
len m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
m9 . n is set
t is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
m9 . n is set
(Sgm (Seg (D + 1))) . n is set
(Sgm (Seg (D + 1))) . n is set
(D + 1) + i is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg ((D + 1) + i) is non empty finite (D + 1) + i -element countable Element of K27(NAT)
Sgm (Seg ((D + 1) + i)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm (Seg (D + (i + 1)))) | (Seg (D + 1)) is Relation-like NAT -defined Seg (D + 1) -defined NAT -defined NAT -valued Function-like finite FinSubsequence-like countable Element of K27(K28(NAT,NAT))
(Seg (D + 1)) /\ (Seg D) is finite countable Element of K27(NAT)
(Sgm (Seg (D + (i + 1)))) | ((Seg (D + 1)) /\ (Seg D)) is Relation-like NAT -defined (Seg (D + 1)) /\ (Seg D) -defined NAT -defined NAT -valued Function-like finite FinSubsequence-like countable Element of K27(K28(NAT,NAT))
(Sgm (Seg (D + (i + 1)))) | (Seg D) is Relation-like NAT -defined Seg D -defined NAT -defined NAT -valued Function-like finite FinSubsequence-like countable Element of K27(K28(NAT,NAT))
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
x + (D + 1) is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable set
Seg (x + (D + 1)) is non empty finite x + (D + 1) -element countable Element of K27(NAT)
Sgm (Seg (x + (D + 1))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
Seg x is finite x -element countable Element of K27(NAT)
(Sgm (Seg (x + (D + 1)))) | (Seg x) is Relation-like NAT -defined Seg x -defined NAT -defined NAT -valued Function-like finite FinSubsequence-like countable Element of K27(K28(NAT,NAT))
Sgm (Seg x) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D + 0 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg (D + 0) is finite D + 0 -element countable Element of K27(NAT)
Sgm (Seg (D + 0)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
Seg D is finite D -element countable Element of K27(NAT)
(Sgm (Seg (D + 0))) | (Seg D) is Relation-like NAT -defined Seg D -defined NAT -defined NAT -valued Function-like finite FinSubsequence-like countable Element of K27(K28(NAT,NAT))
Sgm (Seg D) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D + i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg (D + i) is finite D + i -element countable Element of K27(NAT)
Sgm (Seg (D + i)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
Seg D is finite D -element countable Element of K27(NAT)
(Sgm (Seg (D + i))) | (Seg D) is Relation-like NAT -defined Seg D -defined NAT -defined NAT -valued Function-like finite FinSubsequence-like countable Element of K27(K28(NAT,NAT))
Sgm (Seg D) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i + D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg (i + D) is finite i + D -element countable Element of K27(NAT)
Sgm (Seg (i + D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
Seg i is finite i -element countable Element of K27(NAT)
(Sgm (Seg (i + D))) | (Seg i) is Relation-like NAT -defined Seg i -defined NAT -defined NAT -valued Function-like finite FinSubsequence-like countable Element of K27(K28(NAT,NAT))
Sgm (Seg i) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg i is finite i -element countable Element of K27(NAT)
Sgm (Seg i) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
idseq i is Relation-like NAT -defined Function-like finite i -element FinSequence-like FinSubsequence-like countable set
id (Seg i) is Relation-like Seg i -defined Seg i -valued Function-like one-to-one total quasi_total finite countable Element of K27(K28((Seg i),(Seg i)))
K28((Seg i),(Seg i)) is Relation-like finite countable set
K27(K28((Seg i),(Seg i))) is non empty finite V40() countable set
i + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
idseq (i + 1) is Relation-like NAT -defined Function-like finite i + 1 -element FinSequence-like FinSubsequence-like countable set
Seg (i + 1) is non empty finite i + 1 -element countable Element of K27(NAT)
id (Seg (i + 1)) is Relation-like Seg (i + 1) -defined Seg (i + 1) -valued Function-like one-to-one non empty total quasi_total finite countable Element of K27(K28((Seg (i + 1)),(Seg (i + 1))))
K28((Seg (i + 1)),(Seg (i + 1))) is Relation-like non empty finite countable set
K27(K28((Seg (i + 1)),(Seg (i + 1)))) is non empty finite V40() countable set
len (idseq (i + 1)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Sgm (Seg (i + 1)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
len (Sgm (Seg (i + 1))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom (Sgm (Seg (i + 1))) is finite countable Element of K27(NAT)
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
{(i + 1)} is non empty trivial finite V40() 1 -element countable set
(Seg i) \/ {(i + 1)} is non empty finite countable set
(idseq (i + 1)) . D is set
(Sgm (Seg (i + 1))) | (Seg i) is Relation-like NAT -defined Seg i -defined NAT -defined NAT -valued Function-like finite FinSubsequence-like countable Element of K27(K28(NAT,NAT))
(Sgm (Seg i)) . D is set
(Sgm (Seg (i + 1))) . D is set
rng (Sgm (Seg (i + 1))) is finite countable Element of K27(NAT)
(Sgm (Seg (i + 1))) . D is set
{D} is non empty trivial finite V40() 1 -element countable set
(Seg (i + 1)) \ {(i + 1)} is finite countable Element of K27(NAT)
(Sgm (Seg (i + 1))) | (Seg i) is Relation-like NAT -defined Seg i -defined NAT -defined NAT -valued Function-like finite FinSubsequence-like countable Element of K27(K28(NAT,NAT))
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(Sgm (Seg (i + 1))) . m9 is set
(Sgm (Seg i)) . m9 is set
(idseq (i + 1)) . D is set
(Sgm (Seg (i + 1))) . D is set
(idseq (i + 1)) . D is set
(Sgm (Seg (i + 1))) . D is set
(idseq (i + 1)) . D is set
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg i is finite i -element countable Element of K27(NAT)
Sgm (Seg i) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
idseq i is Relation-like NAT -defined Function-like finite i -element FinSequence-like FinSubsequence-like countable set
id (Seg i) is Relation-like Seg i -defined Seg i -valued Function-like one-to-one total quasi_total finite countable Element of K27(K28((Seg i),(Seg i)))
K28((Seg i),(Seg i)) is Relation-like finite countable set
K27(K28((Seg i),(Seg i))) is non empty finite V40() countable set
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg D is finite D -element countable Element of K27(NAT)
Sgm (Seg D) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
idseq D is Relation-like NAT -defined Function-like finite D -element FinSequence-like FinSubsequence-like countable set
id (Seg D) is Relation-like Seg D -defined Seg D -valued Function-like one-to-one total quasi_total finite countable Element of K27(K28((Seg D),(Seg D)))
K28((Seg D),(Seg D)) is Relation-like finite countable set
K27(K28((Seg D),(Seg D))) is non empty finite V40() countable set
D + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (D + 1) is non empty finite D + 1 -element countable Element of K27(NAT)
Sgm (Seg (D + 1)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
idseq (D + 1) is Relation-like NAT -defined Function-like finite D + 1 -element FinSequence-like FinSubsequence-like countable set
id (Seg (D + 1)) is Relation-like Seg (D + 1) -defined Seg (D + 1) -valued Function-like one-to-one non empty total quasi_total finite countable Element of K27(K28((Seg (D + 1)),(Seg (D + 1))))
K28((Seg (D + 1)),(Seg (D + 1))) is Relation-like non empty finite countable set
K27(K28((Seg (D + 1)),(Seg (D + 1)))) is non empty finite V40() countable set
Seg 0 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty proper V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal 0 -element {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable Element of K27(NAT)
Sgm (Seg 0) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
idseq 0 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable set
id (Seg 0) is Relation-like non-empty empty-yielding Seg 0 -defined Seg 0 -valued Function-like one-to-one constant functional empty total V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() quasi_total V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable Element of K27(K28((Seg 0),(Seg 0)))
K28((Seg 0),(Seg 0)) is Relation-like finite countable set
K27(K28((Seg 0),(Seg 0))) is non empty finite V40() countable set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg D is finite D -element countable Element of K27(NAT)
i | (Seg D) is Relation-like NAT -defined Seg D -defined NAT -defined Function-like finite FinSubsequence-like countable set
Seg (len i) is finite len i -element countable Element of K27(NAT)
dom i is finite countable Element of K27(NAT)
(dom i) /\ (Seg D) is finite countable Element of K27(NAT)
x is set
i . x is set
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg i is finite i -element countable Element of K27(NAT)
idseq i is Relation-like NAT -defined Function-like finite i -element FinSequence-like FinSubsequence-like countable set
id (Seg i) is Relation-like Seg i -defined Seg i -valued Function-like one-to-one total quasi_total finite countable Element of K27(K28((Seg i),(Seg i)))
K28((Seg i),(Seg i)) is Relation-like finite countable set
K27(K28((Seg i),(Seg i))) is non empty finite V40() countable set
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i + D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
idseq (i + D) is Relation-like NAT -defined Function-like finite i + D -element FinSequence-like FinSubsequence-like countable set
Seg (i + D) is finite i + D -element countable Element of K27(NAT)
id (Seg (i + D)) is Relation-like Seg (i + D) -defined Seg (i + D) -valued Function-like one-to-one total quasi_total finite countable Element of K27(K28((Seg (i + D)),(Seg (i + D))))
K28((Seg (i + D)),(Seg (i + D))) is Relation-like finite countable set
K27(K28((Seg (i + D)),(Seg (i + D)))) is non empty finite V40() countable set
(idseq (i + D)) | (Seg i) is Relation-like NAT -defined Seg i -defined NAT -defined Function-like finite FinSubsequence-like countable set
Sgm (Seg i) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
Sgm (Seg (i + D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
idseq i is Relation-like NAT -defined Function-like finite i -element FinSequence-like FinSubsequence-like countable set
Seg i is finite i -element countable Element of K27(NAT)
id (Seg i) is Relation-like Seg i -defined Seg i -valued Function-like one-to-one total quasi_total finite countable Element of K27(K28((Seg i),(Seg i)))
K28((Seg i),(Seg i)) is Relation-like finite countable set
K27(K28((Seg i),(Seg i))) is non empty finite V40() countable set
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg D is finite D -element countable Element of K27(NAT)
(idseq i) | (Seg D) is Relation-like NAT -defined Seg D -defined NAT -defined Function-like finite FinSubsequence-like countable set
idseq D is Relation-like NAT -defined Function-like finite D -element FinSequence-like FinSubsequence-like countable set
id (Seg D) is Relation-like Seg D -defined Seg D -valued Function-like one-to-one total quasi_total finite countable Element of K27(K28((Seg D),(Seg D)))
K28((Seg D),(Seg D)) is Relation-like finite countable set
K27(K28((Seg D),(Seg D))) is non empty finite V40() countable set
len (idseq D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len (idseq i) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D + x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
idseq i is Relation-like NAT -defined Function-like finite i -element FinSequence-like FinSubsequence-like countable set
Seg i is finite i -element countable Element of K27(NAT)
id (Seg i) is Relation-like Seg i -defined Seg i -valued Function-like one-to-one total quasi_total finite countable Element of K27(K28((Seg i),(Seg i)))
K28((Seg i),(Seg i)) is Relation-like finite countable set
K27(K28((Seg i),(Seg i))) is non empty finite V40() countable set
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg D is finite D -element countable Element of K27(NAT)
(idseq i) | (Seg D) is Relation-like NAT -defined Seg D -defined NAT -defined Function-like finite FinSubsequence-like countable set
len (idseq i) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg x is finite x -element countable Element of K27(NAT)
i | (Seg x) is Relation-like NAT -defined Seg x -defined NAT -defined Function-like finite FinSubsequence-like countable set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
x + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom D is finite countable Element of K27(NAT)
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg x is finite x -element countable Element of K27(NAT)
i | (Seg x) is Relation-like NAT -defined Seg x -defined NAT -defined Function-like finite FinSubsequence-like countable set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
x + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
len D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
x + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg x is finite x -element countable Element of K27(NAT)
i | (Seg x) is Relation-like NAT -defined Seg x -defined NAT -defined Function-like finite FinSubsequence-like countable set
i . (x + 1) is set
<*(i . (x + 1))*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
D ^ <*(i . (x + 1))*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable set
dom D is finite countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i . n is set
D . n is set
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom <*(i . (x + 1))*> is non empty trivial finite 1 -element countable Element of K27(NAT)
len D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len D) + m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i . ((len D) + m9) is set
<*(i . (x + 1))*> . m9 is set
(len D) + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
len <*(i . (x + 1))*> is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(len D) + (len <*(i . (x + 1))*>) is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
D is set
i | D is Relation-like NAT -defined D -defined NAT -defined Function-like finite FinSubsequence-like countable set
D /\ (dom i) is finite countable Element of K27(NAT)
dom (i | D) is finite countable Element of K27(D)
K27(D) is non empty set
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg x is finite x -element countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg n is finite n -element countable Element of K27(NAT)
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg x is finite x -element countable Element of K27(NAT)
dom (i | D) is finite countable Element of K27(D)
K27(D) is non empty set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i ^ D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
x is set
(i ^ D) " x is finite countable set
card ((i ^ D) " x) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i " x is finite countable set
card (i " x) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D " x is finite countable set
card (D " x) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(card (i " x)) + (card (D " x)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
{ ((len i) + b₁) where b₁ is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT : b₁ in D " x } is set
(i " x) \/ { ((len i) + b₁) where b₁ is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT : b₁ in D " x } is set
n is set
dom (i ^ D) is finite countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom i is finite countable Element of K27(NAT)
(i ^ D) . n is set
i . n is set
dom D is finite countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D . n is set
(i ^ D) . n is set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom i is finite countable Element of K27(NAT)
dom D is finite countable Element of K27(NAT)
n is set
dom i is finite countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(i ^ D) . n is set
i . n is set
(i ^ D) . n is set
dom (i ^ D) is finite countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom D is finite countable Element of K27(NAT)
(i ^ D) . ((len i) + n) is set
D . n is set
(i ^ D) . n is set
dom (i ^ D) is finite countable Element of K27(NAT)
(i " x) /\ { ((len i) + b₁) where b₁ is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT : b₁ in D " x } is finite countable set
the Element of (i " x) /\ { ((len i) + b₁) where b₁ is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT : b₁ in D " x } is Element of (i " x) /\ { ((len i) + b₁) where b₁ is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT : b₁ in D " x }
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom i is finite countable Element of K27(NAT)
(len i) + 0 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom D is finite countable Element of K27(NAT)
n is finite countable set
card n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(card (i " x)) + (card n) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is set
dom D is finite countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
t is set
n is Relation-like Function-like set
dom n is set
rng n is set
n is set
t is set
n . t is set
g is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + g is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is set
t is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len i) + t is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n . t is set
g is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + g is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is set
n . n is set
t is set
n . t is set
g is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + g is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
a is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + a is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i ^ D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
x is set
i " x is finite countable set
(i ^ D) " x is finite countable set
n is set
dom i is finite countable Element of K27(NAT)
dom (i ^ D) is finite countable Element of K27(NAT)
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i . m9 is set
(i ^ D) . m9 is set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
D is set
i " D is finite countable set
(dom i) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len i) is finite len i -element countable Element of K27(NAT)
(Seg (len i)) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((Seg (len i)) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
rng (Sgm ((Seg (len i)) \ (i " D))) is finite countable Element of K27(NAT)
x is non empty countable Element of K27(NAT)
n is Relation-like NAT -defined x -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of x
n * i is Relation-like NAT -defined Function-like finite countable set
m9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D is set
(i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " D is finite countable set
(dom i) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
len (i,D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card (i " D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len i) - (card (i " D)) is ext-real V25() V26() V33() set
Seg (len i) is finite len i -element countable Element of K27(NAT)
(Seg (len i)) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((Seg (len i)) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
rng (Sgm ((Seg (len i)) \ (i " D))) is finite countable Element of K27(NAT)
dom (Sgm ((Seg (len i)) \ (i " D))) is finite countable Element of K27(NAT)
dom (i,D) is finite countable Element of K27(NAT)
len (Sgm ((Seg (len i)) \ (i " D))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len (Sgm ((Seg (len i)) \ (i " D)))) is finite len (Sgm ((Seg (len i)) \ (i " D))) -element countable Element of K27(NAT)
n is set
card ((Seg (len i)) \ (i " D)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card (Seg (len i)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(card (Seg (len i))) - (card (i " D)) is ext-real V25() V26() V33() set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D is set
(i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " D is finite countable set
(dom i) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
len (i,D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card (i " D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len i) - (card (i " D)) is ext-real V25() V26() V33() set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
rng i is finite countable set
D is set
(i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " D is finite countable set
(dom i) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
len (i,D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card (i " D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len i) - (card (i " D)) is ext-real V25() V26() V33() set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D is set
i " D is finite countable set
card (i " D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len i) - (card (i " D)) is ext-real V25() V26() V33() set
(i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
(dom i) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
dom (i,D) is finite countable Element of K27(NAT)
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg x is finite x -element countable Element of K27(NAT)
len (i,D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
D is set
(i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i " D is finite countable set
(dom i) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
dom (i,D) is finite countable Element of K27(NAT)
len (i,D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len (i,D)) is finite len (i,D) -element countable Element of K27(NAT)
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len i) is finite len i -element countable Element of K27(NAT)
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
rng i is finite countable set
D is set
(i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i " D is finite countable set
(dom i) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
dom (i,D) is finite countable Element of K27(NAT)
len (i,D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len (i,D)) is finite len (i,D) -element countable Element of K27(NAT)
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len i) is finite len i -element countable Element of K27(NAT)
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
rng i is finite countable set
D is set
(i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " D is finite countable set
(dom i) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
rng (i,D) is finite countable set
(rng i) \ D is finite countable Element of K27((rng i))
K27((rng i)) is non empty finite V40() countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len i) is finite len i -element countable Element of K27(NAT)
(Seg (len i)) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((Seg (len i)) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
n is set
(Sgm ((Seg (len i)) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
rng ((Sgm ((Seg (len i)) \ (i " D))) * i) is finite countable set
dom (i,D) is finite countable Element of K27(NAT)
m9 is set
(i,D) . m9 is set
(Sgm ((Seg (len i)) \ (i " D))) . m9 is set
dom (Sgm ((Seg (len i)) \ (i " D))) is finite countable Element of K27(NAT)
i . ((Sgm ((Seg (len i)) \ (i " D))) . m9) is set
rng (Sgm ((Seg (len i)) \ (i " D))) is finite countable Element of K27(NAT)
n is set
m9 is set
i . m9 is set
rng (Sgm ((Seg (len i)) \ (i " D))) is finite countable Element of K27(NAT)
dom (Sgm ((Seg (len i)) \ (i " D))) is finite countable Element of K27(NAT)
n is set
(Sgm ((Seg (len i)) \ (i " D))) . n is set
(i,D) . n is set
dom (i,D) is finite countable Element of K27(NAT)
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
rng i is finite countable set
D is set
(i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " D is finite countable set
(dom i) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
rng (i,D) is finite countable set
(rng i) \ D is finite countable Element of K27((rng i))
K27((rng i)) is non empty finite V40() countable set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
rng i is finite countable set
D is set
(i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " D is finite countable set
(dom i) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
rng (i,D) is finite countable set
(rng i) \ D is finite countable Element of K27((rng i))
K27((rng i)) is non empty finite V40() countable set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
rng i is finite countable set
D is set
(i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " D is finite countable set
(dom i) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
(rng i) \ D is finite countable Element of K27((rng i))
K27((rng i)) is non empty finite V40() countable set
rng (i,D) is finite countable set
rng (i,D) is finite countable set
(rng i) \ D is finite countable Element of K27((rng i))
K27((rng i)) is non empty finite V40() countable set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
rng i is finite countable set
D is set
(i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " D is finite countable set
(dom i) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
len (i,D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len i) is finite len i -element countable Element of K27(NAT)
(Seg (len i)) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((Seg (len i)) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
idseq (len i) is Relation-like NAT -defined Function-like finite len i -element FinSequence-like FinSubsequence-like countable set
id (Seg (len i)) is Relation-like Seg (len i) -defined Seg (len i) -valued Function-like one-to-one total quasi_total finite countable Element of K27(K28((Seg (len i)),(Seg (len i))))
K28((Seg (len i)),(Seg (len i))) is Relation-like finite countable set
K27(K28((Seg (len i)),(Seg (len i)))) is non empty finite V40() countable set
(Sgm ((Seg (len i)) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
rng i is finite countable set
D is set
{D} is non empty trivial finite 1 -element countable set
(i,{D}) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " {D} is finite countable set
(dom i) \ (i " {D}) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " {D})) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " {D}))) * i is Relation-like NAT -defined Function-like finite countable set
x is set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
(i,{}) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " {} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable set
(dom i) \ (i " {}) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " {})) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " {}))) * i is Relation-like NAT -defined Function-like finite countable set
rng i is finite countable set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
rng i is finite countable set
(i,(rng i)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " (rng i) is finite countable set
(dom i) \ (i " (rng i)) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " (rng i))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " (rng i)))) * i is Relation-like NAT -defined Function-like finite countable set
i is set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
D is set
(<*i*>,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*i*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*i*> " D is finite countable set
(dom <*i*>) \ (<*i*> " D) is finite countable Element of K27(NAT)
Sgm ((dom <*i*>) \ (<*i*> " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*i*>) \ (<*i*> " D))) * <*i*> is Relation-like NAT -defined Function-like finite countable set
rng <*i*> is non empty trivial finite 1 -element countable set
{i} is non empty trivial finite 1 -element countable set
rng <*i*> is non empty trivial finite 1 -element countable set
x is set
{i} is non empty trivial finite 1 -element countable set
i is set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
D is set
(<*i*>,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*i*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*i*> " D is finite countable set
(dom <*i*>) \ (<*i*> " D) is finite countable Element of K27(NAT)
Sgm ((dom <*i*>) \ (<*i*> " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*i*>) \ (<*i*> " D))) * <*i*> is Relation-like NAT -defined Function-like finite countable set
rng <*i*> is non empty trivial finite 1 -element countable set
{i} is non empty trivial finite 1 -element countable set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i ^ {} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
D is set
((i ^ {}),D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom (i ^ {}) is finite countable Element of K27(NAT)
(i ^ {}) " D is finite countable set
(dom (i ^ {})) \ ((i ^ {}) " D) is finite countable Element of K27(NAT)
Sgm ((dom (i ^ {})) \ ((i ^ {}) " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom (i ^ {})) \ ((i ^ {}) " D))) * (i ^ {}) is Relation-like NAT -defined Function-like finite countable set
(i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " D is finite countable set
(dom i) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
({},D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom {} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty proper V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable Element of K27(NAT)
{} " D is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable set
(dom {}) \ ({} " D) is Relation-like NAT -defined finite countable Element of K27(NAT)
Sgm ((dom {}) \ ({} " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom {}) \ ({} " D))) * {} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable set
(i,D) ^ ({},D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
D is set
<*D*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
i ^ <*D*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable set
x is set
((i ^ <*D*>),x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom (i ^ <*D*>) is non empty finite countable Element of K27(NAT)
(i ^ <*D*>) " x is finite countable set
(dom (i ^ <*D*>)) \ ((i ^ <*D*>) " x) is finite countable Element of K27(NAT)
Sgm ((dom (i ^ <*D*>)) \ ((i ^ <*D*>) " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom (i ^ <*D*>)) \ ((i ^ <*D*>) " x))) * (i ^ <*D*>) is Relation-like NAT -defined Function-like finite countable set
(i,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " x is finite countable set
(dom i) \ (i " x) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " x))) * i is Relation-like NAT -defined Function-like finite countable set
(<*D*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*D*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*D*> " x is finite countable set
(dom <*D*>) \ (<*D*> " x) is finite countable Element of K27(NAT)
Sgm ((dom <*D*>) \ (<*D*> " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*D*>) \ (<*D*> " x))) * <*D*> is Relation-like NAT -defined Function-like finite countable set
(i,x) ^ (<*D*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len (i ^ <*D*>) is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len <*D*> is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(len i) + (len <*D*>) is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(len i) + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len (i ^ <*D*>)) is non empty finite len (i ^ <*D*>) -element countable Element of K27(NAT)
(Seg (len (i ^ <*D*>))) \ ((i ^ <*D*>) " x) is finite countable Element of K27(NAT)
Sgm ((Seg (len (i ^ <*D*>))) \ ((i ^ <*D*>) " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
t is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom (<*D*>,x) is finite countable Element of K27(NAT)
g is set
i . g is set
a is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(i ^ <*D*>) . a is set
g is set
(i ^ <*D*>) . g is set
a is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
f is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + f is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(i ^ <*D*>) . a is set
i . a is set
f is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + f is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
f is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + f is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(i ^ <*D*>) . (len (i ^ <*D*>)) is set
dom (Sgm ((Seg (len (i ^ <*D*>))) \ ((i ^ <*D*>) " x))) is finite countable Element of K27(NAT)
len (Sgm ((Seg (len (i ^ <*D*>))) \ ((i ^ <*D*>) " x))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len (Sgm ((Seg (len (i ^ <*D*>))) \ ((i ^ <*D*>) " x)))) is finite len (Sgm ((Seg (len (i ^ <*D*>))) \ ((i ^ <*D*>) " x))) -element countable Element of K27(NAT)
rng (Sgm ((Seg (len (i ^ <*D*>))) \ ((i ^ <*D*>) " x))) is finite countable Element of K27(NAT)
g is set
(Sgm ((Seg (len (i ^ <*D*>))) \ ((i ^ <*D*>) " x))) . g is set
len (i,x) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len (i,x)) + t is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card (i " x) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len i) - (card (i " x)) is ext-real V25() V26() V33() set
((len i) - (card (i " x))) + t is ext-real V25() V26() V33() set
card ((i ^ <*D*>) " x) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
((len i) + 1) - (card ((i ^ <*D*>) " x)) is ext-real V25() V26() V33() set
((len i) + (len <*D*>)) - (card ((i ^ <*D*>) " x)) is ext-real V25() V26() V33() set
(len (i ^ <*D*>)) - (card ((i ^ <*D*>) " x)) is ext-real V25() V26() V33() set
len ((i ^ <*D*>),x) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card ((Seg (len (i ^ <*D*>))) \ ((i ^ <*D*>) " x)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card (Seg (len (i ^ <*D*>))) is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(card (Seg (len (i ^ <*D*>)))) - (card ((i ^ <*D*>) " x)) is ext-real V25() V26() V33() set
(len (i ^ <*D*>)) - (card (i " x)) is ext-real V25() V26() V33() set
(len (i,x)) + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(Sgm ((Seg (len (i ^ <*D*>))) \ ((i ^ <*D*>) " x))) . (len (Sgm ((Seg (len (i ^ <*D*>))) \ ((i ^ <*D*>) " x)))) is set
f is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
a is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
((i ^ <*D*>),x) . ((len (i,x)) + t) is set
(<*D*>,x) . t is set
{((len i) + 1)} is non empty trivial finite V40() 1 -element countable set
(i " x) \/ {((len i) + 1)} is non empty finite countable set
n is set
Seg ((len i) + 1) is non empty finite (len i) + 1 -element countable Element of K27(NAT)
Seg (len i) is finite len i -element countable Element of K27(NAT)
(Seg (len i)) \/ {((len i) + 1)} is non empty finite countable set
(i ^ <*D*>) . n is set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i . n is set
(i ^ <*D*>) . n is set
n is set
(i ^ <*D*>) . n is set
n is set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(i ^ <*D*>) . n is set
Seg (len i) is finite len i -element countable Element of K27(NAT)
i . n is set
Seg (len i) is finite len i -element countable Element of K27(NAT)
(Seg (len i)) \ (i " x) is finite countable Element of K27(NAT)
Sgm ((Seg (len i)) \ (i " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
{((len i) + 1)} /\ (i " x) is finite countable set
the Element of {((len i) + 1)} /\ (i " x) is Element of {((len i) + 1)} /\ (i " x)
(Seg (len i)) \/ {((len i) + 1)} is non empty finite countable set
((Seg (len i)) \/ {((len i) + 1)}) \ (i " x) is finite countable Element of K27(((Seg (len i)) \/ {((len i) + 1)}))
K27(((Seg (len i)) \/ {((len i) + 1)})) is non empty finite V40() countable set
{((len i) + 1)} \ (i " x) is trivial finite V40() countable Element of K27({((len i) + 1)})
K27({((len i) + 1)}) is non empty finite V40() countable set
((Seg (len i)) \ (i " x)) \/ ({((len i) + 1)} \ (i " x)) is finite countable set
((Seg (len i)) \ (i " x)) \/ {((len i) + 1)} is non empty finite countable set
(Seg (len i)) /\ {((len i) + 1)} is finite countable Element of K27(NAT)
the Element of (Seg (len i)) /\ {((len i) + 1)} is Element of (Seg (len i)) /\ {((len i) + 1)}
a is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
((Seg (len i)) \/ {((len i) + 1)}) \ ((i " x) \/ {((len i) + 1)}) is finite countable Element of K27(((Seg (len i)) \/ {((len i) + 1)}))
(Seg (len i)) \ ((i " x) \/ {((len i) + 1)}) is finite countable Element of K27(NAT)
{((len i) + 1)} \ ((i " x) \/ {((len i) + 1)}) is trivial finite V40() countable Element of K27({((len i) + 1)})
((Seg (len i)) \ ((i " x) \/ {((len i) + 1)})) \/ ({((len i) + 1)} \ ((i " x) \/ {((len i) + 1)})) is finite countable set
((Seg (len i)) \ ((i " x) \/ {((len i) + 1)})) \/ {} is finite countable set
(Seg (len i)) \ {((len i) + 1)} is finite countable Element of K27(NAT)
((Seg (len i)) \ (i " x)) /\ ((Seg (len i)) \ {((len i) + 1)}) is finite countable Element of K27(NAT)
((Seg (len i)) \ (i " x)) /\ (Seg (len i)) is finite countable Element of K27(NAT)
len (Sgm ((Seg (len i)) \ (i " x))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card ((Seg (len i)) \ (i " x)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card (Seg (len i)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(card (Seg (len i))) - (card (i " x)) is ext-real V25() V26() V33() set
rng (Sgm ((Seg (len i)) \ (i " x))) is finite countable Element of K27(NAT)
t is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom (i,x) is finite countable Element of K27(NAT)
dom (Sgm ((Seg (len i)) \ (i " x))) is finite countable Element of K27(NAT)
(Sgm ((Seg (len i)) \ (i " x))) . t is set
g is set
(card (i " x)) + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len (Sgm ((Seg (len i)) \ (i " x)))) is finite len (Sgm ((Seg (len i)) \ (i " x))) -element countable Element of K27(NAT)
a is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
a + (card (i " x)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(a + (card (i " x))) + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
card (<*D*> " x) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(card (i " x)) + (card (<*D*> " x)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
a + (card ((i ^ <*D*>) " x)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
a + ((card (i " x)) + 1) is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(Sgm ((Seg (len (i ^ <*D*>))) \ ((i ^ <*D*>) " x))) . t is set
((i ^ <*D*>),x) . t is set
g is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(i ^ <*D*>) . g is set
Seg ((len i) + 1) is non empty finite (len i) + 1 -element countable Element of K27(NAT)
a is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
f is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Sgm {((len i) + 1)} is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((Seg (len i)) \ (i " x))) ^ (Sgm {((len i) + 1)}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(i,x) . t is set
i . ((Sgm ((Seg (len i)) \ (i " x))) . t) is set
card (<*D*> " x) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(card (i " x)) + (card (<*D*> " x)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
((len i) + (len <*D*>)) - ((card (i " x)) + (card (<*D*> " x))) is ext-real V25() V26() V33() set
((len i) - (card (i " x))) + (len <*D*>) is ext-real V25() V26() V33() set
- (card (<*D*> " x)) is ext-real non positive V25() V26() V33() set
(((len i) - (card (i " x))) + (len <*D*>)) + (- (card (<*D*> " x))) is ext-real V25() V26() V33() set
(len (i,x)) + (len <*D*>) is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
((len (i,x)) + (len <*D*>)) + (- (card (<*D*> " x))) is ext-real V25() V26() V33() set
(len <*D*>) - (card (<*D*> " x)) is ext-real V25() V26() V33() set
(len (i,x)) + ((len <*D*>) - (card (<*D*> " x))) is ext-real V25() V26() V33() set
len (<*D*>,x) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len (i,x)) + (len (<*D*>,x)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
D is set
<*D*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
i ^ <*D*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable set
x ^ (i ^ <*D*>) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable set
n is set
((x ^ (i ^ <*D*>)),n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom (x ^ (i ^ <*D*>)) is non empty finite countable Element of K27(NAT)
(x ^ (i ^ <*D*>)) " n is finite countable set
(dom (x ^ (i ^ <*D*>))) \ ((x ^ (i ^ <*D*>)) " n) is finite countable Element of K27(NAT)
Sgm ((dom (x ^ (i ^ <*D*>))) \ ((x ^ (i ^ <*D*>)) " n)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom (x ^ (i ^ <*D*>))) \ ((x ^ (i ^ <*D*>)) " n))) * (x ^ (i ^ <*D*>)) is Relation-like NAT -defined Function-like finite countable set
x ^ i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
(x ^ i) ^ <*D*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable set
(((x ^ i) ^ <*D*>),n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom ((x ^ i) ^ <*D*>) is non empty finite countable Element of K27(NAT)
((x ^ i) ^ <*D*>) " n is finite countable set
(dom ((x ^ i) ^ <*D*>)) \ (((x ^ i) ^ <*D*>) " n) is finite countable Element of K27(NAT)
Sgm ((dom ((x ^ i) ^ <*D*>)) \ (((x ^ i) ^ <*D*>) " n)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom ((x ^ i) ^ <*D*>)) \ (((x ^ i) ^ <*D*>) " n))) * ((x ^ i) ^ <*D*>) is Relation-like NAT -defined Function-like finite countable set
((x ^ i),n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom (x ^ i) is finite countable Element of K27(NAT)
(x ^ i) " n is finite countable set
(dom (x ^ i)) \ ((x ^ i) " n) is finite countable Element of K27(NAT)
Sgm ((dom (x ^ i)) \ ((x ^ i) " n)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom (x ^ i)) \ ((x ^ i) " n))) * (x ^ i) is Relation-like NAT -defined Function-like finite countable set
(<*D*>,n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*D*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*D*> " n is finite countable set
(dom <*D*>) \ (<*D*> " n) is finite countable Element of K27(NAT)
Sgm ((dom <*D*>) \ (<*D*> " n)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*D*>) \ (<*D*> " n))) * <*D*> is Relation-like NAT -defined Function-like finite countable set
((x ^ i),n) ^ (<*D*>,n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
(x,n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom x is finite countable Element of K27(NAT)
x " n is finite countable set
(dom x) \ (x " n) is finite countable Element of K27(NAT)
Sgm ((dom x) \ (x " n)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom x) \ (x " n))) * x is Relation-like NAT -defined Function-like finite countable set
(i,n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " n is finite countable set
(dom i) \ (i " n) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " n)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " n))) * i is Relation-like NAT -defined Function-like finite countable set
(x,n) ^ (i,n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
((x,n) ^ (i,n)) ^ (<*D*>,n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
(i,n) ^ (<*D*>,n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
(x,n) ^ ((i,n) ^ (<*D*>,n)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
((i ^ <*D*>),n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom (i ^ <*D*>) is non empty finite countable Element of K27(NAT)
(i ^ <*D*>) " n is finite countable set
(dom (i ^ <*D*>)) \ ((i ^ <*D*>) " n) is finite countable Element of K27(NAT)
Sgm ((dom (i ^ <*D*>)) \ ((i ^ <*D*>) " n)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom (i ^ <*D*>)) \ ((i ^ <*D*>) " n))) * (i ^ <*D*>) is Relation-like NAT -defined Function-like finite countable set
(x,n) ^ ((i ^ <*D*>),n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
D is set
<*D*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
i ^ <*D*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable set
x ^ (i ^ <*D*>) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable set
n is set
((x ^ (i ^ <*D*>)),n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom (x ^ (i ^ <*D*>)) is non empty finite countable Element of K27(NAT)
(x ^ (i ^ <*D*>)) " n is finite countable set
(dom (x ^ (i ^ <*D*>))) \ ((x ^ (i ^ <*D*>)) " n) is finite countable Element of K27(NAT)
Sgm ((dom (x ^ (i ^ <*D*>))) \ ((x ^ (i ^ <*D*>)) " n)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom (x ^ (i ^ <*D*>))) \ ((x ^ (i ^ <*D*>)) " n))) * (x ^ (i ^ <*D*>)) is Relation-like NAT -defined Function-like finite countable set
(x,n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom x is finite countable Element of K27(NAT)
x " n is finite countable set
(dom x) \ (x " n) is finite countable Element of K27(NAT)
Sgm ((dom x) \ (x " n)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom x) \ (x " n))) * x is Relation-like NAT -defined Function-like finite countable set
((i ^ <*D*>),n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom (i ^ <*D*>) is non empty finite countable Element of K27(NAT)
(i ^ <*D*>) " n is finite countable set
(dom (i ^ <*D*>)) \ ((i ^ <*D*>) " n) is finite countable Element of K27(NAT)
Sgm ((dom (i ^ <*D*>)) \ ((i ^ <*D*>) " n)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom (i ^ <*D*>)) \ ((i ^ <*D*>) " n))) * (i ^ <*D*>) is Relation-like NAT -defined Function-like finite countable set
(x,n) ^ ((i ^ <*D*>),n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i ^ {} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
D is set
((i ^ {}),D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom (i ^ {}) is finite countable Element of K27(NAT)
(i ^ {}) " D is finite countable set
(dom (i ^ {})) \ ((i ^ {}) " D) is finite countable Element of K27(NAT)
Sgm ((dom (i ^ {})) \ ((i ^ {}) " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom (i ^ {})) \ ((i ^ {}) " D))) * (i ^ {}) is Relation-like NAT -defined Function-like finite countable set
(i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " D is finite countable set
(dom i) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
({},D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom {} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty proper V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable Element of K27(NAT)
{} " D is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable set
(dom {}) \ ({} " D) is Relation-like NAT -defined finite countable Element of K27(NAT)
Sgm ((dom {}) \ ({} " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom {}) \ ({} " D))) * {} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable set
(i,D) ^ ({},D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
D ^ i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
x is set
((D ^ i),x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom (D ^ i) is finite countable Element of K27(NAT)
(D ^ i) " x is finite countable set
(dom (D ^ i)) \ ((D ^ i) " x) is finite countable Element of K27(NAT)
Sgm ((dom (D ^ i)) \ ((D ^ i) " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom (D ^ i)) \ ((D ^ i) " x))) * (D ^ i) is Relation-like NAT -defined Function-like finite countable set
(D,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom D is finite countable Element of K27(NAT)
D " x is finite countable set
(dom D) \ (D " x) is finite countable Element of K27(NAT)
Sgm ((dom D) \ (D " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom D) \ (D " x))) * D is Relation-like NAT -defined Function-like finite countable set
(i,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " x is finite countable set
(dom i) \ (i " x) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " x))) * i is Relation-like NAT -defined Function-like finite countable set
(D,x) ^ (i,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i ^ D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
x is set
((i ^ D),x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom (i ^ D) is finite countable Element of K27(NAT)
(i ^ D) " x is finite countable set
(dom (i ^ D)) \ ((i ^ D) " x) is finite countable Element of K27(NAT)
Sgm ((dom (i ^ D)) \ ((i ^ D) " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom (i ^ D)) \ ((i ^ D) " x))) * (i ^ D) is Relation-like NAT -defined Function-like finite countable set
(i,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " x is finite countable set
(dom i) \ (i " x) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " x))) * i is Relation-like NAT -defined Function-like finite countable set
(D,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom D is finite countable Element of K27(NAT)
D " x is finite countable set
(dom D) \ (D " x) is finite countable Element of K27(NAT)
Sgm ((dom D) \ (D " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom D) \ (D " x))) * D is Relation-like NAT -defined Function-like finite countable set
(i,x) ^ (D,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i is set
({},i) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom {} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty proper V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable Element of K27(NAT)
{} " i is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable set
(dom {}) \ ({} " i) is Relation-like NAT -defined finite countable Element of K27(NAT)
Sgm ((dom {}) \ ({} " i)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom {}) \ ({} " i))) * {} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable set
i is set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
D is set
(<*i*>,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*i*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*i*> " D is finite countable set
(dom <*i*>) \ (<*i*> " D) is finite countable Element of K27(NAT)
Sgm ((dom <*i*>) \ (<*i*> " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*i*>) \ (<*i*> " D))) * <*i*> is Relation-like NAT -defined Function-like finite countable set
x is set
n is set
<*x*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
(<*x*>,n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*x*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*x*> " n is finite countable set
(dom <*x*>) \ (<*x*> " n) is finite countable Element of K27(NAT)
Sgm ((dom <*x*>) \ (<*x*> " n)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*x*>) \ (<*x*> " n))) * <*x*> is Relation-like NAT -defined Function-like finite countable set
i is set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
D is set
(<*i*>,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*i*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*i*> " D is finite countable set
(dom <*i*>) \ (<*i*> " D) is finite countable Element of K27(NAT)
Sgm ((dom <*i*>) \ (<*i*> " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*i*>) \ (<*i*> " D))) * <*i*> is Relation-like NAT -defined Function-like finite countable set
x is set
n is set
<*x*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
(<*x*>,n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*x*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*x*> " n is finite countable set
(dom <*x*>) \ (<*x*> " n) is finite countable Element of K27(NAT)
Sgm ((dom <*x*>) \ (<*x*> " n)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*x*>) \ (<*x*> " n))) * <*x*> is Relation-like NAT -defined Function-like finite countable set
i is set
D is set
<*i,D*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
x is set
(<*i,D*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*i,D*> is non empty finite 2 -element countable Element of K27(NAT)
<*i,D*> " x is finite countable set
(dom <*i,D*>) \ (<*i,D*> " x) is finite countable Element of K27(NAT)
Sgm ((dom <*i,D*>) \ (<*i,D*> " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*i,D*>) \ (<*i,D*> " x))) * <*i,D*> is Relation-like NAT -defined Function-like finite countable set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
<*D*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
<*i*> ^ <*D*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like countable set
1 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
rng <*i,D*> is non empty finite countable set
{i,D} is non empty finite countable set
(<*D*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*D*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*D*> " x is finite countable set
(dom <*D*>) \ (<*D*> " x) is finite countable Element of K27(NAT)
Sgm ((dom <*D*>) \ (<*D*> " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*D*>) \ (<*D*> " x))) * <*D*> is Relation-like NAT -defined Function-like finite countable set
card {} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable Element of NAT
(card {}) + (card {}) is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable Element of NAT
{} ^ {} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
card ({} ^ {}) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(<*i*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*i*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*i*> " x is finite countable set
(dom <*i*>) \ (<*i*> " x) is finite countable Element of K27(NAT)
Sgm ((dom <*i*>) \ (<*i*> " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*i*>) \ (<*i*> " x))) * <*i*> is Relation-like NAT -defined Function-like finite countable set
i is set
D is set
x is set
<*i,x*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
(<*i,x*>,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*i,x*> is non empty finite 2 -element countable Element of K27(NAT)
<*i,x*> " D is finite countable set
(dom <*i,x*>) \ (<*i,x*> " D) is finite countable Element of K27(NAT)
Sgm ((dom <*i,x*>) \ (<*i,x*> " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*i,x*>) \ (<*i,x*> " D))) * <*i,x*> is Relation-like NAT -defined Function-like finite countable set
<*x*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
(<*x*>,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*x*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*x*> " D is finite countable set
(dom <*x*>) \ (<*x*> " D) is finite countable Element of K27(NAT)
Sgm ((dom <*x*>) \ (<*x*> " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*x*>) \ (<*x*> " D))) * <*x*> is Relation-like NAT -defined Function-like finite countable set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
<*i*> ^ <*x*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like countable set
1 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(<*i*>,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*i*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*i*> " D is finite countable set
(dom <*i*>) \ (<*i*> " D) is finite countable Element of K27(NAT)
Sgm ((dom <*i*>) \ (<*i*> " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*i*>) \ (<*i*> " D))) * <*i*> is Relation-like NAT -defined Function-like finite countable set
{} ^ <*x*> is Relation-like NAT -defined Function-like non empty finite {} + 1 -element FinSequence-like FinSubsequence-like countable set
{} + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
i is set
D is set
<*i,D*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
<*D*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
x is set
(<*i,D*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*i,D*> is non empty finite 2 -element countable Element of K27(NAT)
<*i,D*> " x is finite countable set
(dom <*i,D*>) \ (<*i,D*> " x) is finite countable Element of K27(NAT)
Sgm ((dom <*i,D*>) \ (<*i,D*> " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*i,D*>) \ (<*i,D*> " x))) * <*i,D*> is Relation-like NAT -defined Function-like finite countable set
(<*D*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*D*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*D*> " x is finite countable set
(dom <*D*>) \ (<*D*> " x) is finite countable Element of K27(NAT)
Sgm ((dom <*D*>) \ (<*D*> " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*D*>) \ (<*D*> " x))) * <*D*> is Relation-like NAT -defined Function-like finite countable set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
(<*i*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*i*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*i*> " x is finite countable set
(dom <*i*>) \ (<*i*> " x) is finite countable Element of K27(NAT)
Sgm ((dom <*i*>) \ (<*i*> " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*i*>) \ (<*i*> " x))) * <*i*> is Relation-like NAT -defined Function-like finite countable set
<*i*> . 1 is set
<*i*> ^ <*D*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like countable set
1 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
((<*i*> ^ <*D*>),x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom (<*i*> ^ <*D*>) is non empty finite 1 + 1 -element countable Element of K27(NAT)
(<*i*> ^ <*D*>) " x is finite countable set
(dom (<*i*> ^ <*D*>)) \ ((<*i*> ^ <*D*>) " x) is finite countable Element of K27(NAT)
Sgm ((dom (<*i*> ^ <*D*>)) \ ((<*i*> ^ <*D*>) " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom (<*i*> ^ <*D*>)) \ ((<*i*> ^ <*D*>) " x))) * (<*i*> ^ <*D*>) is Relation-like NAT -defined Function-like finite countable set
(<*i*>,x) ^ (<*D*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i is set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
D is set
x is set
<*i,x*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
(<*i,x*>,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*i,x*> is non empty finite 2 -element countable Element of K27(NAT)
<*i,x*> " D is finite countable set
(dom <*i,x*>) \ (<*i,x*> " D) is finite countable Element of K27(NAT)
Sgm ((dom <*i,x*>) \ (<*i,x*> " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*i,x*>) \ (<*i,x*> " D))) * <*i,x*> is Relation-like NAT -defined Function-like finite countable set
<*x*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
(<*x*>,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*x*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*x*> " D is finite countable set
(dom <*x*>) \ (<*x*> " D) is finite countable Element of K27(NAT)
Sgm ((dom <*x*>) \ (<*x*> " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*x*>) \ (<*x*> " D))) * <*x*> is Relation-like NAT -defined Function-like finite countable set
<*i*> ^ <*x*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like countable set
1 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(<*i*>,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*i*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*i*> " D is finite countable set
(dom <*i*>) \ (<*i*> " D) is finite countable Element of K27(NAT)
Sgm ((dom <*i*>) \ (<*i*> " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*i*>) \ (<*i*> " D))) * <*i*> is Relation-like NAT -defined Function-like finite countable set
<*i*> ^ {} is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable set
i is set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
D is set
<*i,D*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
x is set
(<*i,D*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*i,D*> is non empty finite 2 -element countable Element of K27(NAT)
<*i,D*> " x is finite countable set
(dom <*i,D*>) \ (<*i,D*> " x) is finite countable Element of K27(NAT)
Sgm ((dom <*i,D*>) \ (<*i,D*> " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*i,D*>) \ (<*i,D*> " x))) * <*i,D*> is Relation-like NAT -defined Function-like finite countable set
<*D*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
(<*D*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*D*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*D*> " x is finite countable set
(dom <*D*>) \ (<*D*> " x) is finite countable Element of K27(NAT)
Sgm ((dom <*D*>) \ (<*D*> " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*D*>) \ (<*D*> " x))) * <*D*> is Relation-like NAT -defined Function-like finite countable set
(<*i*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*i*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*i*> " x is finite countable set
(dom <*i*>) \ (<*i*> " x) is finite countable Element of K27(NAT)
Sgm ((dom <*i*>) \ (<*i*> " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*i*>) \ (<*i*> " x))) * <*i*> is Relation-like NAT -defined Function-like finite countable set
<*i*> . 1 is set
<*i*> ^ <*D*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like countable set
1 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
((<*i*> ^ <*D*>),x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom (<*i*> ^ <*D*>) is non empty finite 1 + 1 -element countable Element of K27(NAT)
(<*i*> ^ <*D*>) " x is finite countable set
(dom (<*i*> ^ <*D*>)) \ ((<*i*> ^ <*D*>) " x) is finite countable Element of K27(NAT)
Sgm ((dom (<*i*> ^ <*D*>)) \ ((<*i*> ^ <*D*>) " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom (<*i*> ^ <*D*>)) \ ((<*i*> ^ <*D*>) " x))) * (<*i*> ^ <*D*>) is Relation-like NAT -defined Function-like finite countable set
(<*i*>,x) ^ (<*D*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i is set
D is set
<*i,D*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
x is set
(<*i,D*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*i,D*> is non empty finite 2 -element countable Element of K27(NAT)
<*i,D*> " x is finite countable set
(dom <*i,D*>) \ (<*i,D*> " x) is finite countable Element of K27(NAT)
Sgm ((dom <*i,D*>) \ (<*i,D*> " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*i,D*>) \ (<*i,D*> " x))) * <*i,D*> is Relation-like NAT -defined Function-like finite countable set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
<*D*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
<*i*> ^ <*D*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like countable set
1 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(<*D*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*D*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*D*> " x is finite countable set
(dom <*D*>) \ (<*D*> " x) is finite countable Element of K27(NAT)
Sgm ((dom <*D*>) \ (<*D*> " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*D*>) \ (<*D*> " x))) * <*D*> is Relation-like NAT -defined Function-like finite countable set
(<*i*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*i*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*i*> " x is finite countable set
(dom <*i*>) \ (<*i*> " x) is finite countable Element of K27(NAT)
Sgm ((dom <*i*>) \ (<*i*> " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*i*>) \ (<*i*> " x))) * <*i*> is Relation-like NAT -defined Function-like finite countable set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
x is set
(i,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " x is finite countable set
(dom i) \ (i " x) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " x))) * i is Relation-like NAT -defined Function-like finite countable set
(D,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom D is finite countable Element of K27(NAT)
D " x is finite countable set
(dom D) \ (D " x) is finite countable Element of K27(NAT)
Sgm ((dom D) \ (D " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom D) \ (D " x))) * D is Relation-like NAT -defined Function-like finite countable set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
n + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg n is finite n -element countable Element of K27(NAT)
i | (Seg n) is Relation-like NAT -defined Seg n -defined NAT -defined Function-like finite FinSubsequence-like countable set
i . (n + 1) is set
<*(i . (n + 1))*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
D ^ <*(i . (n + 1))*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable set
((D ^ <*(i . (n + 1))*>),x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom (D ^ <*(i . (n + 1))*>) is non empty finite countable Element of K27(NAT)
(D ^ <*(i . (n + 1))*>) " x is finite countable set
(dom (D ^ <*(i . (n + 1))*>)) \ ((D ^ <*(i . (n + 1))*>) " x) is finite countable Element of K27(NAT)
Sgm ((dom (D ^ <*(i . (n + 1))*>)) \ ((D ^ <*(i . (n + 1))*>) " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom (D ^ <*(i . (n + 1))*>)) \ ((D ^ <*(i . (n + 1))*>) " x))) * (D ^ <*(i . (n + 1))*>) is Relation-like NAT -defined Function-like finite countable set
(<*(i . (n + 1))*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*(i . (n + 1))*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*(i . (n + 1))*> " x is finite countable set
(dom <*(i . (n + 1))*>) \ (<*(i . (n + 1))*> " x) is finite countable Element of K27(NAT)
Sgm ((dom <*(i . (n + 1))*>) \ (<*(i . (n + 1))*> " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*(i . (n + 1))*>) \ (<*(i . (n + 1))*> " x))) * <*(i . (n + 1))*> is Relation-like NAT -defined Function-like finite countable set
(D,x) ^ (<*(i . (n + 1))*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
(D,x) ^ {} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
<*(i . (n + 1))*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
D ^ <*(i . (n + 1))*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable set
((D ^ <*(i . (n + 1))*>),x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom (D ^ <*(i . (n + 1))*>) is non empty finite countable Element of K27(NAT)
(D ^ <*(i . (n + 1))*>) " x is finite countable set
(dom (D ^ <*(i . (n + 1))*>)) \ ((D ^ <*(i . (n + 1))*>) " x) is finite countable Element of K27(NAT)
Sgm ((dom (D ^ <*(i . (n + 1))*>)) \ ((D ^ <*(i . (n + 1))*>) " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom (D ^ <*(i . (n + 1))*>)) \ ((D ^ <*(i . (n + 1))*>) " x))) * (D ^ <*(i . (n + 1))*>) is Relation-like NAT -defined Function-like finite countable set
(<*(i . (n + 1))*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*(i . (n + 1))*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*(i . (n + 1))*> " x is finite countable set
(dom <*(i . (n + 1))*>) \ (<*(i . (n + 1))*> " x) is finite countable Element of K27(NAT)
Sgm ((dom <*(i . (n + 1))*>) \ (<*(i . (n + 1))*> " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*(i . (n + 1))*>) \ (<*(i . (n + 1))*> " x))) * <*(i . (n + 1))*> is Relation-like NAT -defined Function-like finite countable set
(D,x) ^ (<*(i . (n + 1))*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
(D,x) ^ <*(i . (n + 1))*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
x is set
(i,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " x is finite countable set
(dom i) \ (i " x) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " x))) * i is Relation-like NAT -defined Function-like finite countable set
(D,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom D is finite countable Element of K27(NAT)
D " x is finite countable set
(dom D) \ (D " x) is finite countable Element of K27(NAT)
Sgm ((dom D) \ (D " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom D) \ (D " x))) * D is Relation-like NAT -defined Function-like finite countable set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
n + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg n is finite n -element countable Element of K27(NAT)
i | (Seg n) is Relation-like NAT -defined Seg n -defined NAT -defined Function-like finite FinSubsequence-like countable set
i . (n + 1) is set
<*(i . (n + 1))*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
(D,x) ^ <*(i . (n + 1))*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable set
D ^ <*(i . (n + 1))*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable set
((D ^ <*(i . (n + 1))*>),x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom (D ^ <*(i . (n + 1))*>) is non empty finite countable Element of K27(NAT)
(D ^ <*(i . (n + 1))*>) " x is finite countable set
(dom (D ^ <*(i . (n + 1))*>)) \ ((D ^ <*(i . (n + 1))*>) " x) is finite countable Element of K27(NAT)
Sgm ((dom (D ^ <*(i . (n + 1))*>)) \ ((D ^ <*(i . (n + 1))*>) " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom (D ^ <*(i . (n + 1))*>)) \ ((D ^ <*(i . (n + 1))*>) " x))) * (D ^ <*(i . (n + 1))*>) is Relation-like NAT -defined Function-like finite countable set
(<*(i . (n + 1))*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom <*(i . (n + 1))*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*(i . (n + 1))*> " x is finite countable set
(dom <*(i . (n + 1))*>) \ (<*(i . (n + 1))*> " x) is finite countable Element of K27(NAT)
Sgm ((dom <*(i . (n + 1))*>) \ (<*(i . (n + 1))*> " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom <*(i . (n + 1))*>) \ (<*(i . (n + 1))*> " x))) * <*(i . (n + 1))*> is Relation-like NAT -defined Function-like finite countable set
(D,x) ^ (<*(i . (n + 1))*>,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom D is finite countable Element of K27(NAT)
x is set
(D,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
D " x is finite countable set
(dom D) \ (D " x) is finite countable Element of K27(NAT)
Sgm ((dom D) \ (D " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom D) \ (D " x))) * D is Relation-like NAT -defined Function-like finite countable set
Seg i is finite i -element countable Element of K27(NAT)
D | (Seg i) is Relation-like NAT -defined Seg i -defined NAT -defined Function-like finite FinSubsequence-like countable set
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
{ b₁ where b₁ is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT : ( b₁ in dom D & b₁ <= m9 & D . b₁ in x ) } is set
D . m9 is set
dom n is finite countable Element of K27(NAT)
{ b₁ where b₁ is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT : ( b₁ in dom n & b₁ <= m9 & n . b₁ in x ) } is set
n is set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n . n is set
n is finite countable set
card n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
m9 - (card n) is ext-real V25() V26() V33() set
(D,x) . (m9 - (card n)) is set
D . (i + 1) is set
Seg (i + 1) is non empty finite i + 1 -element countable Element of K27(NAT)
{(i + 1)} is non empty trivial finite V40() 1 -element countable set
(Seg (i + 1)) \ {(i + 1)} is finite countable Element of K27(NAT)
n is finite countable set
t is set
g is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n . g is set
D . g is set
t is set
g is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D . g is set
Seg (len D) is finite len D -element countable Element of K27(NAT)
n . g is set
(n,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
n " x is finite countable set
(dom n) \ (n " x) is finite countable Element of K27(NAT)
Sgm ((dom n) \ (n " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom n) \ (n " x))) * n is Relation-like NAT -defined Function-like finite countable set
n . m9 is set
D . (i + 1) is set
(n,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
n " x is finite countable set
(dom n) \ (n " x) is finite countable Element of K27(NAT)
Sgm ((dom n) \ (n " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom n) \ (n " x))) * n is Relation-like NAT -defined Function-like finite countable set
<*(D . (i + 1))*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
(n,x) ^ <*(D . (i + 1))*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable set
t is set
D . t is set
g is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg m9 is finite m9 -element countable Element of K27(NAT)
t is set
g is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D . g is set
len (D,x) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len <*(D . (i + 1))*> is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
len (n,x) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len (n,x)) + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(D,x) . ((len (n,x)) + 1) is set
{(i + 1)} is non empty trivial finite V40() 1 -element countable set
Seg (i + 1) is non empty finite i + 1 -element countable Element of K27(NAT)
(Seg (i + 1)) \ {(i + 1)} is finite countable Element of K27(NAT)
Seg m9 is finite m9 -element countable Element of K27(NAT)
{m9} is non empty trivial finite V40() 1 -element countable set
n is finite countable set
(Seg m9) \ n is finite countable Element of K27(NAT)
(Seg i) \ (n " x) is finite countable Element of K27(NAT)
t is set
g is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n . g is set
t is set
g is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n . g is set
D . g is set
t is set
g is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D . g is set
Seg (len D) is finite len D -element countable Element of K27(NAT)
n . g is set
(n " x) \/ ((Seg i) \ (n " x)) is finite countable set
(n " x) \/ (Seg i) is finite countable set
card (Seg i) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card (n " x) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card ((Seg i) \ (n " x)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(card (n " x)) + (card ((Seg i) \ (n " x))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len n) is finite len n -element countable Element of K27(NAT)
(Seg (len n)) \ (n " x) is finite countable Element of K27(NAT)
card ((Seg (len n)) \ (n " x)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(card (n " x)) + (card ((Seg (len n)) \ (n " x))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
m9 - (card n) is ext-real V25() V26() V33() set
card (Seg m9) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n . m9 is set
(Seg m9) \ {m9} is finite countable Element of K27(NAT)
a is set
f is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n . f is set
card ((Seg m9) \ {m9}) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card {m9} is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(card (Seg m9)) - (card {m9}) is ext-real V25() V26() V33() set
(card (Seg m9)) - 1 is ext-real V25() V26() V33() set
m9 - 1 is ext-real V25() V26() V33() set
(card n) + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(m9 - (card n)) + (card n) is ext-real V25() V26() V33() set
0 + (card n) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
a is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card ((Seg m9) \ n) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len n) - (card (n " x)) is ext-real V25() V26() V33() set
len (n,x) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len (n,x)) is finite len (n,x) -element countable Element of K27(NAT)
dom (n,x) is finite countable Element of K27(NAT)
(n,x) . (m9 - (card n)) is set
D . (i + 1) is set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom i is finite countable Element of K27(NAT)
D is set
(i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i " D is finite countable set
(dom i) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
n is finite countable set
{ b₁ where b₁ is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT : ( b₁ in dom i & b₁ <= x & i . b₁ in D ) } is set
i . x is set
card n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
x - (card n) is ext-real V25() V26() V33() set
(i,D) . (x - (card n)) is set
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
dom D is finite countable Element of K27(NAT)
m9 is finite countable set
x is set
{ b₁ where b₁ is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT : ( b₁ in dom D & b₁ <= n & D . b₁ in x ) } is set
D . n is set
(D,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
D " x is finite countable set
(dom D) \ (D " x) is finite countable Element of K27(NAT)
Sgm ((dom D) \ (D " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom D) \ (D " x))) * D is Relation-like NAT -defined Function-like finite countable set
card m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n - (card m9) is ext-real V25() V26() V33() set
(D,x) . (n - (card m9)) is set
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
dom D is finite countable Element of K27(NAT)
m9 is finite countable set
x is set
{ b₁ where b₁ is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT : ( b₁ in dom D & b₁ <= n & D . b₁ in x ) } is set
D . n is set
(D,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
D " x is finite countable set
(dom D) \ (D " x) is finite countable Element of K27(NAT)
Sgm ((dom D) \ (D " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom D) \ (D " x))) * D is Relation-like NAT -defined Function-like finite countable set
card m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n - (card m9) is ext-real V25() V26() V33() set
(D,x) . (n - (card m9)) is set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
D is set
(i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i " D is finite countable set
(dom i) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
{ b₁ where b₁ is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT : ( b₁ in dom i & b₁ <= x & i . b₁ in D ) } is set
i . x is set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is finite countable set
card n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
x - (card n) is ext-real V25() V26() V33() set
(i,D) . (x - (card n)) is set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
D is set
x is set
(i,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " x is finite countable set
(dom i) \ (i " x) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " x)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " x))) * i is Relation-like NAT -defined Function-like finite countable set
rng i is finite countable set
rng (i,x) is finite countable set
(rng i) \ x is finite countable Element of K27((rng i))
K27((rng i)) is non empty finite V40() countable set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
D is set
(i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " D is finite countable set
(dom i) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len i) is finite len i -element countable Element of K27(NAT)
(Seg (len i)) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((Seg (len i)) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((Seg (len i)) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
rng i is finite countable set
D is set
(i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " D is finite countable set
(dom i) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
len (i,D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D /\ (rng i) is finite countable set
card (D /\ (rng i)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len i) - (card (D /\ (rng i))) is ext-real V25() V26() V33() set
x is Relation-like Function-like set
dom x is set
rng x is set
n is set
x . n is set
m9 is set
x . m9 is set
i . m9 is set
i . n is set
n is set
m9 is set
x . m9 is set
i . m9 is set
n is set
m9 is set
i . m9 is set
x . m9 is set
card (i " D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
rng i is finite countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D is finite countable set
(i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " D is finite countable set
(dom i) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
len (i,D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len i) - (card D) is ext-real V25() V26() V33() set
D /\ (rng i) is finite countable set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
rng i is finite countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len i) - 1 is ext-real V25() V26() V33() set
D is set
{D} is non empty trivial finite 1 -element countable set
(i,{D}) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
i " {D} is finite countable set
(dom i) \ (i " {D}) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " {D})) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " {D}))) * i is Relation-like NAT -defined Function-like finite countable set
len (i,{D}) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card {D} is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(len i) - (card {D}) is ext-real V25() V26() V33() set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
rng i is finite countable set
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
rng D is finite countable set
i ^ D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
x is set
dom (i ^ D) is finite countable set
(i ^ D) . x is set
n is set
(i ^ D) . n is set
dom (i ^ D) is finite countable Element of K27(NAT)
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom i is finite countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(i ^ D) . n is set
i . n is set
(i ^ D) . m9 is set
i . m9 is set
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom i is finite countable Element of K27(NAT)
dom D is finite countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D . n is set
(i ^ D) . m9 is set
i . m9 is set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(i ^ D) . n is set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom i is finite countable Element of K27(NAT)
dom D is finite countable Element of K27(NAT)
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D . n is set
(i ^ D) . n is set
i . n is set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(i ^ D) . m9 is set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom D is finite countable Element of K27(NAT)
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(i ^ D) . n is set
D . n is set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
t is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + t is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(i ^ D) . m9 is set
D . n is set
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom i is finite countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom D is finite countable Element of K27(NAT)
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
x is set
dom i is finite countable Element of K27(NAT)
n is set
i . n is set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len i) is finite len i -element countable Element of K27(NAT)
dom D is finite countable Element of K27(NAT)
m9 is set
D . m9 is set
len D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len D) is finite len D -element countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom (i ^ D) is finite countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(i ^ D) . n is set
i . n is set
(i ^ D) . ((len i) + n) is set
D . n is set
n + 0 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
x is set
dom i is finite countable set
i . x is set
n is set
i . n is set
dom i is finite countable Element of K27(NAT)
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(i ^ D) . m9 is set
i . m9 is set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(i ^ D) . n is set
i . n is set
dom (i ^ D) is finite countable Element of K27(NAT)
x is set
dom D is finite countable set
D . x is set
n is set
D . n is set
dom D is finite countable Element of K27(NAT)
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom (i ^ D) is finite countable Element of K27(NAT)
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(i ^ D) . ((len i) + m9) is set
D . m9 is set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(len i) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(i ^ D) . ((len i) + n) is set
D . n is set
i is set
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg D is finite D -element countable Element of K27(NAT)
Sgm i is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
i is set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
D is set
dom <*i*> is non empty trivial finite 1 -element countable set
<*i*> . D is set
x is set
<*i*> . x is set
dom <*i*> is non empty trivial finite 1 -element countable Element of K27(NAT)
i is set
D is set
<*i,D*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
<*i,D*> . 2 is set
dom <*i,D*> is non empty finite 2 -element countable Element of K27(NAT)
x is set
dom <*i,D*> is non empty finite 2 -element countable set
<*i,D*> . x is set
n is set
<*i,D*> . n is set
<*i,D*> . 1 is set
i is set
D is set
x is set
<*i,D,x*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like countable set
<*i,D,x*> . 1 is set
<*i,D,x*> . 3 is set
{i,D} is non empty finite countable set
{x} is non empty trivial finite 1 -element countable set
{i,D} /\ {x} is finite countable set
the Element of {i,D} /\ {x} is Element of {i,D} /\ {x}
<*i,D*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
rng <*i,D*> is non empty finite countable set
(rng <*i,D*>) /\ {x} is finite countable set
<*x*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
rng <*x*> is non empty trivial finite 1 -element countable set
(rng <*i,D*>) /\ (rng <*x*>) is finite countable set
<*i,D*> ^ <*x*> is Relation-like NAT -defined Function-like non empty finite 2 + 1 -element FinSequence-like FinSubsequence-like countable set
2 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
<*i,D,x*> . 2 is set
dom <*i,D,x*> is non empty finite 3 -element countable Element of K27(NAT)
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
rng i is finite countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D is set
{D} is non empty trivial finite 1 -element countable set
dom i is finite countable Element of K27(NAT)
x is set
n is set
i . n is set
i . x is set
the Element of dom i is Element of dom i
{ the Element of dom i} is non empty trivial finite 1 -element countable set
n is set
n is set
Seg (len i) is finite len i -element countable Element of K27(NAT)
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
rng i is finite countable set
D is set
{D} is non empty trivial finite 1 -element countable set
<*D*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
rng i is finite countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D is set
x is set
{D,x} is non empty finite countable set
<*D,x*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
rng <*D,x*> is non empty finite countable set
len <*D,x*> is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
rng i is finite countable set
D is set
x is set
{D,x} is non empty finite countable set
<*D,x*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
<*x,D*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom i is finite countable Element of K27(NAT)
i . 2 is set
i . 1 is set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
rng i is finite countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D is set
x is set
n is set
{D,x,n} is non empty finite countable set
<*D,x,n*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like countable set
len <*D,x,n*> is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
rng <*D,x,n*> is non empty finite countable set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
rng i is finite countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D is set
x is set
n is set
{D,x,n} is non empty finite countable set
<*D,x,n*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like countable set
i is non empty set
D is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of i
D . 1 is set
len D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len D) - 1 is ext-real V25() V26() V33() set
dom D is finite countable Element of K27(NAT)
n is Element of i
<*n*> is Relation-like NAT -defined i -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable FinSequence of i
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
m9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom m9 is finite countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg (len m9) is finite len m9 -element countable Element of K27(NAT)
n + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(len m9) + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg ((len m9) + 1) is non empty finite (len m9) + 1 -element countable Element of K27(NAT)
D . (n + 1) is set
m9 . n is set
n is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of i
<*n*> ^ n is Relation-like NAT -defined i -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable FinSequence of i
len (<*n*> ^ n) is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
len <*n*> is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len <*n*>) + (len n) is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
1 + ((len D) - 1) is ext-real V25() V26() V33() set
Seg (len D) is finite len D -element countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D . n is set
(<*n*> ^ n) . n is set
n - 1 is ext-real V25() V26() V33() set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom n is finite countable Element of K27(NAT)
(<*n*> ^ n) . n is set
n . n is set
n + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
D . (n + 1) is set
D . n is set
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom D is finite countable Element of K27(NAT)
D . i is set
x is set
<*x*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
<*x*> ^ D is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable set
(<*x*> ^ D) . (i + 1) is set
len (<*x*> ^ D) is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
len <*x*> is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
len D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len <*x*>) + (len D) is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
1 + (len D) is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len D) is finite len D -element countable Element of K27(NAT)
Seg (len (<*x*> ^ D)) is non empty finite len (<*x*> ^ D) -element countable Element of K27(NAT)
dom (<*x*> ^ D) is non empty finite countable Element of K27(NAT)
(i + 1) - (len <*x*>) is ext-real V25() V26() V33() set
D . ((i + 1) - (len <*x*>)) is set
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom D is finite countable Element of K27(NAT)
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
{i} is non empty trivial finite V40() 1 -element countable set
(dom D) \ {i} is finite countable Element of K27(NAT)
Sgm ((dom D) \ {i}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom D) \ {i})) * D is Relation-like NAT -defined Function-like finite countable set
len D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len D) is finite len D -element countable Element of K27(NAT)
(Seg (len D)) \ {i} is finite countable Element of K27(NAT)
rng (Sgm ((dom D) \ {i})) is finite countable Element of K27(NAT)
dom ((Sgm ((dom D) \ {i})) * D) is finite countable Element of K27(NAT)
dom (Sgm ((dom D) \ {i})) is finite countable Element of K27(NAT)
len (Sgm ((dom D) \ {i})) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len (Sgm ((dom D) \ {i}))) is finite len (Sgm ((dom D) \ {i})) -element countable Element of K27(NAT)
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom D is finite countable Element of K27(NAT)
len D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
{i} is non empty trivial finite V40() 1 -element countable set
(dom D) \ {i} is finite countable Element of K27(NAT)
Sgm ((dom D) \ {i}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom D) \ {i})) * D is Relation-like NAT -defined Function-like finite countable set
len (i,D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len D) is finite len D -element countable Element of K27(NAT)
(Seg (len D)) \ {i} is finite countable Element of K27(NAT)
((Seg (len D)) \ {i}) \/ {i} is non empty finite countable set
card (((Seg (len D)) \ {i}) \/ {i}) is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
card ((Seg (len D)) \ {i}) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(card ((Seg (len D)) \ {i})) + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
rng D is finite countable set
x is non empty set
n is non empty set
K28(x,n) is Relation-like non empty set
K27(K28(x,n)) is non empty set
n is set
Sgm ((Seg (len D)) \ {i}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
rng (Sgm ((Seg (len D)) \ {i})) is finite countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
n + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
n is Relation-like NAT -defined x -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of x
m9 is Relation-like x -defined n -valued Function-like non empty total quasi_total Element of K27(K28(x,n))
m9 * n is Relation-like NAT -defined n -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of n
len (m9 * n) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
t is set
card (Seg (len D)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
n + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
len (Sgm ((Seg (len D)) \ {i})) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
x is set
Sgm (dom D) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm (dom D)) * D is Relation-like NAT -defined Function-like finite countable set
Sgm (Seg (len D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm (Seg (len D))) * D is Relation-like NAT -defined Function-like finite countable set
idseq (len D) is Relation-like NAT -defined Function-like finite len D -element FinSequence-like FinSubsequence-like countable set
id (Seg (len D)) is Relation-like Seg (len D) -defined Seg (len D) -valued Function-like one-to-one total quasi_total finite countable Element of K27(K28((Seg (len D)),(Seg (len D))))
K28((Seg (len D)),(Seg (len D))) is Relation-like finite countable set
K27(K28((Seg (len D)),(Seg (len D)))) is non empty finite V40() countable set
(idseq (len D)) * D is Relation-like NAT -defined Function-like finite countable set
D | (Seg (len D)) is Relation-like NAT -defined Seg (len D) -defined NAT -defined Function-like finite FinSubsequence-like countable set
D | (dom D) is Relation-like NAT -defined dom D -defined NAT -defined Function-like finite FinSubsequence-like countable set
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D is non empty set
x is Relation-like NAT -defined D -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of D
(i,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom x is finite countable Element of K27(NAT)
{i} is non empty trivial finite V40() 1 -element countable set
(dom x) \ {i} is finite countable Element of K27(NAT)
Sgm ((dom x) \ {i}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom x) \ {i})) * x is Relation-like NAT -defined D -valued Function-like finite countable set
len x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len x) is finite len x -element countable Element of K27(NAT)
(Seg (len x)) \ {i} is finite countable Element of K27(NAT)
m9 is set
Sgm ((Seg (len x)) \ {i}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
rng (Sgm ((Seg (len x)) \ {i})) is finite countable Element of K27(NAT)
n is non empty set
m9 is Relation-like NAT -defined n -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of n
x * m9 is Relation-like NAT -defined D -valued Function-like finite countable Element of K27(K28(NAT,D))
K28(NAT,D) is Relation-like non empty non trivial non finite set
K27(K28(NAT,D)) is non empty non trivial non finite set
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
(i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom D is finite countable Element of K27(NAT)
{i} is non empty trivial finite V40() 1 -element countable set
(dom D) \ {i} is finite countable Element of K27(NAT)
Sgm ((dom D) \ {i}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom D) \ {i})) * D is Relation-like NAT -defined Function-like finite countable set
rng (i,D) is finite countable set
rng D is finite countable set
x is set
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg i is finite i -element countable Element of K27(NAT)
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
{x} is non empty trivial finite V40() 1 -element countable set
(Seg i) \ {x} is finite countable Element of K27(NAT)
Sgm ((Seg i) \ {x}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
len (Sgm ((Seg i) \ {x})) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card ((Seg i) \ {x}) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(card ((Seg i) \ {x})) + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
((Seg i) \ {x}) \/ {x} is non empty finite countable set
card (((Seg i) \ {x}) \/ {x}) is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(Seg i) \/ {x} is non empty finite countable set
card ((Seg i) \/ {x}) is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
card (Seg i) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
x + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg n is finite n -element countable Element of K27(NAT)
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg x is finite x -element countable Element of K27(NAT)
{D} is non empty trivial finite V40() 1 -element countable set
(Seg n) \ {D} is finite countable Element of K27(NAT)
Sgm ((Seg n) \ {D}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((Seg n) \ {D})) . i is set
i + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
m9 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg m9 is finite m9 -element countable Element of K27(NAT)
(m9 + 1) + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (m9 + 1) is non empty finite m9 + 1 -element countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg n is finite n -element countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
{n} is non empty trivial finite V40() 1 -element countable set
(Seg n) \ {n} is finite countable Element of K27(NAT)
Sgm ((Seg n) \ {n}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((Seg n) \ {n})) . n is set
n + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(m9 + 1) + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
len (Sgm ((Seg n) \ {n})) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
rng (Sgm ((Seg n) \ {n})) is finite countable Element of K27(NAT)
g is set
{ b₁ where b₁ is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT : ( 1 <= b₁ & b₁ <= n ) } is set
a is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
g is set
{ b₁ where b₁ is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT : ( 1 <= b₁ & b₁ <= m9 + 1 ) } is set
a is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
idseq (m9 + 1) is Relation-like NAT -defined Function-like finite m9 + 1 -element FinSequence-like FinSubsequence-like countable set
id (Seg (m9 + 1)) is Relation-like Seg (m9 + 1) -defined Seg (m9 + 1) -valued Function-like one-to-one non empty total quasi_total finite countable Element of K27(K28((Seg (m9 + 1)),(Seg (m9 + 1))))
K28((Seg (m9 + 1)),(Seg (m9 + 1))) is Relation-like non empty finite countable set
K27(K28((Seg (m9 + 1)),(Seg (m9 + 1)))) is non empty finite V40() countable set
{ b₁ where b₁ is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT : ( 1 <= b₁ & b₁ <= n & not b₁ = n ) } is set
a is set
{ b₁ where b₁ is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT : ( 1 <= b₁ & b₁ <= n ) } is set
f is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
a is set
f is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom (Sgm ((Seg n) \ {n})) is finite countable Element of K27(NAT)
(Sgm ((Seg n) \ {n})) . (m9 + 1) is set
a is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(Sgm ((Seg n) \ {n})) . a is set
f is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(Seg (m9 + 1)) \ {n} is finite countable Element of K27(NAT)
w is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
s is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
{n} is non empty trivial finite V40() 1 -element countable set
((Seg (m9 + 1)) \ {n}) \/ {n} is non empty finite countable set
w is set
s is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
w is set
{ b₁ where b₁ is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT : ( 1 <= b₁ & b₁ <= m9 + 1 ) } is set
s is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Sgm ((Seg (m9 + 1)) \ {n}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
Sgm {n} is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((Seg (m9 + 1)) \ {n})) ^ (Sgm {n}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
len (Sgm ((Seg (m9 + 1)) \ {n})) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom (Sgm ((Seg (m9 + 1)) \ {n})) is finite countable Element of K27(NAT)
(Sgm ((Seg (m9 + 1)) \ {n})) . n is set
Seg (len (Sgm ((Seg (m9 + 1)) \ {n}))) is finite len (Sgm ((Seg (m9 + 1)) \ {n})) -element countable Element of K27(NAT)
0 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg 0 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty proper V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal 0 -element {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable Element of K27(NAT)
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg m9 is finite m9 -element countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
{n} is non empty trivial finite V40() 1 -element countable set
(Seg m9) \ {n} is finite countable Element of K27(NAT)
Sgm ((Seg m9) \ {n}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((Seg m9) \ {n})) . n is set
n + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom x is finite countable Element of K27(NAT)
(D,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
{D} is non empty trivial finite V40() 1 -element countable set
(dom x) \ {D} is finite countable Element of K27(NAT)
Sgm ((dom x) \ {D}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom x) \ {D})) * x is Relation-like NAT -defined Function-like finite countable set
len (D,x) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
n + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
(D,x) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom x is finite countable Element of K27(NAT)
{D} is non empty trivial finite V40() 1 -element countable set
(dom x) \ {D} is finite countable Element of K27(NAT)
Sgm ((dom x) \ {D}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom x) \ {D})) * x is Relation-like NAT -defined Function-like finite countable set
(D,x) . i is set
x . i is set
len x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
n + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
dom (Sgm ((dom x) \ {D})) is finite countable Element of K27(NAT)
len (Sgm ((dom x) \ {D})) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len (Sgm ((dom x) \ {D}))) is finite len (Sgm ((dom x) \ {D})) -element countable Element of K27(NAT)
Seg (len x) is finite len x -element countable Element of K27(NAT)
rng (Sgm ((dom x) \ {D})) is finite countable Element of K27(NAT)
dom ((Sgm ((dom x) \ {D})) * x) is finite countable Element of K27(NAT)
Seg n is finite n -element countable Element of K27(NAT)
(Sgm ((dom x) \ {D})) . i is set
len (D,x) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len (D,x)) is finite len (D,x) -element countable Element of K27(NAT)
Seg n is finite n -element countable Element of K27(NAT)
dom (D,x) is finite countable Element of K27(NAT)
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
x + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom n is finite countable Element of K27(NAT)
(D,n) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
{D} is non empty trivial finite V40() 1 -element countable set
(dom n) \ {D} is finite countable Element of K27(NAT)
Sgm ((dom n) \ {D}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom n) \ {D})) * n is Relation-like NAT -defined Function-like finite countable set
(D,n) . x is set
n . (x + 1) is set
Seg (len n) is finite len n -element countable Element of K27(NAT)
rng (Sgm ((dom n) \ {D})) is finite countable Element of K27(NAT)
dom ((Sgm ((dom n) \ {D})) * n) is finite countable Element of K27(NAT)
dom (Sgm ((dom n) \ {D})) is finite countable Element of K27(NAT)
len (Sgm ((dom n) \ {D})) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len (Sgm ((dom n) \ {D}))) is finite len (Sgm ((dom n) \ {D})) -element countable Element of K27(NAT)
Seg i is finite i -element countable Element of K27(NAT)
(Sgm ((dom n) \ {D})) . x is set
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
x | D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
(x | D) . i is set
x . i is set
dom x is finite countable Element of K27(NAT)
dom (x | D) is finite countable Element of K27(NAT)
Seg D is finite D -element countable Element of K27(NAT)
x | (Seg D) is Relation-like NAT -defined Seg D -defined NAT -defined Function-like finite FinSubsequence-like countable set
(x | (Seg D)) . i is set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
D | (len i) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom i is finite countable Element of K27(NAT)
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
i . x is set
(D | (len i)) . x is set
D . x is set
len D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len (D | (len i)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom (D | (len i)) is finite countable Element of K27(NAT)
i is set
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
D " i is finite countable set
Sgm (D " i) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
rng D is finite countable set
(rng D) \ i is finite countable Element of K27((rng D))
K27((rng D)) is non empty finite V40() countable set
D " ((rng D) \ i) is finite countable set
Sgm (D " ((rng D) \ i)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm (D " i)) ^ (Sgm (D " ((rng D) \ i))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
dom D is finite countable Element of K27(NAT)
K28((dom D),(dom D)) is Relation-like finite countable set
K27(K28((dom D),(dom D))) is non empty finite V40() countable set
len D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len D) is finite len D -element countable Element of K27(NAT)
i /\ ((rng D) \ i) is finite countable Element of K27((rng D))
(D " i) /\ (D " ((rng D) \ i)) is finite countable set
D " (i /\ ((rng D) \ i)) is finite countable set
rng (Sgm (D " i)) is finite countable Element of K27(NAT)
rng (Sgm (D " ((rng D) \ i))) is finite countable Element of K27(NAT)
(rng (Sgm (D " i))) /\ (rng (Sgm (D " ((rng D) \ i)))) is finite countable Element of K27(NAT)
(D " i) /\ (rng (Sgm (D " ((rng D) \ i)))) is finite countable Element of K27(NAT)
rng ((Sgm (D " i)) ^ (Sgm (D " ((rng D) \ i)))) is finite countable Element of K27(NAT)
(rng (Sgm (D " i))) \/ (rng (Sgm (D " ((rng D) \ i)))) is finite countable Element of K27(NAT)
(D " i) \/ (rng (Sgm (D " ((rng D) \ i)))) is finite countable set
(D " i) \/ (D " ((rng D) \ i)) is finite countable set
i \/ ((rng D) \ i) is set
D " (i \/ ((rng D) \ i)) is finite countable set
(rng D) \/ i is set
D " ((rng D) \/ i) is finite countable set
D " (rng D) is finite countable set
(D " (rng D)) \/ (D " i) is finite countable set
(dom D) \/ (D " i) is finite countable set
len ((Sgm (D " i)) ^ (Sgm (D " ((rng D) \ i)))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len (Sgm (D " i)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len (Sgm (D " ((rng D) \ i))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len (Sgm (D " i))) + (len (Sgm (D " ((rng D) \ i)))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card (D " i) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(card (D " i)) + (len (Sgm (D " ((rng D) \ i)))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card (D " ((rng D) \ i)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(card (D " i)) + (card (D " ((rng D) \ i))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card ((D " i) \/ (D " ((rng D) \ i))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Sgm ((D " i) \/ (D " ((rng D) \ i))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
len (Sgm ((D " i) \/ (D " ((rng D) \ i)))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Sgm (D " (i \/ ((rng D) \ i))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
len (Sgm (D " (i \/ ((rng D) \ i)))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Sgm (D " ((rng D) \/ i)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
len (Sgm (D " ((rng D) \/ i))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Sgm ((D " (rng D)) \/ (D " i)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
len (Sgm ((D " (rng D)) \/ (D " i))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Sgm ((dom D) \/ (D " i)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
len (Sgm ((dom D) \/ (D " i))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Sgm (dom D) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
len (Sgm (dom D)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card (Seg (len D)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom ((Sgm (D " i)) ^ (Sgm (D " ((rng D) \ i)))) is finite countable Element of K27(NAT)
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
rng i is finite countable set
K27((rng i)) is non empty finite V40() countable set
dom i is finite countable Element of K27(NAT)
K28((dom i),(dom i)) is Relation-like finite countable set
K27(K28((dom i),(dom i))) is non empty finite V40() countable set
D is finite countable Element of K27((rng i))
D ` is finite countable Element of K27((rng i))
(i,(D `)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i " (D `) is finite countable set
(dom i) \ (i " (D `)) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " (D `))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " (D `)))) * i is Relation-like NAT -defined Function-like finite countable set
(i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
i " D is finite countable set
(dom i) \ (i " D) is finite countable Element of K27(NAT)
Sgm ((dom i) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
(i,(D `)) ^ (i,D) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
(rng i) \ D is finite countable Element of K27((rng i))
card (i " (D `)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card (i " D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(card (i " (D `))) + (card (i " D)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(i " (D `)) \/ (i " D) is finite countable set
card ((i " (D `)) \/ (i " D)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(D `) \/ D is finite countable Element of K27((rng i))
i " ((D `) \/ D) is finite countable set
card (i " ((D `) \/ D)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
[#] (rng i) is non proper finite countable Element of K27((rng i))
i " ([#] (rng i)) is finite countable set
card (i " ([#] (rng i))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i " (rng i) is finite countable set
card (i " (rng i)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card (dom i) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len i) - (card (i " (D `))) is ext-real V25() V26() V33() set
(len i) - (card (i " D)) is ext-real V25() V26() V33() set
((len i) - (card (i " (D `)))) + ((len i) - (card (i " D))) is ext-real V25() V26() V33() set
len (i,(D `)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len (i,(D `))) + ((len i) - (card (i " D))) is ext-real V25() V26() V33() set
len (i,D) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len (i,(D `))) + (len (i,D)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
rng (i,(D `)) is finite countable set
(rng i) \ (rng (i,(D `))) is finite countable Element of K27((rng i))
(rng i) \ (D `) is finite countable Element of K27((rng i))
(rng i) \ ((rng i) \ (D `)) is finite countable Element of K27((rng i))
(rng i) \ ((rng i) \ D) is finite countable Element of K27((rng i))
(rng i) \ ((rng i) \ ((rng i) \ D)) is finite countable Element of K27((rng i))
(rng i) /\ D is finite countable Element of K27((rng i))
(rng i) \ ((rng i) /\ D) is finite countable Element of K27((rng i))
rng (i,D) is finite countable set
i " (rng (i,(D `))) is finite countable set
Sgm (i " (rng (i,(D `)))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
i " (rng (i,D)) is finite countable set
Sgm (i " (rng (i,D))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm (i " (rng (i,(D `))))) ^ (Sgm (i " (rng (i,D)))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
m9 is Relation-like dom i -defined dom i -valued Function-like one-to-one total quasi_total onto bijective finite countable Element of K27(K28((dom i),(dom i)))
m9 * i is Relation-like dom i -defined Function-like finite countable set
i " ((rng i) \ D) is finite countable set
(i " (rng i)) \ (i " D) is finite countable Element of K27((i " (rng i)))
K27((i " (rng i))) is non empty finite V40() countable set
(i " (rng i)) \ (i " (D `)) is finite countable Element of K27((i " (rng i)))
card ((i " (rng i)) \ (i " (D `))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(card (i " (rng i))) - (card (i " (D `))) is ext-real V25() V26() V33() set
Seg (len i) is finite len i -element countable Element of K27(NAT)
card (Seg (len i)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(card (Seg (len i))) - (card (i " (D `))) is ext-real V25() V26() V33() set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom (i,(D `)) is finite countable Element of K27(NAT)
dom (Sgm (i " (rng (i,(D `))))) is finite countable Element of K27(NAT)
len (Sgm (i " (rng (i,(D `))))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len (Sgm (i " (rng (i,(D `)))))) is finite len (Sgm (i " (rng (i,(D `))))) -element countable Element of K27(NAT)
card (i " (rng (i,(D `)))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (card (i " (rng (i,(D `))))) is finite card (i " (rng (i,(D `)))) -element countable Element of K27(NAT)
i " ((rng i) \ (D `)) is finite countable set
card (i " ((rng i) \ (D `))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (card (i " ((rng i) \ (D `)))) is finite card (i " ((rng i) \ (D `))) -element countable Element of K27(NAT)
Seg (len (i,(D `))) is finite len (i,(D `)) -element countable Element of K27(NAT)
dom m9 is finite countable Element of K27((dom i))
K27((dom i)) is non empty finite V40() countable set
(m9 * i) . n is set
m9 . n is set
i . (m9 . n) is set
(Sgm (i " (rng (i,(D `))))) . n is set
i . ((Sgm (i " (rng (i,(D `))))) . n) is set
(Sgm (i " (rng (i,(D `))))) * i is Relation-like NAT -defined Function-like finite countable set
((Sgm (i " (rng (i,(D `))))) * i) . n is set
Sgm (i " ((rng i) \ (D `))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm (i " ((rng i) \ (D `)))) * i is Relation-like NAT -defined Function-like finite countable set
((Sgm (i " ((rng i) \ (D `)))) * i) . n is set
i " ((rng i) \ ((rng i) \ D)) is finite countable set
Sgm (i " ((rng i) \ ((rng i) \ D))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm (i " ((rng i) \ ((rng i) \ D)))) * i is Relation-like NAT -defined Function-like finite countable set
((Sgm (i " ((rng i) \ ((rng i) \ D)))) * i) . n is set
i " ((rng i) /\ D) is finite countable set
Sgm (i " ((rng i) /\ D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm (i " ((rng i) /\ D))) * i is Relation-like NAT -defined Function-like finite countable set
((Sgm (i " ((rng i) /\ D))) * i) . n is set
(i " (rng i)) /\ (i " D) is finite countable set
Sgm ((i " (rng i)) /\ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((i " (rng i)) /\ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
((Sgm ((i " (rng i)) /\ (i " D))) * i) . n is set
(dom i) /\ (i " D) is finite countable Element of K27(NAT)
Sgm ((dom i) /\ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((dom i) /\ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
((Sgm ((dom i) /\ (i " D))) * i) . n is set
(i,(D `)) . n is set
card ((i " (rng i)) \ (i " D)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(card (i " (rng i))) - (card (i " D)) is ext-real V25() V26() V33() set
(card (Seg (len i))) - (card (i " D)) is ext-real V25() V26() V33() set
len (Sgm (i " (rng (i,D)))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card (i " (rng (i,D))) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
card (i " ((rng i) \ D)) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom (Sgm (i " (rng (i,D)))) is finite countable Element of K27(NAT)
dom (i,D) is finite countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(len (i,(D `))) + n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(m9 * i) . ((len (i,(D `))) + n) is set
m9 . ((len (i,(D `))) + n) is set
i . (m9 . ((len (i,(D `))) + n)) is set
(Sgm (i " (rng (i,D)))) . n is set
i . ((Sgm (i " (rng (i,D)))) . n) is set
(Sgm (i " (rng (i,D)))) * i is Relation-like NAT -defined Function-like finite countable set
((Sgm (i " (rng (i,D)))) * i) . n is set
Sgm (i " ((rng i) \ D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm (i " ((rng i) \ D))) * i is Relation-like NAT -defined Function-like finite countable set
((Sgm (i " ((rng i) \ D))) * i) . n is set
Sgm ((i " (rng i)) \ (i " D)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm ((i " (rng i)) \ (i " D))) * i is Relation-like NAT -defined Function-like finite countable set
((Sgm ((i " (rng i)) \ (i " D))) * i) . n is set
(i,D) . n is set
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i is Relation-like NAT -defined Function-like FinSubsequence-like set
Seq i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
dom D is finite countable Element of K27(NAT)
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
Seg x is finite x -element countable Element of K27(NAT)
len D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Sgm (Seg x) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
(Sgm (Seg x)) * i is Relation-like NAT -defined Function-like finite countable set
idseq x is Relation-like NAT -defined Function-like finite x -element FinSequence-like FinSubsequence-like countable set
id (Seg x) is Relation-like Seg x -defined Seg x -valued Function-like one-to-one total quasi_total finite countable Element of K27(K28((Seg x),(Seg x)))
K28((Seg x),(Seg x)) is Relation-like finite countable set
K27(K28((Seg x),(Seg x))) is non empty finite V40() countable set
(idseq x) * i is Relation-like NAT -defined Function-like finite countable set
i is Relation-like NAT -defined INT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of INT
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
dom i is finite countable Element of K27(NAT)
i . D is set
rng i is finite countable Element of K27(INT)
K27(INT) is non empty set
i is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom i is finite countable Element of K27(NAT)
D is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom D is finite countable Element of K27(NAT)
i is set
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D -tuples_on i is functional FinSequence-membered FinSequenceSet of i
i * is functional non empty FinSequence-membered FinSequenceSet of i
{ b₁ where b₁ is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of i * : len b₁ = D } is set
0 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
x is functional non empty FinSequence-membered FinSequenceSet of i
the Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of x is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of x
dom the Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of x is finite countable Element of K27(NAT)
m9 is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of i *
len m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
rng the Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of x is finite countable Element of K27(i)
K27(i) is non empty set
<*> i is Relation-like non-empty empty-yielding NAT -defined i -valued Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable FinSequence of i
len (<*> i) is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable Element of NAT
x is non empty set
D -tuples_on x is functional non empty FinSequence-membered FinSequenceSet of x
x * is functional non empty FinSequence-membered FinSequenceSet of x
{ b₁ where b₁ is Relation-like NAT -defined x -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of x * : len b₁ = D } is set
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D is set
i -tuples_on D is functional FinSequence-membered FinSequenceSet of D
D * is functional non empty FinSequence-membered FinSequenceSet of D
{ b₁ where b₁ is Relation-like NAT -defined D -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of D * : len b₁ = i } is set
n is Relation-like Function-like set
m9 is Relation-like Function-like set
dom n is set
dom m9 is set
n is Relation-like NAT -defined D -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of D *
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is Relation-like NAT -defined D -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of D *
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D is set
i -tuples_on D is functional FinSequence-membered with_common_domain FinSequenceSet of D
D * is functional non empty FinSequence-membered FinSequenceSet of D
{ b₁ where b₁ is Relation-like NAT -defined D -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of D * : len b₁ = i } is set
<*> D is Relation-like non-empty empty-yielding NAT -defined D -valued Function-like one-to-one constant functional empty V15() V16() V17() V19() V20() V21() ext-real non positive non negative V25() V26() V33() Function-yielding V35() finite finite-yielding V40() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Cardinal-yielding countable FinSequence of D
{(<*> D)} is functional non empty trivial finite V40() 1 -element with_common_domain countable set
{0} is functional non empty trivial finite V40() 1 -element with_common_domain countable set
0 .--> {} is Relation-like NAT -defined {0} -defined Function-like one-to-one constant trivial Function-yielding V35() finite Cardinal-yielding countable set
{0} --> {} is Relation-like {0} -defined {{}} -valued Function-like constant non empty total quasi_total Function-yielding V35() finite Cardinal-yielding countable Element of K27(K28({0},{{}}))
K28({0},{{}}) is Relation-like non empty finite countable set
K27(K28({0},{{}})) is non empty finite V40() countable set
n is Relation-like NAT -defined {0} -defined Function-like one-to-one constant trivial Function-yielding V35() finite Cardinal-yielding countable set
product n is functional with_common_domain product-like set
rng n is trivial finite countable set
n is non empty set
i -tuples_on n is functional non empty FinSequence-membered with_common_domain FinSequenceSet of n
n * is functional non empty FinSequence-membered FinSequenceSet of n
{ b₁ where b₁ is Relation-like NAT -defined n -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of n * : len b₁ = i } is set
product" (i -tuples_on n) is Relation-like Function-like set
product (product" (i -tuples_on n)) is functional with_common_domain product-like set
n is set
dom (product" (i -tuples_on n)) is set
n is Relation-like Function-like set
dom n is set
the Relation-like NAT -defined n -valued Function-like finite i -element FinSequence-like FinSubsequence-like countable Element of i -tuples_on n is Relation-like NAT -defined n -valued Function-like finite i -element FinSequence-like FinSubsequence-like countable Element of i -tuples_on n
t is Relation-like NAT -defined n -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of n *
len t is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
DOM (i -tuples_on n) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of i -tuples_on n : verum } is set
meet { (dom b₁) where b₁ is Relation-like Function-like Element of i -tuples_on n : verum } is set
dom the Relation-like NAT -defined n -valued Function-like finite i -element FinSequence-like FinSubsequence-like countable Element of i -tuples_on n is finite i -element countable Element of K27(NAT)
Seg (len t) is finite len t -element countable Element of K27(NAT)
rng n is set
g is set
a is set
n . a is set
(product" (i -tuples_on n)) . a is set
pi ((i -tuples_on n),a) is set
f is Relation-like Function-like set
f . a is set
w is Relation-like NAT -defined n -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of n *
len w is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom w is finite countable Element of K27(NAT)
w . a is set
rng w is finite countable Element of K27(n)
K27(n) is non empty set
g is Relation-like NAT -defined n -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of n
len g is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i is non empty set
D is non empty set
K28(i,D) is Relation-like non empty set
K27(K28(i,D)) is non empty set
x is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of i
dom x is finite countable Element of K27(NAT)
len x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is Relation-like i -defined D -valued Function-like non empty total quasi_total Element of K27(K28(i,D))
n * x is Relation-like NAT -defined D -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of D
dom (n * x) is finite countable Element of K27(NAT)
len (n * x) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
rng x is finite countable Element of K27(i)
K27(i) is non empty set
dom n is non empty Element of K27(i)
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
(n * x) . m9 is set
x . m9 is set
n . (x . m9) is set
i is non empty set
K28(i,i) is Relation-like non empty set
K27(K28(i,i)) is non empty set
i * is functional non empty FinSequence-membered FinSequenceSet of i
K28((i *),(i *)) is Relation-like non empty set
K27(K28((i *),(i *))) is non empty set
D is Relation-like i -defined i -valued Element of K27(K28(i,i))
x is Relation-like i * -defined i * -valued Element of K27(K28((i *),(i *)))
n is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of i
m9 is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of i
[n,m9] is V21() set
{n,m9} is functional non empty finite V40() countable set
{n} is functional non empty trivial finite V40() 1 -element with_common_domain countable set
{{n,m9},{n}} is non empty finite V40() countable set
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom n is finite countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n . n is set
m9 . n is set
[(n . n),(m9 . n)] is V21() set
{(n . n),(m9 . n)} is non empty finite countable set
{(n . n)} is non empty trivial finite 1 -element countable set
{{(n . n),(m9 . n)},{(n . n)}} is non empty finite V40() countable set
n is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of i
n is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of i
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom n is finite countable Element of K27(NAT)
n . n is set
n . n is set
[(n . n),(n . n)] is V21() set
{(n . n),(n . n)} is non empty finite countable set
{(n . n)} is non empty trivial finite 1 -element countable set
{{(n . n),(n . n)},{(n . n)}} is non empty finite V40() countable set
x is Relation-like i * -defined i * -valued Element of K27(K28((i *),(i *)))
n is Relation-like i * -defined i * -valued Element of K27(K28((i *),(i *)))
m9 is set
n is set
[m9,n] is V21() set
{m9,n} is non empty finite countable set
{m9} is non empty trivial finite 1 -element countable set
{{m9,n},{m9}} is non empty finite V40() countable set
n is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of i *
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of i *
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom n is finite countable Element of K27(NAT)
t is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n . t is set
n . t is set
[(n . t),(n . t)] is V21() set
{(n . t),(n . t)} is non empty finite countable set
{(n . t)} is non empty trivial finite 1 -element countable set
{{(n . t),(n . t)},{(n . t)}} is non empty finite V40() countable set
n is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of i *
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of i *
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom n is finite countable Element of K27(NAT)
t is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n . t is set
n . t is set
[(n . t),(n . t)] is V21() set
{(n . t),(n . t)} is non empty finite countable set
{(n . t)} is non empty trivial finite 1 -element countable set
{{(n . t),(n . t)},{(n . t)}} is non empty finite V40() countable set
i is non empty set
i * is functional non empty FinSequence-membered FinSequenceSet of i
id i is Relation-like i -defined i -valued Function-like one-to-one non empty total quasi_total Element of K27(K28(i,i))
K28(i,i) is Relation-like non empty set
K27(K28(i,i)) is non empty set
(i,(id i)) is Relation-like i * -defined i * -valued Element of K27(K28((i *),(i *)))
K28((i *),(i *)) is Relation-like non empty set
K27(K28((i *),(i *))) is non empty set
id (i *) is Relation-like i * -defined i * -valued Function-like one-to-one non empty total quasi_total Function-yielding V35() Element of K27(K28((i *),(i *)))
n is set
m9 is set
[n,m9] is V21() set
{n,m9} is non empty finite countable set
{n} is non empty trivial finite 1 -element countable set
{{n,m9},{n}} is non empty finite V40() countable set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
n is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of i *
dom n is finite countable Element of K27(NAT)
n . n is set
n is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of i *
n . n is set
[(n . n),(n . n)] is V21() set
{(n . n),(n . n)} is non empty finite countable set
{(n . n)} is non empty trivial finite 1 -element countable set
{{(n . n),(n . n)},{(n . n)}} is non empty finite V40() countable set
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of i *
n is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of i *
dom n is finite countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n . n is set
n . n is set
[(n . n),(n . n)] is V21() set
{(n . n),(n . n)} is non empty finite countable set
{(n . n)} is non empty trivial finite 1 -element countable set
{{(n . n),(n . n)},{(n . n)}} is non empty finite V40() countable set
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i is non empty set
K28(i,i) is Relation-like non empty set
K27(K28(i,i)) is non empty set
D is Relation-like i -defined i -valued total quasi_total V58() V63() Element of K27(K28(i,i))
Class D is non empty with_non-empty_elements a_partition of i
i is non empty set
K28(i,i) is Relation-like non empty set
K27(K28(i,i)) is non empty set
D is Relation-like i -defined i -valued total quasi_total V58() V63() Element of K27(K28(i,i))
Class D is non empty with_non-empty_elements a_partition of i
x is Relation-like NAT -defined Class D -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of Class D
dom x is finite countable Element of K27(NAT)
n is set
x . n is set
rng x is finite countable Element of K27((Class D))
K27((Class D)) is non empty set
m9 is Element of i
Class (D,m9) is Element of K27(i)
K27(i) is non empty set
n is set
n is Element of i
Class (D,n) is Element of K27(i)
n is Relation-like Function-like set
dom n is set
rng n is set
len x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len x) is finite len x -element countable Element of K27(NAT)
m9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
n is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of i
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
dom n is finite countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n . n is set
Class (D,(n . n)) is Element of K27(i)
K27(i) is non empty set
x . n is set
rng n is finite countable Element of K27(i)
n is Element of i
Class (D,n) is Element of K27(i)
i is set
D is set
<*D*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
product <*D*> is functional with_common_domain product-like set
dom <*D*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*D*> . 1 is set
x is Relation-like Function-like set
dom x is set
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
n . 1 is set
<*(n . 1)*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
x is set
<*x*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
n is set
<*x*> . n is set
<*D*> . n is set
dom <*x*> is non empty trivial finite 1 -element countable Element of K27(NAT)
i is set
D is set
x is set
<*D,x*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
product <*D,x*> is functional with_common_domain product-like set
<*D,x*> . 1 is set
<*D,x*> . 2 is set
len <*D,x*> is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
dom <*D,x*> is non empty finite 2 -element countable Element of K27(NAT)
n is Relation-like Function-like set
dom n is set
m9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
m9 . 1 is set
m9 . 2 is set
<*(m9 . 1),(m9 . 2)*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
len m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is set
m9 is set
<*n,m9*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
n is set
<*n,m9*> . n is set
<*D,x*> . n is set
len <*n,m9*> is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
dom <*n,m9*> is non empty finite 2 -element countable Element of K27(NAT)
i is set
D is set
x is set
n is set
<*D,x,n*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like countable set
product <*D,x,n*> is functional with_common_domain product-like set
<*D,x,n*> . 1 is set
<*D,x,n*> . 2 is set
<*D,x,n*> . 3 is set
len <*D,x,n*> is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
dom <*D,x,n*> is non empty finite 3 -element countable Element of K27(NAT)
m9 is Relation-like Function-like set
dom m9 is set
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
n . 1 is set
n . 2 is set
n . 3 is set
<*(n . 1),(n . 2),(n . 3)*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like countable set
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
m9 is set
n is set
n is set
<*m9,n,n*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like countable set
n is set
<*m9,n,n*> . n is set
<*D,x,n*> . n is set
len <*m9,n,n*> is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
dom <*m9,n,n*> is non empty finite 3 -element countable Element of K27(NAT)
i is non empty set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
product <*i*> is functional with_common_domain product-like set
1 -tuples_on i is functional non empty FinSequence-membered with_common_domain product-like FinSequenceSet of i
i * is functional non empty FinSequence-membered FinSequenceSet of i
{ b₁ where b₁ is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of i * : len b₁ = 1 } is set
1 |-> i is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
(Seg 1) --> i is Relation-like non-empty NAT -defined Seg 1 -defined Seg 1 -defined {i} -valued Function-like constant non empty total total quasi_total finite FinSequence-like FinSubsequence-like countable Element of K27(K28((Seg 1),{i}))
{i} is non empty trivial finite 1 -element countable set
K28((Seg 1),{i}) is Relation-like non empty finite countable set
K27(K28((Seg 1),{i})) is non empty finite V40() countable set
Funcs ((Seg 1),i) is functional non empty FUNCTION_DOMAIN of Seg 1,i
i is non empty set
D is non empty set
<*i,D*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
product <*i,D*> is functional with_common_domain product-like set
{ <*b₁,b₂*> where b₁ is Element of i, b₂ is Element of D : verum } is set
x is set
n is set
m9 is set
<*n,m9*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
x is set
n is Element of i
m9 is Element of D
<*n,m9*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
i is non empty set
<*i,i*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
product <*i,i*> is functional with_common_domain product-like set
2 -tuples_on i is functional non empty FinSequence-membered with_common_domain product-like FinSequenceSet of i
i * is functional non empty FinSequence-membered FinSequenceSet of i
{ b₁ where b₁ is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of i * : len b₁ = 2 } is set
{ <*b₁,b₂*> where b₁, b₂ is Element of i : verum } is set
i is non empty set
D is non empty set
x is non empty set
<*i,D,x*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like countable set
product <*i,D,x*> is functional with_common_domain product-like set
{ <*b₁,b₂,b₃*> where b₁ is Element of i, b₂ is Element of D, b₃ is Element of x : verum } is set
n is set
m9 is set
n is set
n is set
<*m9,n,n*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like countable set
n is set
m9 is Element of i
n is Element of D
n is Element of x
<*m9,n,n*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like countable set
i is non empty set
<*i,i,i*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like countable set
product <*i,i,i*> is functional with_common_domain product-like set
3 -tuples_on i is functional non empty FinSequence-membered with_common_domain product-like FinSequenceSet of i
i * is functional non empty FinSequence-membered FinSequenceSet of i
{ b₁ where b₁ is Relation-like NAT -defined i -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of i * : len b₁ = 3 } is set
{ <*b₁,b₂,b₃*> where b₁, b₂, b₃ is Element of i : verum } is set
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D is set
i |-> D is Relation-like NAT -defined Function-like finite i -element FinSequence-like FinSubsequence-like countable set
Seg i is finite i -element countable Element of K27(NAT)
(Seg i) --> D is Relation-like NAT -defined Seg i -defined Seg i -defined {D} -valued Function-like constant total total quasi_total finite FinSequence-like FinSubsequence-like countable Element of K27(K28((Seg i),{D}))
{D} is non empty trivial finite 1 -element countable set
K28((Seg i),{D}) is Relation-like finite countable set
K27(K28((Seg i),{D})) is non empty finite V40() countable set
product (i |-> D) is functional with_common_domain product-like set
i -tuples_on D is functional FinSequence-membered with_common_domain product-like FinSequenceSet of D
D * is functional non empty FinSequence-membered FinSequenceSet of D
{ b₁ where b₁ is Relation-like NAT -defined D -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of D * : len b₁ = i } is set
product ((Seg i) --> D) is functional with_common_domain product-like set
Funcs ((Seg i),D) is functional set
i is Relation-like Function-like set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
doms <*i*> is Relation-like Function-like set
dom i is set
<*(dom i)*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
rngs <*i*> is Relation-like Function-like set
rng i is set
<*(rng i)*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
rng <*i*> is non empty trivial finite 1 -element countable set
{i} is functional non empty trivial finite 1 -element with_common_domain countable set
<*i*> " (rng <*i*>) is finite countable set
dom <*i*> is non empty trivial finite 1 -element countable Element of K27(NAT)
dom (doms <*i*>) is set
SubFuncs (rng <*i*>) is set
<*i*> " (SubFuncs (rng <*i*>)) is finite countable set
dom <*(dom i)*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*i*> . 1 is set
SubFuncs {i} is set
<*(rng i)*> . 1 is set
D is set
(rngs <*i*>) . D is set
<*(rng i)*> . D is set
<*(dom i)*> . 1 is set
D is set
(doms <*i*>) . D is set
<*(dom i)*> . D is set
dom (rngs <*i*>) is set
dom <*(rng i)*> is non empty trivial finite 1 -element countable Element of K27(NAT)
i is Relation-like Function-like set
dom i is set
rng i is set
D is Relation-like Function-like set
<*i,D*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
doms <*i,D*> is Relation-like Function-like set
dom D is set
<*(dom i),(dom D)*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
rngs <*i,D*> is Relation-like Function-like set
rng D is set
<*(rng i),(rng D)*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
rng <*i,D*> is non empty finite countable set
{i,D} is functional non empty finite countable set
<*i,D*> " (rng <*i,D*>) is finite countable set
dom <*i,D*> is non empty finite 2 -element countable Element of K27(NAT)
dom (doms <*i,D*>) is set
SubFuncs (rng <*i,D*>) is set
<*i,D*> " (SubFuncs (rng <*i,D*>)) is finite countable set
dom <*(dom i),(dom D)*> is non empty finite 2 -element countable Element of K27(NAT)
<*i,D*> . 1 is set
<*i,D*> . 2 is set
SubFuncs {i,D} is set
<*(rng i),(rng D)*> . 1 is set
<*(rng i),(rng D)*> . 2 is set
x is set
(rngs <*i,D*>) . x is set
<*(rng i),(rng D)*> . x is set
<*(dom i),(dom D)*> . 1 is set
<*(dom i),(dom D)*> . 2 is set
x is set
(doms <*i,D*>) . x is set
<*(dom i),(dom D)*> . x is set
dom (rngs <*i,D*>) is set
dom <*(rng i),(rng D)*> is non empty finite 2 -element countable Element of K27(NAT)
i is Relation-like Function-like set
dom i is set
rng i is set
D is Relation-like Function-like set
dom D is set
rng D is set
x is Relation-like Function-like set
<*i,D,x*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like countable set
doms <*i,D,x*> is Relation-like Function-like set
dom x is set
<*(dom i),(dom D),(dom x)*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like countable set
rngs <*i,D,x*> is Relation-like Function-like set
rng x is set
<*(rng i),(rng D),(rng x)*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like countable set
rng <*i,D,x*> is non empty finite countable set
{i,D,x} is non empty finite countable set
<*i,D,x*> " (rng <*i,D,x*>) is finite countable set
dom <*i,D,x*> is non empty finite 3 -element countable Element of K27(NAT)
<*(rng i),(rng D),(rng x)*> . 3 is set
<*i,D,x*> . 1 is set
<*i,D,x*> . 2 is set
<*i,D,x*> . 3 is set
SubFuncs {i,D,x} is set
<*(rng i),(rng D),(rng x)*> . 1 is set
<*(rng i),(rng D),(rng x)*> . 2 is set
n is set
(rngs <*i,D,x*>) . n is set
<*(rng i),(rng D),(rng x)*> . n is set
dom (doms <*i,D,x*>) is set
SubFuncs (rng <*i,D,x*>) is set
<*i,D,x*> " (SubFuncs (rng <*i,D,x*>)) is finite countable set
dom <*(dom i),(dom D),(dom x)*> is non empty finite 3 -element countable Element of K27(NAT)
<*(dom i),(dom D),(dom x)*> . 3 is set
<*(dom i),(dom D),(dom x)*> . 1 is set
<*(dom i),(dom D),(dom x)*> . 2 is set
n is set
(doms <*i,D,x*>) . n is set
<*(dom i),(dom D),(dom x)*> . n is set
dom (rngs <*i,D,x*>) is set
dom <*(rng i),(rng D),(rng x)*> is non empty finite 3 -element countable Element of K27(NAT)
i is set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
Union <*i*> is set
rng <*i*> is non empty trivial finite 1 -element countable set
union (rng <*i*>) is set
meet <*i*> is set
meet (rng <*i*>) is set
{i} is non empty trivial finite 1 -element countable set
union {i} is set
meet {i} is set
i is set
D is set
<*i,D*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
Union <*i,D*> is set
rng <*i,D*> is non empty finite countable set
union (rng <*i,D*>) is set
i \/ D is set
meet <*i,D*> is set
meet (rng <*i,D*>) is set
i /\ D is set
{i,D} is non empty finite countable set
union {i,D} is set
meet {i,D} is set
i is set
D is set
i \/ D is set
i /\ D is set
x is set
<*i,D,x*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like countable set
Union <*i,D,x*> is set
rng <*i,D,x*> is non empty finite countable set
union (rng <*i,D,x*>) is set
(i \/ D) \/ x is set
meet <*i,D,x*> is set
meet (rng <*i,D,x*>) is set
(i /\ D) /\ x is set
{i,D} is non empty finite countable set
{x} is non empty trivial finite 1 -element countable set
{i,D} \/ {x} is non empty finite countable set
union ({i,D} \/ {x}) is set
union {i,D} is set
union {x} is set
(union {i,D}) \/ (union {x}) is set
{i,D,x} is non empty finite countable set
meet {x} is set
meet ({i,D} \/ {x}) is set
meet {i,D} is set
(meet {i,D}) /\ (meet {x}) is set
i is set
D is Relation-like Function-like set
dom D is set
<*D*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
<*D*> .. (1,i) is set
uncurry <*D*> is Relation-like Function-like set
(uncurry <*D*>) . (1,i) is set
D . i is set
x is Relation-like Function-like set
<*D,x*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
<*D,x*> .. (1,i) is set
uncurry <*D,x*> is Relation-like Function-like set
(uncurry <*D,x*>) . (1,i) is set
n is Relation-like Function-like set
<*D,x,n*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like countable set
<*D,x,n*> .. (1,i) is set
uncurry <*D,x,n*> is Relation-like Function-like set
(uncurry <*D,x,n*>) . (1,i) is set
<*D,x,n*> . 1 is set
dom <*D*> is non empty trivial finite 1 -element countable Element of K27(NAT)
dom <*D,x*> is non empty finite 2 -element countable Element of K27(NAT)
dom <*D,x,n*> is non empty finite 3 -element countable Element of K27(NAT)
<*D*> . 1 is set
<*D,x*> . 1 is set
i is set
D is Relation-like Function-like set
dom D is set
D . i is set
x is Relation-like Function-like set
<*x,D*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
<*x,D*> .. (2,i) is set
uncurry <*x,D*> is Relation-like Function-like set
(uncurry <*x,D*>) . (2,i) is set
n is Relation-like Function-like set
<*x,D,n*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like countable set
<*x,D,n*> .. (2,i) is set
uncurry <*x,D,n*> is Relation-like Function-like set
(uncurry <*x,D,n*>) . (2,i) is set
dom <*x,D*> is non empty finite 2 -element countable Element of K27(NAT)
dom <*x,D,n*> is non empty finite 3 -element countable Element of K27(NAT)
<*x,D*> . 2 is set
<*x,D,n*> . 2 is set
i is set
D is Relation-like Function-like set
dom D is set
D . i is set
x is Relation-like Function-like set
n is Relation-like Function-like set
<*x,n,D*> is Relation-like NAT -defined Function-like non empty finite 3 -element FinSequence-like FinSubsequence-like countable set
<*x,n,D*> .. (3,i) is set
uncurry <*x,n,D*> is Relation-like Function-like set
(uncurry <*x,n,D*>) . (3,i) is set
dom <*x,n,D*> is non empty finite 3 -element countable Element of K27(NAT)
<*x,n,D*> . 3 is set
i is Relation-like Function-like set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
<:<*i*>:> is Relation-like Function-like set
uncurry' <*i*> is Relation-like Function-like set
doms <*i*> is Relation-like Function-like set
meet (doms <*i*>) is set
rng (doms <*i*>) is set
meet (rng (doms <*i*>)) is set
dom <*i*> is non empty trivial finite 1 -element countable set
K28((meet (doms <*i*>)),(dom <*i*>)) is Relation-like set
(uncurry' <*i*>) | K28((meet (doms <*i*>)),(dom <*i*>)) is Relation-like Function-like set
curry ((uncurry' <*i*>) | K28((meet (doms <*i*>)),(dom <*i*>))) is Relation-like Function-like set
dom <:<*i*>:> is set
dom i is set
rng <:<*i*>:> is set
rngs <*i*> is Relation-like Function-like set
product (rngs <*i*>) is functional with_common_domain product-like set
rng i is set
<*(rng i)*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
<*(dom i)*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
meet <*(dom i)*> is set
rng <*(dom i)*> is non empty trivial finite 1 -element countable set
meet (rng <*(dom i)*>) is set
D is set
<:<*i*>:> . D is set
i . D is set
<*(i . D)*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
dom <*(rng i)*> is non empty trivial finite 1 -element countable Element of K27(NAT)
x is Relation-like Function-like set
dom x is set
dom <*i*> is non empty trivial finite 1 -element countable Element of K27(NAT)
<*i*> . 1 is set
uncurry <*i*> is Relation-like Function-like set
(uncurry <*i*>) . (1,D) is set
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n . 1 is set
i is Relation-like Function-like set
dom i is set
D is Relation-like Function-like set
<*i,D*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
<:<*i,D*>:> is Relation-like Function-like set
uncurry' <*i,D*> is Relation-like Function-like set
doms <*i,D*> is Relation-like Function-like set
meet (doms <*i,D*>) is set
rng (doms <*i,D*>) is set
meet (rng (doms <*i,D*>)) is set
dom <*i,D*> is non empty finite 2 -element countable set
K28((meet (doms <*i,D*>)),(dom <*i,D*>)) is Relation-like set
(uncurry' <*i,D*>) | K28((meet (doms <*i,D*>)),(dom <*i,D*>)) is Relation-like Function-like set
curry ((uncurry' <*i,D*>) | K28((meet (doms <*i,D*>)),(dom <*i,D*>))) is Relation-like Function-like set
dom <:<*i,D*>:> is set
dom D is set
(dom i) /\ (dom D) is set
dom <*i,D*> is non empty finite 2 -element countable Element of K27(NAT)
rng <:<*i,D*>:> is set
rngs <*i,D*> is Relation-like Function-like set
product (rngs <*i,D*>) is functional with_common_domain product-like set
rng i is set
rng D is set
<*(rng i),(rng D)*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
<*(dom i),(dom D)*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
meet <*(dom i),(dom D)*> is set
rng <*(dom i),(dom D)*> is non empty finite countable set
meet (rng <*(dom i),(dom D)*>) is set
x is set
<:<*i,D*>:> . x is set
i . x is set
D . x is set
<*(i . x),(D . x)*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
dom <*(rng i),(rng D)*> is non empty finite 2 -element countable Element of K27(NAT)
n is Relation-like Function-like set
dom n is set
m9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
m9 . 2 is set
uncurry <*i,D*> is Relation-like Function-like set
(uncurry <*i,D*>) . (2,x) is set
<*i,D*> . 2 is set
len m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
<*i,D*> . 1 is set
(uncurry <*i,D*>) . (1,x) is set
m9 . 1 is set
i is Relation-like Function-like set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
Frege <*i*> is Relation-like Function-like set
dom (Frege <*i*>) is set
dom i is set
<*(dom i)*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
product <*(dom i)*> is functional with_common_domain product-like set
rng (Frege <*i*>) is set
rng i is set
<*(rng i)*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
product <*(rng i)*> is functional with_common_domain product-like set
<*i*> . 1 is set
rngs <*i*> is Relation-like Function-like set
doms <*i*> is Relation-like Function-like set
D is set
<*D*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
(Frege <*i*>) . <*D*> is set
i . D is set
<*(i . D)*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
product (doms <*i*>) is functional with_common_domain product-like set
rng <*i*> is non empty trivial finite 1 -element countable set
SubFuncs (rng <*i*>) is set
<*i*> " (SubFuncs (rng <*i*>)) is finite countable set
uncurry <*i*> is Relation-like Function-like set
x is Relation-like Function-like set
dom x is set
dom <*i*> is non empty trivial finite 1 -element countable Element of K27(NAT)
dom <*(rng i)*> is non empty trivial finite 1 -element countable Element of K27(NAT)
product (rngs <*i*>) is functional with_common_domain product-like set
<*D*> . 1 is set
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
n . 1 is set
i . (<*D*> . 1) is set
i is Relation-like Function-like set
dom i is set
rng i is set
D is Relation-like Function-like set
<*i,D*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
Frege <*i,D*> is Relation-like Function-like set
dom (Frege <*i,D*>) is set
dom D is set
<*(dom i),(dom D)*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
product <*(dom i),(dom D)*> is functional with_common_domain product-like set
rng (Frege <*i,D*>) is set
rng D is set
<*(rng i),(rng D)*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
product <*(rng i),(rng D)*> is functional with_common_domain product-like set
rngs <*i,D*> is Relation-like Function-like set
len <*(rng i),(rng D)*> is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
dom <*(rng i),(rng D)*> is non empty finite 2 -element countable Element of K27(NAT)
len <*i,D*> is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
dom <*i,D*> is non empty finite 2 -element countable Element of K27(NAT)
doms <*i,D*> is Relation-like Function-like set
x is set
i . x is set
n is set
<*x,n*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
(Frege <*i,D*>) . <*x,n*> is set
D . n is set
<*(i . x),(D . n)*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
product (doms <*i,D*>) is functional with_common_domain product-like set
rng <*i,D*> is non empty finite countable set
SubFuncs (rng <*i,D*>) is set
<*i,D*> " (SubFuncs (rng <*i,D*>)) is finite countable set
uncurry <*i,D*> is Relation-like Function-like set
m9 is Relation-like Function-like set
dom m9 is set
<*x,n*> . 1 is set
<*x,n*> . 2 is set
<*i,D*> . 1 is set
product (rngs <*i,D*>) is functional with_common_domain product-like set
<*i,D*> . 2 is set
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
n . 2 is set
D . (<*x,n*> . 2) is set
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n . 1 is set
i . (<*x,n*> . 1) is set
i is set
D is Relation-like Function-like set
dom D is set
x is Relation-like Function-like set
dom x is set
<:D,x:> is Relation-like Function-like set
<:D,x:> . i is set
<*D,x*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
<:<*D,x*>:> is Relation-like Function-like set
uncurry' <*D,x*> is Relation-like Function-like set
doms <*D,x*> is Relation-like Function-like set
meet (doms <*D,x*>) is set
rng (doms <*D,x*>) is set
meet (rng (doms <*D,x*>)) is set
dom <*D,x*> is non empty finite 2 -element countable set
K28((meet (doms <*D,x*>)),(dom <*D,x*>)) is Relation-like set
(uncurry' <*D,x*>) | K28((meet (doms <*D,x*>)),(dom <*D,x*>)) is Relation-like Function-like set
curry ((uncurry' <*D,x*>) | K28((meet (doms <*D,x*>)),(dom <*D,x*>))) is Relation-like Function-like set
<:<*D,x*>:> . i is set
D . i is set
x . i is set
<*(D . i),(x . i)*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
<*(D . i),(x . i)*> . 1 is set
<*(D . i),(x . i)*> . 2 is set
(dom D) /\ (dom x) is set
n is set
m9 is set
[n,m9] is V21() set
{n,m9} is non empty finite countable set
{n} is non empty trivial finite 1 -element countable set
{{n,m9},{n}} is non empty finite V40() countable set
<*n,m9*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
<*n,m9*> . 1 is set
<*n,m9*> . 2 is set
[(D . i),(x . i)] is V21() set
{(D . i),(x . i)} is non empty finite countable set
{(D . i)} is non empty trivial finite 1 -element countable set
{{(D . i),(x . i)},{(D . i)}} is non empty finite V40() countable set
i is set
D is set
<*i,D*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
x is Relation-like Function-like set
dom x is set
n is Relation-like Function-like set
dom n is set
[:x,n:] is Relation-like Function-like set
[:x,n:] . (i,D) is set
<*x,n*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
Frege <*x,n*> is Relation-like Function-like set
(Frege <*x,n*>) . <*i,D*> is set
m9 is set
n is set
[m9,n] is V21() set
{m9,n} is non empty finite countable set
{m9} is non empty trivial finite 1 -element countable set
{{m9,n},{m9}} is non empty finite V40() countable set
<*m9,n*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
x . i is set
n . D is set
<*(x . i),(n . D)*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
<*(x . i),(n . D)*> . 1 is set
<*(x . i),(n . D)*> . 2 is set
<*m9,n*> . 1 is set
<*m9,n*> . 2 is set
[(x . i),(n . D)] is V21() set
{(x . i),(n . D)} is non empty finite countable set
{(x . i)} is non empty trivial finite 1 -element countable set
{{(x . i),(n . D)},{(x . i)}} is non empty finite V40() countable set
i is set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
D is set
Funcs (<*i*>,D) is Relation-like Function-like set
Funcs (i,D) is functional set
<*(Funcs (i,D))*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
dom <*i*> is non empty trivial finite 1 -element countable Element of K27(NAT)
dom (Funcs (<*i*>,D)) is set
<*i*> . 1 is set
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
x . 1 is set
i is set
D is set
<*i,D*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
x is set
Funcs (<*i,D*>,x) is Relation-like Function-like set
Funcs (i,x) is functional set
Funcs (D,x) is functional set
<*(Funcs (i,x)),(Funcs (D,x))*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
len <*i,D*> is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len <*i,D*>) is non empty finite len <*i,D*> -element countable Element of K27(NAT)
dom <*i,D*> is non empty finite 2 -element countable Element of K27(NAT)
dom (Funcs (<*i,D*>,x)) is set
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
<*i,D*> . 2 is set
n . 2 is set
<*i,D*> . 1 is set
n . 1 is set
i is set
D is set
<*D*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
Funcs (i,<*D*>) is Relation-like Function-like set
Funcs (i,D) is functional set
<*(Funcs (i,D))*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable set
dom <*D*> is non empty trivial finite 1 -element countable Element of K27(NAT)
dom (Funcs (i,<*D*>)) is set
<*D*> . 1 is set
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
x . 1 is set
i is set
D is set
Funcs (i,D) is functional set
x is set
<*D,x*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
Funcs (i,<*D,x*>) is Relation-like Function-like set
Funcs (i,x) is functional set
<*(Funcs (i,D)),(Funcs (i,x))*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable set
len <*D,x*> is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg (len <*D,x*>) is non empty finite len <*D,x*> -element countable Element of K27(NAT)
dom <*D,x*> is non empty finite 2 -element countable Element of K27(NAT)
dom (Funcs (i,<*D,x*>)) is set
n is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
len n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
<*D,x*> . 2 is set
n . 2 is set
<*D,x*> . 1 is set
n . 1 is set
i is set
D is set
{i,D} is non empty finite countable set
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable set
rng x is finite countable set
len x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
x . 1 is set
x . 2 is set
dom x is finite countable Element of K27(NAT)
n is set
x . n is set
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
1 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
1 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
n is set
x . n is set
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
1 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
1 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
i is set
Sgm i is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like countable FinSequence of NAT
dom (Sgm i) is finite countable Element of K27(NAT)
D is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
Seg D is finite D -element countable Element of K27(NAT)
x is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable set
(Sgm i) . x is set
x + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
x + 0 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(Sgm i) . (x + 1) is set
rng (Sgm i) is finite countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
len (Sgm i) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
m9 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
0 + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
len (Sgm i) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
x + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(len (Sgm i)) + 0 is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(Sgm i) . (x + 1) is set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
x + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(Sgm i) . (x + 1) is set
x + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(Sgm i) . (x + 1) is set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
x is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(Sgm i) . x is set
x + 1 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(Sgm i) . (x + 1) is set
x is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
(Sgm i) . x is set
(Sgm i) . 1 is set
len (Sgm i) is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
rng (Sgm i) is finite countable Element of K27(NAT)
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
m9 is non empty V15() V16() V17() V21() ext-real positive non negative V25() V26() V33() finite cardinal countable Element of NAT
(Sgm i) . m9 is set
n is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable Element of NAT
i is V15() V16() V17() V21() ext-real non negative V25() V26() V33() finite cardinal countable set
D is finite countable set
i -tuples_on D is functional FinSequence-membered with_common_domain product-like FinSequenceSet of D
D * is functional non empty FinSequence-membered FinSequenceSet of D
{ b₁ where b₁ is Relation-like NAT -defined D -valued Function-like finite FinSequence-like FinSubsequence-like countable Element of D * : len b₁ = i } is set
x is set
i |-> D is Relation-like NAT -defined Function-like finite i -element FinSequence-like FinSubsequence-like countable set
Seg i is finite i -element countable Element of K27(NAT)
(Seg i) --> D is Relation-like NAT -defined Seg i -defined Seg i -defined {D} -valued Function-like constant total total quasi_total finite FinSequence-like FinSubsequence-like countable Element of K27(K28((Seg i),{D}))
{D} is non empty trivial finite V40() 1 -element countable set
K28((Seg i),{D}) is Relation-like finite countable set
K27(K28((Seg i),{D})) is non empty finite V40() countable set
dom (i |-> D) is finite i -element countable Element of K27(NAT)
(i |-> D) . x is set
product (i |-> D) is functional with_common_domain product-like set