:: FOMODEL0 semantic presentation

REAL is non empty non trivial non finite non empty-membered set
NAT is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal non empty-membered countable denumerable Element of bool REAL
bool REAL is non empty non trivial non finite non empty-membered set
omega is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal non empty-membered countable denumerable set
bool omega is non empty non trivial non finite non empty-membered set
bool NAT is non empty non trivial non finite non empty-membered set
COMPLEX is non empty non trivial non finite non empty-membered set
RAT is non empty non trivial non finite non empty-membered set
INT is non empty non trivial non finite non empty-membered set
[:REAL,REAL:] is Relation-like non empty non trivial non finite non empty-membered set
bool [:REAL,REAL:] is non empty non trivial non finite non empty-membered set
K281() is non empty strict multMagma
the U1 of K281() is set
<REAL,+> is non empty strict V94() V95() associative commutative left-invertible right-invertible invertible left-cancelable right-cancelable V153() multMagma
K287() is non empty strict associative commutative left-cancelable right-cancelable V153() SubStr of <REAL,+>
<NAT,+> is non empty strict V94() associative commutative left-cancelable right-cancelable V153() uniquely-decomposable SubStr of K287()
<REAL,*> is non empty strict V94() associative commutative multMagma
<NAT,*> is non empty strict V94() associative commutative uniquely-decomposable SubStr of <REAL,*>
{} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like Cardinal-yielding countable FinSequence-yielding finite-support set
the Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like Cardinal-yielding countable FinSequence-yielding finite-support set is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like Cardinal-yielding countable FinSequence-yielding finite-support set
2 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
{{},1} is non empty finite finite-membered countable set
K391(NAT) is V165() set
BOOLEAN is set
0 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like Cardinal-yielding countable FinSequence-yielding finite-support Element of NAT
{0,1} is non empty finite finite-membered countable set
[:{},{}:] is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like Cardinal-yielding countable FinSequence-yielding finite-support set
3 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
{{}} is functional non empty trivial finite finite-membered 1 -element with_common_domain countable set
[:{{}},omega:] is Relation-like non empty non trivial non finite non empty-membered set
omega \/ [:{{}},omega:] is non empty set
[{},{}] is non empty V15() set
{[{},{}]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
(omega \/ [:{{}},omega:]) \ {[{},{}]} is Element of bool (omega \/ [:{{}},omega:])
bool (omega \/ [:{{}},omega:]) is non empty set
Seg 1 is non empty trivial finite 1 -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= 1 ) } is set
{} * is functional non empty FinSequence-membered FinSequenceSet of {}
K587() is set
K588() is set
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
U is set
pr1 (U,U) is Relation-like [:U,U:] -defined U -valued Function-like quasi_total Element of bool [:[:U,U:],U:]
[:U,U:] is Relation-like set
[:[:U,U:],U:] is Relation-like set
bool [:[:U,U:],U:] is non empty set
U is set
q1 is Relation-like Function-like set
q11 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
proj2 q11 is finite countable set
U is set
union U is set
q1 is set
q2 is set
Funcs (q1,q2) is functional set
[:q1,q2:] is Relation-like set
bool [:q1,q2:] is non empty Element of bool (bool [:q1,q2:])
bool [:q1,q2:] is non empty set
bool (bool [:q1,q2:]) is non empty set
bool (bool [:q1,q2:]) is non empty set
p is Element of bool (bool [:q1,q2:])
union p is Relation-like q1 -defined q2 -valued Element of bool [:q1,q2:]
U is set
q1 is Relation-like Function-like set
proj1 q1 is set
(proj1 q1) /\ U is set
q1 | U is Relation-like Function-like set
f is set
q11 is set
q1 . f is set
q1 . q11 is set
proj1 (q1 | U) is set
(q1 | U) . f is set
(q1 | U) . q11 is set
f is set
proj1 (q1 | U) is set
q11 is set
(q1 | U) . f is set
(q1 | U) . q11 is set
q1 . f is set
q1 . q11 is set
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
q1 is set
q2 is set
f is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
f | q2 is Relation-like [:U,U:] -defined q2 -defined [:U,U:] -defined U -valued Function-like Element of bool [:[:U,U:],U:]
f | q1 is Relation-like [:U,U:] -defined q1 -defined [:U,U:] -defined U -valued Function-like Element of bool [:[:U,U:],U:]
(f | q2) | q1 is Relation-like [:U,U:] -defined q1 -defined [:U,U:] -defined U -valued Function-like Element of bool [:[:U,U:],U:]
U is set
q1 is set
q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 -tuples_on U is functional FinSequence-membered FinSequenceSet of U
f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
f -tuples_on q1 is functional FinSequence-membered FinSequenceSet of q1
(q2 -tuples_on U) /\ (f -tuples_on q1) is set
q11 is set
F is Relation-like NAT -defined Function-like finite q2 -element FinSequence-like FinSubsequence-like countable finite-support set
len F is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
p is Relation-like NAT -defined Function-like finite f -element FinSequence-like FinSubsequence-like countable finite-support set
len p is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
U is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
Seg U is finite U -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= U ) } is set
q1 is set
U -tuples_on q1 is functional FinSequence-membered FinSequenceSet of q1
Funcs ((Seg U),q1) is functional set
q2 is non empty set
U -tuples_on q2 is functional non empty FinSequence-membered FinSequenceSet of q2
Funcs ((Seg U),q2) is functional non empty FUNCTION_DOMAIN of Seg U,q2
U is set
q1 is set
q1 * is functional non empty FinSequence-membered FinSequenceSet of q1
q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 -tuples_on U is functional FinSequence-membered FinSequenceSet of U
(q2 -tuples_on U) /\ (q1 *) is set
q2 -tuples_on q1 is functional FinSequence-membered FinSequenceSet of q1
p is set
C is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
len C is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
dom C is finite countable Element of bool NAT
Seg q2 is finite q2 -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= q2 ) } is set
rng C is finite countable Element of bool q1
bool q1 is non empty set
Funcs ((Seg q2),q1) is functional set
U is set
q1 is set
q1 * is functional non empty FinSequence-membered FinSequenceSet of q1
q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 -tuples_on U is functional FinSequence-membered FinSequenceSet of U
(q2 -tuples_on U) /\ (q1 *) is set
q2 -tuples_on q1 is functional FinSequence-membered FinSequenceSet of q1
(q2 -tuples_on U) /\ (q2 -tuples_on q1) is set
(q2 -tuples_on U) /\ ((q2 -tuples_on U) /\ (q1 *)) is set
(q2 -tuples_on U) /\ (q2 -tuples_on U) is set
((q2 -tuples_on U) /\ (q2 -tuples_on U)) /\ (q1 *) is set
p is set
C is Relation-like NAT -defined Function-like finite q2 -element FinSequence-like FinSubsequence-like countable finite-support set
f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
f -tuples_on q1 is functional FinSequence-membered FinSequenceSet of q1
len C is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
proj2 C is finite countable set
U is set
q1 is set
Funcs (U,q1) is functional set
q2 is set
Funcs (U,q2) is functional set
(Funcs (U,q1)) /\ (Funcs (U,q2)) is set
q1 /\ q2 is set
Funcs (U,(q1 /\ q2)) is functional set
F is set
p is Relation-like Function-like set
proj1 p is set
proj2 p is set
C is Relation-like Function-like set
proj1 C is set
proj2 C is set
U is set
q1 is set
q1 * is functional non empty FinSequence-membered FinSequenceSet of q1
U /\ q1 is set
q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 -tuples_on U is functional FinSequence-membered FinSequenceSet of U
(q2 -tuples_on U) /\ (q1 *) is set
q2 -tuples_on (U /\ q1) is functional FinSequence-membered FinSequenceSet of U /\ q1
Seg q2 is finite q2 -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= q2 ) } is set
Funcs ((Seg q2),(U /\ q1)) is functional set
Funcs ((Seg q2),U) is functional set
Funcs ((Seg q2),q1) is functional set
(Funcs ((Seg q2),U)) /\ (Funcs ((Seg q2),q1)) is set
(q2 -tuples_on U) /\ (Funcs ((Seg q2),q1)) is set
q2 -tuples_on q1 is functional FinSequence-membered FinSequenceSet of q1
(q2 -tuples_on U) /\ (q2 -tuples_on q1) is set
U is set
q1 is set
U /\ q1 is set
q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 -tuples_on (U /\ q1) is functional FinSequence-membered FinSequenceSet of U /\ q1
q2 -tuples_on U is functional FinSequence-membered FinSequenceSet of U
q2 -tuples_on q1 is functional FinSequence-membered FinSequenceSet of q1
(q2 -tuples_on U) /\ (q2 -tuples_on q1) is set
q1 * is functional non empty FinSequence-membered FinSequenceSet of q1
(q2 -tuples_on U) /\ (q1 *) is set
U is non empty set
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
U * is functional non empty FinSequence-membered FinSequenceSet of U
[:(U *),(U *):] is Relation-like non empty set
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
q1 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
q2 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
(U -concatenation) . (q1,q2) is set
[q1,q2] is non empty V15() set
(U -concatenation) . [q1,q2] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 ^ q2 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
U *+^ is non empty strict V94() associative constituted-Functions constituted-FinSeqs left-cancelable right-cancelable V153() uniquely-decomposable multMagma
the U1 of (U *+^) is set
f is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
q11 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
the multF of (U *+^) is Relation-like [: the U1 of (U *+^), the U1 of (U *+^):] -defined the U1 of (U *+^) -valued Function-like quasi_total Element of bool [:[: the U1 of (U *+^), the U1 of (U *+^):], the U1 of (U *+^):]
[: the U1 of (U *+^), the U1 of (U *+^):] is Relation-like set
[:[: the U1 of (U *+^), the U1 of (U *+^):], the U1 of (U *+^):] is Relation-like set
bool [:[: the U1 of (U *+^), the U1 of (U *+^):], the U1 of (U *+^):] is non empty set
F is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of the U1 of (U *+^)
p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of the U1 of (U *+^)
F ^ p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
F [*] p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of the U1 of (U *+^)
(U -concatenation) . (F,p) is set
[F,p] is non empty V15() set
(U -concatenation) . [F,p] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U is non empty set
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
U * is functional non empty FinSequence-membered FinSequenceSet of U
[:(U *),(U *):] is Relation-like non empty set
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U -concatenation) . (q1,q2) is set
[q1,q2] is non empty V15() set
(U -concatenation) . [q1,q2] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 ^ q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q11 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
F is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
(U -concatenation) . (q11,F) is set
[q11,F] is non empty V15() set
(U -concatenation) . [q11,F] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q11 ^ F is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
U is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) \ {{}} is functional FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
q1 is set
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
q1 is set
q2 is set
f is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
[:q1,U:] is Relation-like set
[:q2,U:] is Relation-like set
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
q1 is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
[:{},U:] is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like Cardinal-yielding countable FinSequence-yielding finite-support set
q2 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like Cardinal-yielding countable FinSequence-yielding finite-support set
q1 | q2 is Relation-like non-empty empty-yielding NAT -defined [:U,U:] -defined q2 -defined [:U,U:] -defined U -valued Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like Cardinal-yielding countable FinSequence-yielding finite-support Element of bool [:[:U,U:],U:]
U is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
<:U,q1:> is Relation-like Function-like set
proj1 <:U,q1:> is set
len U is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
len q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
min ((len U),(len q1)) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
Seg (min ((len U),(len q1))) is finite min ((len U),(len q1)) -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= min ((len U),(len q1)) ) } is set
dom U is finite countable Element of bool NAT
dom q1 is finite countable Element of bool NAT
(dom U) /\ (dom q1) is finite countable Element of bool NAT
Seg (len U) is finite len U -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= len U ) } is set
(Seg (len U)) /\ (dom q1) is finite countable Element of bool NAT
Seg (len q1) is finite len q1 -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= len q1 ) } is set
(Seg (len U)) /\ (Seg (len q1)) is finite countable Element of bool NAT
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
(U) is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
pr1 (U,U) is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
q1 is Element of U
q2 is Element of U
f is Element of U
(U) . (q2,f) is Element of U
[q2,f] is non empty V15() set
(U) . [q2,f] is set
(U) . (q1,((U) . (q2,f))) is Element of U
[q1,((U) . (q2,f))] is non empty V15() set
(U) . [q1,((U) . (q2,f))] is set
(U) . (q1,q2) is Element of U
[q1,q2] is non empty V15() set
(U) . [q1,q2] is set
(U) . (((U) . (q1,q2)),f) is Element of U
[((U) . (q1,q2)),f] is non empty V15() set
(U) . [((U) . (q1,q2)),f] is set
(U) . (q1,f) is Element of U
[q1,f] is non empty V15() set
(U) . [q1,f] is set
q1 is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
U is set
[:U,U:] is Relation-like set
[:[:U,U:],U:] is Relation-like set
bool [:[:U,U:],U:] is non empty set
q1 is non empty set
(q1) is Relation-like [:q1,q1:] -defined q1 -valued Function-like non empty total quasi_total associative Element of bool [:[:q1,q1:],q1:]
[:q1,q1:] is Relation-like non empty set
[:[:q1,q1:],q1:] is Relation-like non empty set
bool [:[:q1,q1:],q1:] is non empty set
pr1 (q1,q1) is Relation-like [:q1,q1:] -defined q1 -valued Function-like non empty total quasi_total Element of bool [:[:q1,q1:],q1:]
q2 is Relation-like [:U,U:] -defined U -valued Function-like quasi_total Element of bool [:[:U,U:],U:]
[:[:{},{}:],{}:] is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like Cardinal-yielding countable FinSequence-yielding finite-support set
bool [:[:{},{}:],{}:] is non empty finite finite-membered countable set
the Relation-like non-empty empty-yielding [:{},{}:] -defined {} -valued Function-like one-to-one constant functional empty trivial non proper total quasi_total complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative commutative associative Function-yielding V159() FuncSeq-like Cardinal-yielding countable FinSequence-yielding finite-support Element of bool [:[:{},{}:],{}:] is Relation-like non-empty empty-yielding [:{},{}:] -defined {} -valued Function-like one-to-one constant functional empty trivial non proper total quasi_total complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative commutative associative Function-yielding V159() FuncSeq-like Cardinal-yielding countable FinSequence-yielding finite-support Element of bool [:[:{},{}:],{}:]
q1 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like Cardinal-yielding countable FinSequence-yielding finite-support set
[:q1,q1:] is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like Cardinal-yielding countable FinSequence-yielding finite-support set
[:[:q1,q1:],q1:] is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like Cardinal-yielding countable FinSequence-yielding finite-support set
bool [:[:q1,q1:],q1:] is non empty finite finite-membered countable set
U is set
bool U is non empty set
q1 is Element of bool U
q1 * is functional non empty FinSequence-membered set
U * is functional non empty FinSequence-membered FinSequenceSet of U
bool (U *) is non empty set
U is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
[:(U *),(U *):] is Relation-like non empty set
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
q1 is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
U is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) \ {{}} is functional FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
the Element of U is Element of U
<* the Element of U*> is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
[1, the Element of U] is non empty V15() set
{[1, the Element of U]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
U is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
the Relation-like NAT -defined U -valued Function-like finite q1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U is Relation-like NAT -defined U -valued Function-like finite q1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
f is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
U is set
q1 is Relation-like Function-like set
proj1 q1 is set
U /\ (proj1 q1) is set
q2 is set
f is set
q1 . q2 is set
q1 . f is set
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
q1 is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
U is Relation-like Function-like set
q1 is set
{q1} is non empty trivial finite 1 -element countable set
U | {q1} is Relation-like Function-like finite countable finite-support set
proj1 U is set
U . q1 is set
q1 .--> (U . q1) is Relation-like {q1} -defined Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{q1} --> (U . q1) is Relation-like {q1} -defined {(U . q1)} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{q1},{(U . q1)}:]
{(U . q1)} is non empty trivial finite 1 -element countable set
[:{q1},{(U . q1)}:] is Relation-like non empty finite countable set
bool [:{q1},{(U . q1)}:] is non empty finite finite-membered countable set
proj1 U is set
f is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like Cardinal-yielding countable FinSequence-yielding finite-support set
proj1 U is set
U is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like Cardinal-yielding countable FinSequence-yielding finite-support set
U * is functional non empty FinSequence-membered FinSequenceSet of U
{U} is functional non empty trivial finite finite-membered 1 -element with_common_domain countable set
U is set
U is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
{U} is functional non empty trivial finite finite-membered 1 -element with_common_domain countable set
U * is functional non empty FinSequence-membered FinSequenceSet of U
q1 is non empty set
q1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
U is non empty set
q1 -tuples_on U is functional non empty FinSequence-membered FinSequenceSet of U
len {} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of NAT
U is empty-membered set
bool U is non empty set
q1 is Element of bool U
q2 is non empty set
q1 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
U is set
q1 -tuples_on U is functional FinSequence-membered FinSequenceSet of U
q2 is set
q1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
U is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
q1 -tuples_on U is functional FinSequence-membered FinSequenceSet of U
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
q1 is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
q2 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
q2 /\ q1 is Relation-like NAT -defined [:U,U:] -defined U -valued finite countable Element of bool [:[:U,U:],U:]
U is non empty set
q1 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
q1 /\ U is Relation-like finite countable set
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
U * is functional non empty FinSequence-membered FinSequenceSet of U
[:(U *),(U *):] is Relation-like non empty set
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
q1 /\ (U -concatenation) is Relation-like NAT -defined [:(U *),(U *):] -defined U * -valued finite countable (U * ,U -concatenation ) Element of bool [:[:(U *),(U *):],(U *):]
U is non empty set
{} /\ U is Relation-like finite countable (U) set
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
q2 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
q2 . 1 is set
q1 is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
f is Relation-like Function-like set
proj1 f is set
f . {} is set
q11 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q11 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
f . (q11 + 1) is set
f . q11 is set
q11 + 2 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
q2 . (q11 + 2) is set
q1 . ((f . q11),(q2 . (q11 + 2))) is set
[(f . q11),(q2 . (q11 + 2))] is non empty V15() set
q1 . [(f . q11),(q2 . (q11 + 2))] is set
f is Relation-like Function-like set
proj1 f is set
f . {} is set
q11 is Relation-like Function-like set
proj1 q11 is set
q11 . {} is set
F is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
F + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
f . (F + 1) is set
f . F is set
F + 2 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
q2 . (F + 2) is set
q1 . ((f . F),(q2 . (F + 2))) is set
[(f . F),(q2 . (F + 2))] is non empty V15() set
q1 . [(f . F),(q2 . (F + 2))] is set
F is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
F + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
q11 . (F + 1) is set
q11 . F is set
F + 2 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
q2 . (F + 2) is set
q1 . ((q11 . F),(q2 . (F + 2))) is set
[(q11 . F),(q2 . (F + 2))] is non empty V15() set
q1 . [(q11 . F),(q2 . (F + 2))] is set
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
q1 is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
q2 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
len q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
(U,q1,q2) is Relation-like Function-like set
{} + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(U,q1,q2) . {} is set
Seg (len q2) is finite len q2 -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= len q2 ) } is set
dom q2 is finite countable Element of bool NAT
q2 . 1 is set
rng q2 is finite countable Element of bool U
bool U is non empty set
f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
f + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(U,q1,q2) . f is set
(f + 1) + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(U,q1,q2) . (f + 1) is set
f + 2 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
Seg (len q2) is finite len q2 -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= len q2 ) } is set
dom q2 is finite countable Element of bool NAT
q2 . (f + 2) is set
rng q2 is finite countable Element of bool U
bool U is non empty set
[((U,q1,q2) . f),(q2 . (f + 2))] is non empty V15() set
q1 . (((U,q1,q2) . f),(q2 . (f + 2))) is set
q1 . [((U,q1,q2) . f),(q2 . (f + 2))] is set
f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 | f is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
Seg f is finite f -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= f ) } is set
q2 | (Seg f) is Relation-like NAT -defined Seg f -defined NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U,q1,(q2 | f)) is Relation-like Function-like set
(U,q1,(q2 | f)) . {} is set
(q2 | f) . 1 is set
q2 . 1 is set
f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
f + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(U,q1,q2) . f is set
(f + 1) + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(U,q1,q2) . (f + 1) is set
q11 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 | q11 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
Seg q11 is finite q11 -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= q11 ) } is set
q2 | (Seg q11) is Relation-like NAT -defined Seg q11 -defined NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U,q1,(q2 | q11)) is Relation-like Function-like set
(U,q1,(q2 | q11)) . (f + 1) is set
f + 2 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(U,q1,(q2 | q11)) . f is set
(q2 | q11) . (f + 2) is set
q1 . (((U,q1,(q2 | q11)) . f),((q2 | q11) . (f + 2))) is set
[((U,q1,(q2 | q11)) . f),((q2 | q11) . (f + 2))] is non empty V15() set
q1 . [((U,q1,(q2 | q11)) . f),((q2 | q11) . (f + 2))] is set
q1 . (((U,q1,q2) . f),((q2 | q11) . (f + 2))) is set
[((U,q1,q2) . f),((q2 | q11) . (f + 2))] is non empty V15() set
q1 . [((U,q1,q2) . f),((q2 | q11) . (f + 2))] is set
q2 . (f + 2) is set
q1 . (((U,q1,q2) . f),(q2 . (f + 2))) is set
[((U,q1,q2) . f),(q2 . (f + 2))] is non empty V15() set
q1 . [((U,q1,q2) . f),(q2 . (f + 2))] is set
f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 | f is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
Seg f is finite f -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= f ) } is set
q2 | (Seg f) is Relation-like NAT -defined Seg f -defined NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U,q1,(q2 | f)) is Relation-like Function-like set
(U,q1,(q2 | f)) . {} is set
f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
f + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(U,q1,q2) . f is set
(f + 1) + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
q11 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 | q11 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
Seg q11 is finite q11 -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= q11 ) } is set
q2 | (Seg q11) is Relation-like NAT -defined Seg q11 -defined NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U,q1,(q2 | q11)) is Relation-like Function-like set
(U,q1,(q2 | q11)) . (f + 1) is set
(U,q1,q2) . (f + 1) is set
f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
f + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(U,q1,q2) . f is set
q11 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q11 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
F is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 | F is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
Seg F is finite F -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
q2 | (Seg F) is Relation-like NAT -defined Seg F -defined NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U,q1,(q2 | F)) is Relation-like Function-like set
(U,q1,(q2 | F)) . q11 is set
(U,q1,q2) . q11 is set
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) \ {{}} is functional non empty FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
q1 is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (U *) \ {{}}
(U,q1,q2) is Relation-like Function-like set
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) \ {{}} is functional non empty FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
[:((U *) \ {{}}),U:] is Relation-like non empty set
bool [:((U *) \ {{}}),U:] is non empty set
q1 is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (U *) \ {{}}
(U,q1,q2) is Relation-like Function-like set
(U,q1,q2) is Relation-like Function-like set
len q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
(len q2) - 1 is complex real integer finite ext-real countable set
(U,q1,q2) . ((len q2) - 1) is set
f is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
len f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
(len f) - 1 is complex real integer finite ext-real countable set
q11 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q11 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(U,q1,f) is Relation-like Function-like set
(U,q1,f) . q11 is set
F is Element of U
q2 is Relation-like (U *) \ {{}} -defined U -valued Function-like non empty total quasi_total Element of bool [:((U *) \ {{}}),U:]
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (U *) \ {{}}
q2 . f is Element of U
(U,q1,f) is Relation-like Function-like set
(U,q1,f) is Relation-like Function-like set
len f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
(len f) - 1 is complex real integer finite ext-real countable set
(U,q1,f) . ((len f) - 1) is set
q2 is Relation-like (U *) \ {{}} -defined U -valued Function-like non empty total quasi_total Element of bool [:((U *) \ {{}}),U:]
f is Relation-like (U *) \ {{}} -defined U -valued Function-like non empty total quasi_total Element of bool [:((U *) \ {{}}),U:]
dom q2 is functional non empty FinSequence-membered Element of bool ((U *) \ {{}})
bool ((U *) \ {{}}) is non empty set
dom f is functional non empty FinSequence-membered Element of bool ((U *) \ {{}})
q11 is set
q2 . q11 is set
F is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (U *) \ {{}}
(U,q1,F) is Relation-like Function-like set
(U,q1,F) is Relation-like Function-like set
len F is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
(len F) - 1 is complex real integer finite ext-real countable set
(U,q1,F) . ((len F) - 1) is set
f . q11 is set
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
q1 is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
(U,q1) is Relation-like (U *) \ {{}} -defined U -valued Function-like non empty total quasi_total Element of bool [:((U *) \ {{}}),U:]
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) \ {{}} is functional non empty FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
[:((U *) \ {{}}),U:] is Relation-like non empty set
bool [:((U *) \ {{}}),U:] is non empty set
f is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
(U,q1) . f is set
q11 is Element of U
<*q11*> is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
[1,q11] is non empty V15() set
{[1,q11]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
(U,q1) . <*q11*> is set
f ^ <*q11*> is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
(U,q1) . (f ^ <*q11*>) is set
q1 . (((U,q1) . f),q11) is set
[((U,q1) . f),q11] is non empty V15() set
q1 . [((U,q1) . f),q11] is set
len f is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
F is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
F + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
dom <*q11*> is non empty trivial finite 1 -element countable Element of bool NAT
C is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
(len f) + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
C . ((len f) + 1) is set
<*q11*> . 1 is set
C | (len f) is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
Seg (len f) is non empty finite len f -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= len f ) } is set
C | (Seg (len f)) is Relation-like NAT -defined Seg (len f) -defined NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f | (len f) is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
f | (Seg (len f)) is Relation-like NAT -defined Seg (len f) -defined NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
len <*q11*> is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
len C is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
y1 is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (U *) \ {{}}
len x is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
(len x) - 1 is complex real integer finite ext-real countable set
(U,q1) . x is Element of U
(U,q1,x) is Relation-like Function-like set
(U,q1,x) is Relation-like Function-like set
(U,q1,x) . {} is set
x . 1 is set
y is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (U *) \ {{}}
(U,q1) . y is Element of U
(U,q1,y) is Relation-like Function-like set
(U,q1,y) is Relation-like Function-like set
len y is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
(len y) - 1 is complex real integer finite ext-real countable set
(U,q1,y) . ((len y) - 1) is set
(U,q1,y) . F is set
F + 2 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
y . (F + 2) is set
q1 . (((U,q1,y) . F),(y . (F + 2))) is set
[((U,q1,y) . F),(y . (F + 2))] is non empty V15() set
q1 . [((U,q1,y) . F),(y . (F + 2))] is set
p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (U *) \ {{}}
(U,q1,p) is Relation-like Function-like set
(U,q1,p) is Relation-like Function-like set
(len f) - 1 is complex real integer finite ext-real countable set
(U,q1,p) . ((len f) - 1) is set
y . ((len f) + 1) is set
q1 . (((U,q1,p) . ((len f) - 1)),(y . ((len f) + 1))) is set
[((U,q1,p) . ((len f) - 1)),(y . ((len f) + 1))] is non empty V15() set
q1 . [((U,q1,p) . ((len f) - 1)),(y . ((len f) + 1))] is set
(U,q1) . p is Element of U
q1 . (((U,q1) . p),q11) is Element of U
[((U,q1) . p),q11] is non empty V15() set
q1 . [((U,q1) . p),q11] is set
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
q1 is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
dom q1 is Relation-like U -defined U -valued non empty Element of bool [:U,U:]
bool [:U,U:] is non empty set
q2 is set
[:q2,U:] is Relation-like set
q2 /\ U is set
f is set
q11 is set
F is set
p is set
q1 . (f,F) is set
[f,F] is non empty V15() set
q1 . [f,F] is set
q1 . (q11,p) is set
[q11,p] is non empty V15() set
q1 . [q11,p] is set
U /\ U is set
[:(q2 /\ U),(U /\ U):] is Relation-like set
[:q2,U:] /\ [:U,U:] is Relation-like set
f is set
[:q2,U:] /\ (dom q1) is Relation-like U -defined U -valued Element of bool [:U,U:]
q11 is set
q1 . f is set
q1 . q11 is set
U /\ U is set
[:(q2 /\ U),(U /\ U):] is Relation-like set
F is set
p is set
[F,p] is non empty V15() set
C is set
y1 is set
[C,y1] is non empty V15() set
q1 . (F,p) is set
q1 . [F,p] is set
q1 . (C,y1) is set
q1 . [C,y1] is set
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
q1 is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
q2 is set
q2 /\ U is set
[:q2,U:] is Relation-like set
f is set
q11 is set
F is set
p is set
q1 . (f,F) is set
[f,F] is non empty V15() set
q1 . [f,F] is set
q1 . (q11,p) is set
[q11,p] is non empty V15() set
q1 . [q11,p] is set
[:q2,U:] is Relation-like set
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
q1 is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
(U,q1) is Relation-like (U *) \ {{}} -defined U -valued Function-like non empty total quasi_total Element of bool [:((U *) \ {{}}),U:]
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) \ {{}} is functional non empty FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
[:((U *) \ {{}}),U:] is Relation-like non empty set
bool [:((U *) \ {{}}),U:] is non empty set
f is Element of U
<*f*> is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
[1,f] is non empty V15() set
{[1,f]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
{} + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
({} + 1) -tuples_on U is functional non empty FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of U
q11 is Relation-like NAT -defined U -valued Function-like non empty finite {} + 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of ({} + 1) -tuples_on U
<*f*> ^ q11 is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
(U,q1) . (<*f*> ^ q11) is set
(U,q1) . q11 is set
q1 . (f,((U,q1) . q11)) is set
[f,((U,q1) . q11)] is non empty V15() set
q1 . [f,((U,q1) . q11)] is set
F is Element of U
<*F*> is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
[1,F] is non empty V15() set
{[1,F]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
(U,q1) . <*f*> is set
q1 . (((U,q1) . <*f*>),F) is set
[((U,q1) . <*f*>),F] is non empty V15() set
q1 . [((U,q1) . <*f*>),F] is set
q1 . (f,F) is Element of U
[f,F] is non empty V15() set
q1 . [f,F] is set
q11 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q11 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(q11 + 1) -tuples_on U is functional non empty FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of U
(q11 + 1) + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
((q11 + 1) + 1) -tuples_on U is functional non empty FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of U
F is Relation-like NAT -defined U -valued Function-like non empty finite (q11 + 1) + 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of ((q11 + 1) + 1) -tuples_on U
<*f*> ^ F is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
(U,q1) . (<*f*> ^ F) is set
(U,q1) . F is set
q1 . (f,((U,q1) . F)) is set
[f,((U,q1) . F)] is non empty V15() set
q1 . [f,((U,q1) . F)] is set
(q11 + 1) + {} is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
len F is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
F | (q11 + 1) is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
Seg (q11 + 1) is non empty finite q11 + 1 -element q11 + 1 -element countable Element of bool NAT
q11 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= q11 + 1 ) } is set
F | (Seg (q11 + 1)) is Relation-like NAT -defined Seg (q11 + 1) -defined NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
len (F | (q11 + 1)) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
p is Relation-like NAT -defined U -valued Function-like non empty finite q11 + 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of (q11 + 1) -tuples_on U
F /. (len F) is Element of U
C is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
(U,q1) . C is set
y1 is Element of U
<*y1*> is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
[1,y1] is non empty V15() set
{[1,y1]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
(F | (q11 + 1)) ^ <*y1*> is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
<*f*> ^ ((F | (q11 + 1)) ^ <*y1*>) is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
(U,q1) . (<*f*> ^ ((F | (q11 + 1)) ^ <*y1*>)) is set
<*f*> ^ p is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
(<*f*> ^ p) ^ <*y1*> is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
(U,q1) . ((<*f*> ^ p) ^ <*y1*>) is set
(U,q1) . (<*f*> ^ p) is set
q1 . (((U,q1) . (<*f*> ^ p)),y1) is set
[((U,q1) . (<*f*> ^ p)),y1] is non empty V15() set
q1 . [((U,q1) . (<*f*> ^ p)),y1] is set
(U,q1) . p is set
q1 . (f,((U,q1) . p)) is set
[f,((U,q1) . p)] is non empty V15() set
q1 . [f,((U,q1) . p)] is set
q1 . ((q1 . (f,((U,q1) . p))),y1) is set
[(q1 . (f,((U,q1) . p))),y1] is non empty V15() set
q1 . [(q1 . (f,((U,q1) . p))),y1] is set
x is Element of U
q1 . (x,y1) is Element of U
[x,y1] is non empty V15() set
q1 . [x,y1] is set
q1 . (f,(q1 . (x,y1))) is Element of U
[f,(q1 . (x,y1))] is non empty V15() set
q1 . [f,(q1 . (x,y1))] is set
C ^ <*y1*> is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
(U,q1) . (C ^ <*y1*>) is set
q1 . (f,((U,q1) . (C ^ <*y1*>))) is set
[f,((U,q1) . (C ^ <*y1*>))] is non empty V15() set
q1 . [f,((U,q1) . (C ^ <*y1*>))] is set
U is non empty set
bool U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) \ {{}} is functional non empty FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
q1 is non empty Element of bool U
q2 is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
(U,q2) is Relation-like (U *) \ {{}} -defined U -valued Function-like non empty total quasi_total Element of bool [:((U *) \ {{}}),U:]
[:((U *) \ {{}}),U:] is Relation-like non empty set
bool [:((U *) \ {{}}),U:] is non empty set
f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
f + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(f + 1) -tuples_on q1 is functional non empty FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of q1
(U,q2) .: ((f + 1) -tuples_on q1) is Element of bool U
{} + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
({} + 1) -tuples_on q1 is functional non empty FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of q1
(U,q2) .: (({} + 1) -tuples_on q1) is Element of bool U
((U,q2) .: (({} + 1) -tuples_on q1)) /\ U is Element of bool U
C is set
y1 is set
x is set
y is set
q2 . (C,x) is set
[C,x] is non empty V15() set
q2 . [C,x] is set
q2 . (y1,y) is set
[y1,y] is non empty V15() set
q2 . [y1,y] is set
dom (U,q2) is functional non empty FinSequence-membered Element of bool ((U *) \ {{}})
bool ((U *) \ {{}}) is non empty set
pb is set
[pb,C] is non empty V15() set
q1 is set
[q1,y1] is non empty V15() set
1 -tuples_on q1 is functional non empty FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of q1
q2 is Relation-like NAT -defined q1 -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on q1
(U,q2) . q2 is set
x2 is Relation-like NAT -defined q1 -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on q1
(U,q2) . x2 is set
p1 is Element of q1
<*p1*> is Relation-like NAT -defined q1 -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
[1,p1] is non empty V15() set
{[1,p1]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
p2 is Element of q1
<*p2*> is Relation-like NAT -defined q1 -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
[1,p2] is non empty V15() set
{[1,p2]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
u1 is Element of U
<*u1*> is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
[1,u1] is non empty V15() set
{[1,u1]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
(U,q2) . <*u1*> is set
q2 . (((U,q2) . <*u1*>),x) is set
[((U,q2) . <*u1*>),x] is non empty V15() set
q2 . [((U,q2) . <*u1*>),x] is set
u2 is Element of U
<*u2*> is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
[1,u2] is non empty V15() set
{[1,u2]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
(U,q2) . <*u2*> is set
q2 . (((U,q2) . <*u2*>),y) is set
[((U,q2) . <*u2*>),y] is non empty V15() set
q2 . [((U,q2) . <*u2*>),y] is set
q1 /\ U is Element of bool U
x1 is Element of U
p2 is Element of U
q2 . (p1,x1) is Element of U
[p1,x1] is non empty V15() set
q2 . [p1,x1] is set
q2 . (p2,p2) is Element of U
[p2,p2] is non empty V15() set
q2 . [p2,p2] is set
F is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
F + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(F + 1) -tuples_on q1 is functional non empty FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of q1
(U,q2) .: ((F + 1) -tuples_on q1) is Element of bool U
(F + 1) + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
((F + 1) + 1) -tuples_on q1 is functional non empty FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of q1
(U,q2) .: (((F + 1) + 1) -tuples_on q1) is Element of bool U
((U,q2) .: (((F + 1) + 1) -tuples_on q1)) /\ U is Element of bool U
y1 is set
x is set
y is set
pb is set
q2 . (y1,y) is set
[y1,y] is non empty V15() set
q2 . [y1,y] is set
q2 . (x,pb) is set
[x,pb] is non empty V15() set
q2 . [x,pb] is set
dom (U,q2) is functional non empty FinSequence-membered Element of bool ((U *) \ {{}})
bool ((U *) \ {{}}) is non empty set
q1 is set
[q1,y1] is non empty V15() set
x1 is set
[x1,x] is non empty V15() set
x2 is Relation-like NAT -defined q1 -valued Function-like non empty finite (F + 1) + 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of ((F + 1) + 1) -tuples_on q1
len x2 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
p1 is Relation-like NAT -defined q1 -valued Function-like non empty finite (F + 1) + 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of ((F + 1) + 1) -tuples_on q1
len p1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
x2 | (F + 1) is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
Seg (F + 1) is non empty finite F + 1 -element F + 1 -element countable Element of bool NAT
F + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= F + 1 ) } is set
x2 | (Seg (F + 1)) is Relation-like NAT -defined Seg (F + 1) -defined NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
x2 /. (len x2) is Element of q1
<*(x2 /. (len x2))*> is Relation-like NAT -defined q1 -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
[1,(x2 /. (len x2))] is non empty V15() set
{[1,(x2 /. (len x2))]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
(x2 | (F + 1)) ^ <*(x2 /. (len x2))*> is Relation-like NAT -defined q1 -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support Element of q1 *
q1 * is functional non empty FinSequence-membered FinSequenceSet of q1
p1 | (F + 1) is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
p1 | (Seg (F + 1)) is Relation-like NAT -defined Seg (F + 1) -defined NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
p1 /. (len p1) is Element of q1
<*(p1 /. (len p1))*> is Relation-like NAT -defined q1 -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
[1,(p1 /. (len p1))] is non empty V15() set
{[1,(p1 /. (len p1))]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
(p1 | (F + 1)) ^ <*(p1 /. (len p1))*> is Relation-like NAT -defined q1 -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support Element of q1 *
len (x2 | (F + 1)) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
len (p1 | (F + 1)) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
p2 is Relation-like NAT -defined q1 -valued Function-like finite F + 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
rng p2 is finite countable Element of bool q1
bool q1 is non empty set
u1 is Relation-like NAT -defined q1 -valued Function-like finite F + 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
rng u1 is finite countable Element of bool q1
u2 is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
v2 is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
v3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (U *) \ {{}}
ul is Element of U
q1 /\ U is Element of bool U
vl is Element of U
<*ul*> is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
[1,ul] is non empty V15() set
{[1,ul]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
u2 ^ <*ul*> is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
(U,q2) . (u2 ^ <*ul*>) is set
(U,q2) . u2 is set
q2 . (((U,q2) . u2),ul) is set
[((U,q2) . u2),ul] is non empty V15() set
q2 . [((U,q2) . u2),ul] is set
<*vl*> is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
[1,vl] is non empty V15() set
{[1,vl]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
v2 ^ <*vl*> is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
(U,q2) . (v2 ^ <*vl*>) is set
(U,q2) . v2 is set
q2 . (((U,q2) . v2),vl) is set
[((U,q2) . v2),vl] is non empty V15() set
q2 . [((U,q2) . v2),vl] is set
u3 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (U *) \ {{}}
(U,q2) . u3 is Element of U
q2 . (((U,q2) . u3),ul) is Element of U
[((U,q2) . u3),ul] is non empty V15() set
q2 . [((U,q2) . u3),ul] is set
p2 is Element of U
q2 . ((q2 . (((U,q2) . u3),ul)),p2) is Element of U
[(q2 . (((U,q2) . u3),ul)),p2] is non empty V15() set
q2 . [(q2 . (((U,q2) . u3),ul)),p2] is set
q2 . (ul,p2) is Element of U
[ul,p2] is non empty V15() set
q2 . [ul,p2] is set
q2 . (((U,q2) . u3),(q2 . (ul,p2))) is Element of U
[((U,q2) . u3),(q2 . (ul,p2))] is non empty V15() set
q2 . [((U,q2) . u3),(q2 . (ul,p2))] is set
(U,q2) . v3 is Element of U
q2 . (((U,q2) . v3),vl) is Element of U
[((U,q2) . v3),vl] is non empty V15() set
q2 . [((U,q2) . v3),vl] is set
q2 is Element of U
q2 . ((q2 . (((U,q2) . v3),vl)),q2) is Element of U
[(q2 . (((U,q2) . v3),vl)),q2] is non empty V15() set
q2 . [(q2 . (((U,q2) . v3),vl)),q2] is set
q2 . (vl,q2) is Element of U
[vl,q2] is non empty V15() set
q2 . [vl,q2] is set
q2 . (((U,q2) . v3),(q2 . (vl,q2))) is Element of U
[((U,q2) . v3),(q2 . (vl,q2))] is non empty V15() set
q2 . [((U,q2) . v3),(q2 . (vl,q2))] is set
(U,q2) . x2 is set
(U,q2) . p1 is set
u4 is Relation-like NAT -defined q1 -valued Function-like non empty finite F + 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of (F + 1) -tuples_on q1
v4 is Relation-like NAT -defined q1 -valued Function-like non empty finite F + 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of (F + 1) -tuples_on q1
(U,q2) . u4 is set
(U,q2) . v4 is set
((U,q2) .: ((F + 1) -tuples_on q1)) /\ U is Element of bool U
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) \ {{}} is functional non empty FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
q1 is set
q2 is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
(U,q2) is Relation-like (U *) \ {{}} -defined U -valued Function-like non empty total quasi_total Element of bool [:((U *) \ {{}}),U:]
[:((U *) \ {{}}),U:] is Relation-like non empty set
bool [:((U *) \ {{}}),U:] is non empty set
f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
f + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(f + 1) -tuples_on q1 is functional FinSequence-membered FinSequenceSet of q1
(U,q2) .: ((f + 1) -tuples_on q1) is Element of bool U
bool U is non empty set
dom (U,q2) is functional non empty FinSequence-membered Element of bool ((U *) \ {{}})
bool ((U *) \ {{}}) is non empty set
q1 /\ U is set
(f + 1) -tuples_on (q1 /\ U) is functional FinSequence-membered FinSequenceSet of q1 /\ U
{} -tuples_on q1 is functional FinSequence-membered empty-membered FinSequenceSet of q1
((U *) \ {{}}) /\ ((f + 1) -tuples_on q1) is functional FinSequence-membered Element of bool (U *)
(U,q2) .: (((U *) \ {{}}) /\ ((f + 1) -tuples_on q1)) is Element of bool U
(U *) /\ ((f + 1) -tuples_on q1) is set
((U *) /\ ((f + 1) -tuples_on q1)) \ {{}} is Element of bool ((U *) /\ ((f + 1) -tuples_on q1))
bool ((U *) /\ ((f + 1) -tuples_on q1)) is non empty set
(U,q2) .: (((U *) /\ ((f + 1) -tuples_on q1)) \ {{}}) is Element of bool U
((f + 1) -tuples_on (q1 /\ U)) \ {{}} is functional FinSequence-membered Element of bool ((f + 1) -tuples_on (q1 /\ U))
bool ((f + 1) -tuples_on (q1 /\ U)) is non empty set
(U,q2) .: (((f + 1) -tuples_on (q1 /\ U)) \ {{}}) is Element of bool U
((f + 1) -tuples_on (q1 /\ U)) \ ({} -tuples_on q1) is functional FinSequence-membered Element of bool ((f + 1) -tuples_on (q1 /\ U))
(U,q2) .: (((f + 1) -tuples_on (q1 /\ U)) \ ({} -tuples_on q1)) is Element of bool U
(U,q2) .: ((f + 1) -tuples_on (q1 /\ U)) is Element of bool U
F is non empty Element of bool U
(f + 1) -tuples_on F is functional non empty FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of F
(U,q2) .: ((f + 1) -tuples_on F) is Element of bool U
(U,q2) .: {} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of bool U
U is non empty set
bool U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
q1 is non empty Element of bool U
q2 is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
(U,q2) is Relation-like (U *) \ {{}} -defined U -valued Function-like non empty total quasi_total Element of bool [:((U *) \ {{}}),U:]
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) \ {{}} is functional non empty FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
[:((U *) \ {{}}),U:] is Relation-like non empty set
bool [:((U *) \ {{}}),U:] is non empty set
f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
f + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(f + 1) -tuples_on q1 is functional non empty FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of q1
dom (U,q2) is functional non empty FinSequence-membered Element of bool ((U *) \ {{}})
bool ((U *) \ {{}}) is non empty set
{} + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
({} + 1) -tuples_on q1 is functional non empty FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of q1
F is set
(({} + 1) -tuples_on q1) /\ (dom (U,q2)) is functional FinSequence-membered Element of bool ((U *) \ {{}})
p is set
(U,q2) . F is set
(U,q2) . p is set
1 -tuples_on q1 is functional non empty FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of q1
C is Element of q1
<*C*> is Relation-like NAT -defined q1 -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
[1,C] is non empty V15() set
{[1,C]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
y1 is Element of q1
<*y1*> is Relation-like NAT -defined q1 -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
[1,y1] is non empty V15() set
{[1,y1]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
x is Element of U
y is Element of U
F is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
F + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(F + 1) -tuples_on q1 is functional non empty FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of q1
(F + 1) + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
((F + 1) + 1) -tuples_on q1 is functional non empty FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of q1
C is set
(((F + 1) + 1) -tuples_on q1) /\ (dom (U,q2)) is functional FinSequence-membered Element of bool ((U *) \ {{}})
y1 is set
(U,q2) . C is set
(U,q2) . y1 is set
x is Relation-like NAT -defined q1 -valued Function-like non empty finite (F + 1) + 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of ((F + 1) + 1) -tuples_on q1
len x is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
y is Relation-like NAT -defined q1 -valued Function-like non empty finite (F + 1) + 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of ((F + 1) + 1) -tuples_on q1
len y is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
(F + 1) + {} is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
x | (F + 1) is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
Seg (F + 1) is non empty finite F + 1 -element F + 1 -element countable Element of bool NAT
F + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= F + 1 ) } is set
x | (Seg (F + 1)) is Relation-like NAT -defined Seg (F + 1) -defined NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
len (x | (F + 1)) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
y | (F + 1) is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
y | (Seg (F + 1)) is Relation-like NAT -defined Seg (F + 1) -defined NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
len (y | (F + 1)) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
pb is Relation-like NAT -defined q1 -valued Function-like non empty finite F + 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of (F + 1) -tuples_on q1
q1 is Relation-like NAT -defined q1 -valued Function-like non empty finite F + 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of (F + 1) -tuples_on q1
x1 is Relation-like NAT -defined q1 -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
rng x1 is non empty finite countable Element of bool q1
bool q1 is non empty set
p2 is Relation-like NAT -defined q1 -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
rng p2 is non empty finite countable Element of bool q1
x /. (len x) is Element of q1
y /. (len y) is Element of q1
q2 is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
p1 is Element of U
<*p1*> is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
[1,p1] is non empty V15() set
{[1,p1]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
q2 ^ <*p1*> is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
(U,q2) . (q2 ^ <*p1*>) is set
(U,q2) . q2 is set
q2 . (((U,q2) . q2),p1) is set
[((U,q2) . q2),p1] is non empty V15() set
q2 . [((U,q2) . q2),p1] is set
x2 is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
p2 is Element of U
<*p2*> is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
[1,p2] is non empty V15() set
{[1,p2]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
x2 ^ <*p2*> is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
(U,q2) . (x2 ^ <*p2*>) is set
(U,q2) . x2 is set
q2 . (((U,q2) . x2),p2) is set
[((U,q2) . x2),p2] is non empty V15() set
q2 . [((U,q2) . x2),p2] is set
pb ^ <*p1*> is Relation-like NAT -defined Function-like non empty finite (F + 1) + 1 -element FinSequence-like FinSubsequence-like countable finite-support set
(F + 1) + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
q1 ^ <*p2*> is Relation-like NAT -defined Function-like non empty finite (F + 1) + 1 -element FinSequence-like FinSubsequence-like countable finite-support set
(U,q2) . pb is set
(U,q2) .: ((F + 1) -tuples_on q1) is Element of bool U
(U,q2) . q1 is set
((U,q2) .: ((F + 1) -tuples_on q1)) /\ U is Element of bool U
q2 . (((U,q2) . pb),p1) is set
[((U,q2) . pb),p1] is non empty V15() set
q2 . [((U,q2) . pb),p1] is set
q2 . (((U,q2) . q1),p2) is set
[((U,q2) . q1),p2] is non empty V15() set
q2 . [((U,q2) . q1),p2] is set
((F + 1) -tuples_on q1) /\ (dom (U,q2)) is functional FinSequence-membered Element of bool ((U *) \ {{}})
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
q1 is set
q2 is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
(U,q2) is Relation-like (U *) \ {{}} -defined U -valued Function-like non empty total quasi_total Element of bool [:((U *) \ {{}}),U:]
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) \ {{}} is functional non empty FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
[:((U *) \ {{}}),U:] is Relation-like non empty set
bool [:((U *) \ {{}}),U:] is non empty set
f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
f + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(f + 1) -tuples_on q1 is functional FinSequence-membered FinSequenceSet of q1
{} -tuples_on q1 is functional FinSequence-membered empty-membered FinSequenceSet of q1
dom (U,q2) is functional non empty FinSequence-membered Element of bool ((U *) \ {{}})
bool ((U *) \ {{}}) is non empty set
(U,q2) | ((f + 1) -tuples_on q1) is Relation-like (U *) \ {{}} -defined (f + 1) -tuples_on q1 -defined (U *) \ {{}} -defined U -valued Function-like Element of bool [:((U *) \ {{}}),U:]
(U,q2) | ((U *) \ {{}}) is Relation-like (U *) \ {{}} -defined (U *) \ {{}} -defined U -valued Function-like Element of bool [:((U *) \ {{}}),U:]
((U,q2) | ((U *) \ {{}})) | ((f + 1) -tuples_on q1) is Relation-like (U *) \ {{}} -defined (f + 1) -tuples_on q1 -defined (U *) \ {{}} -defined U -valued Function-like Element of bool [:((U *) \ {{}}),U:]
((U *) \ {{}}) /\ ((f + 1) -tuples_on q1) is functional FinSequence-membered Element of bool (U *)
(U,q2) | (((U *) \ {{}}) /\ ((f + 1) -tuples_on q1)) is Relation-like (U *) \ {{}} -defined ((U *) \ {{}}) /\ ((f + 1) -tuples_on q1) -defined (U *) \ {{}} -defined U -valued Function-like Element of bool [:((U *) \ {{}}),U:]
(U *) /\ ((f + 1) -tuples_on q1) is set
((U *) /\ ((f + 1) -tuples_on q1)) \ {{}} is Element of bool ((U *) /\ ((f + 1) -tuples_on q1))
bool ((U *) /\ ((f + 1) -tuples_on q1)) is non empty set
(U,q2) | (((U *) /\ ((f + 1) -tuples_on q1)) \ {{}}) is Relation-like (U *) \ {{}} -defined ((U *) /\ ((f + 1) -tuples_on q1)) \ {{}} -defined (U *) \ {{}} -defined U -valued Function-like Element of bool [:((U *) \ {{}}),U:]
((f + 1) -tuples_on q1) \ {{}} is functional FinSequence-membered Element of bool ((f + 1) -tuples_on q1)
bool ((f + 1) -tuples_on q1) is non empty set
(U *) /\ (((f + 1) -tuples_on q1) \ {{}}) is functional FinSequence-membered Element of bool ((f + 1) -tuples_on q1)
(U,q2) | ((U *) /\ (((f + 1) -tuples_on q1) \ {{}})) is Relation-like (U *) \ {{}} -defined (U *) /\ (((f + 1) -tuples_on q1) \ {{}}) -defined (U *) \ {{}} -defined U -valued Function-like Element of bool [:((U *) \ {{}}),U:]
((f + 1) -tuples_on q1) \ ({} -tuples_on q1) is functional FinSequence-membered Element of bool ((f + 1) -tuples_on q1)
(U *) /\ (((f + 1) -tuples_on q1) \ ({} -tuples_on q1)) is functional FinSequence-membered Element of bool ((f + 1) -tuples_on q1)
(U,q2) | ((U *) /\ (((f + 1) -tuples_on q1) \ ({} -tuples_on q1))) is Relation-like (U *) \ {{}} -defined (U *) /\ (((f + 1) -tuples_on q1) \ ({} -tuples_on q1)) -defined (U *) \ {{}} -defined U -valued Function-like Element of bool [:((U *) \ {{}}),U:]
(U,q2) | ((U *) /\ ((f + 1) -tuples_on q1)) is Relation-like (U *) \ {{}} -defined (U *) /\ ((f + 1) -tuples_on q1) -defined (U *) \ {{}} -defined U -valued Function-like Element of bool [:((U *) \ {{}}),U:]
q1 /\ U is set
(f + 1) -tuples_on (q1 /\ U) is functional FinSequence-membered FinSequenceSet of q1 /\ U
(U,q2) | ((f + 1) -tuples_on (q1 /\ U)) is Relation-like (U *) \ {{}} -defined (f + 1) -tuples_on (q1 /\ U) -defined (U *) \ {{}} -defined U -valued Function-like Element of bool [:((U *) \ {{}}),U:]
U /\ q1 is set
bool U is non empty set
F is non empty Element of bool U
(f + 1) -tuples_on F is functional non empty FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of F
U /\ q1 is set
U /\ q1 is set
U is non empty set
(U) is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total associative Element of bool [:[:U,U:],U:]
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
pr1 (U,U) is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
(U,(U)) is Relation-like (U *) \ {{}} -defined U -valued Function-like non empty total quasi_total Element of bool [:((U *) \ {{}}),U:]
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) \ {{}} is functional non empty FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
[:((U *) \ {{}}),U:] is Relation-like non empty set
bool [:((U *) \ {{}}),U:] is non empty set
U is non empty set
(U) is Relation-like (U *) \ {{}} -defined U -valued Function-like non empty total quasi_total Element of bool [:((U *) \ {{}}),U:]
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) \ {{}} is functional non empty FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
[:((U *) \ {{}}),U:] is Relation-like non empty set
bool [:((U *) \ {{}}),U:] is non empty set
(U) is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total associative Element of bool [:[:U,U:],U:]
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
pr1 (U,U) is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
(U,(U)) is Relation-like (U *) \ {{}} -defined U -valued Function-like non empty total quasi_total Element of bool [:((U *) \ {{}}),U:]
q1 is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
(U) . q1 is set
q1 . 1 is set
q2 is Element of U
<*q2*> is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
[1,q2] is non empty V15() set
{[1,q2]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
f is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
<*q2*> ^ f is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
len q1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
{} + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
len q1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
len <*q2*> is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
len f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
(len <*q2*>) + (len f) is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
1 + (len f) is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
p is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
p + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(p + 1) -tuples_on U is functional non empty FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of U
C is Relation-like NAT -defined U -valued Function-like non empty finite p + 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of (p + 1) -tuples_on U
(U,(U)) . q1 is set
y1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (U *) \ {{}}
(U,(U)) . y1 is Element of U
(pr1 (U,U)) . (q2,((U,(U)) . y1)) is Element of U
[q2,((U,(U)) . y1)] is non empty V15() set
(pr1 (U,U)) . [q2,((U,(U)) . y1)] is set
len q1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
U is non empty set
(U) is Relation-like (U *) \ {{}} -defined U -valued Function-like non empty total quasi_total Element of bool [:((U *) \ {{}}),U:]
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) \ {{}} is functional non empty FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
[:((U *) \ {{}}),U:] is Relation-like non empty set
bool [:((U *) \ {{}}),U:] is non empty set
(U) is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total associative Element of bool [:[:U,U:],U:]
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
pr1 (U,U) is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
(U,(U)) is Relation-like (U *) \ {{}} -defined U -valued Function-like non empty total quasi_total Element of bool [:((U *) \ {{}}),U:]
q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U) . q1 is set
q1 . 1 is set
q2 is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
(U) . q2 is set
q2 . 1 is set
{} .--> {} is Relation-like {{}} -defined Function-like one-to-one constant non empty trivial finite 1 -element Function-yielding V159() Cardinal-yielding countable finite-support set
{{}} --> {} is Relation-like {{}} -defined {{}} -valued Function-like constant non empty total quasi_total finite Function-yielding V159() Cardinal-yielding countable finite-support Element of bool [:{{}},{{}}:]
[:{{}},{{}}:] is Relation-like non empty finite countable set
bool [:{{}},{{}}:] is non empty finite finite-membered countable set
U is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
[:(U *),(U *):] is Relation-like non empty set
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
((U *),(U -concatenation)) is Relation-like ((U *) *) \ {{}} -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(((U *) *) \ {{}}),(U *):]
(U *) * is functional non empty FinSequence-membered FinSequenceSet of U *
((U *) *) \ {{}} is functional non empty FinSequence-membered Element of bool ((U *) *)
bool ((U *) *) is non empty set
[:(((U *) *) \ {{}}),(U *):] is Relation-like non empty set
bool [:(((U *) *) \ {{}}),(U *):] is non empty set
({} .--> {}) +* ((U *),(U -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
U is non empty set
(U) is Relation-like Function-like set
U * is functional non empty FinSequence-membered FinSequenceSet of U
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
[:(U *),(U *):] is Relation-like non empty set
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
((U *),(U -concatenation)) is Relation-like ((U *) *) \ {{}} -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(((U *) *) \ {{}}),(U *):]
(U *) * is functional non empty FinSequence-membered FinSequenceSet of U *
((U *) *) \ {{}} is functional non empty FinSequence-membered Element of bool ((U *) *)
bool ((U *) *) is non empty set
[:(((U *) *) \ {{}}),(U *):] is Relation-like non empty set
bool [:(((U *) *) \ {{}}),(U *):] is non empty set
({} .--> {}) +* ((U *),(U -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
[:((U *) *),(U *):] is Relation-like non empty set
bool [:((U *) *),(U *):] is non empty set
{{}} \/ ((U *) *) is non empty set
{{}} \/ (U *) is non empty set
dom ({} .--> {}) is functional non empty trivial finite finite-membered 1 -element empty-membered with_common_domain countable Element of bool {{}}
bool {{}} is non empty finite finite-membered countable set
proj2 ({} .--> {}) is non empty trivial finite 1 -element countable set
dom ((U *),(U -concatenation)) is functional non empty FinSequence-membered Element of bool (((U *) *) \ {{}})
bool (((U *) *) \ {{}}) is non empty set
rng ((U *),(U -concatenation)) is functional non empty FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
(dom ({} .--> {})) \/ (dom ((U *),(U -concatenation))) is non empty set
(proj2 ({} .--> {})) \/ (rng ((U *),(U -concatenation))) is non empty set
proj2 (({} .--> {}) +* ((U *),(U -concatenation))) is non empty set
proj1 (U) is set
proj2 (U) is set
U is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) * is functional non empty FinSequence-membered FinSequenceSet of U *
(U) is Relation-like (U *) * -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:((U *) *),(U *):]
[:((U *) *),(U *):] is Relation-like non empty set
bool [:((U *) *),(U *):] is non empty set
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
[:(U *),(U *):] is Relation-like non empty set
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
((U *),(U -concatenation)) is Relation-like ((U *) *) \ {{}} -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(((U *) *) \ {{}}),(U *):]
((U *) *) \ {{}} is functional non empty FinSequence-membered Element of bool ((U *) *)
bool ((U *) *) is non empty set
[:(((U *) *) \ {{}}),(U *):] is Relation-like non empty set
bool [:(((U *) *) \ {{}}),(U *):] is non empty set
({} .--> {}) +* ((U *),(U -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
(U) | (((U *) *) \ {{}}) is Relation-like (U *) * -defined ((U *) *) \ {{}} -defined (U *) * -defined U * -valued Function-like Function-yielding V159() Element of bool [:((U *) *),(U *):]
dom ((U *),(U -concatenation)) is functional non empty FinSequence-membered Element of bool (((U *) *) \ {{}})
bool (((U *) *) \ {{}}) is non empty set
U is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) * is functional non empty FinSequence-membered FinSequenceSet of U *
(U) is Relation-like (U *) * -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:((U *) *),(U *):]
[:((U *) *),(U *):] is Relation-like non empty set
bool [:((U *) *),(U *):] is non empty set
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
[:(U *),(U *):] is Relation-like non empty set
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
((U *),(U -concatenation)) is Relation-like ((U *) *) \ {{}} -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(((U *) *) \ {{}}),(U *):]
((U *) *) \ {{}} is functional non empty FinSequence-membered Element of bool ((U *) *)
bool ((U *) *) is non empty set
[:(((U *) *) \ {{}}),(U *):] is Relation-like non empty set
bool [:(((U *) *) \ {{}}),(U *):] is non empty set
({} .--> {}) +* ((U *),(U -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
q1 is set
q1 \ {{}} is Element of bool q1
bool q1 is non empty set
(U) | (q1 \ {{}}) is Relation-like (U *) * -defined q1 \ {{}} -defined (U *) * -defined U * -valued Function-like Function-yielding V159() Element of bool [:((U *) *),(U *):]
((U *),(U -concatenation)) | q1 is Relation-like ((U *) *) \ {{}} -defined q1 -defined ((U *) *) \ {{}} -defined U * -valued Function-like Function-yielding V159() Element of bool [:(((U *) *) \ {{}}),(U *):]
dom (U) is functional non empty FinSequence-membered Element of bool ((U *) *)
(U) | ((U *) *) is Relation-like (U *) * -defined (U *) * -defined U * -valued Function-like Function-yielding V159() Element of bool [:((U *) *),(U *):]
((U) | ((U *) *)) | (q1 \ {{}}) is Relation-like (U *) * -defined q1 \ {{}} -defined (U *) * -defined U * -valued Function-like Function-yielding V159() Element of bool [:((U *) *),(U *):]
((U *) *) /\ (q1 \ {{}}) is Element of bool q1
(U) | (((U *) *) /\ (q1 \ {{}})) is Relation-like (U *) * -defined ((U *) *) /\ (q1 \ {{}}) -defined (U *) * -defined U * -valued Function-like Function-yielding V159() Element of bool [:((U *) *),(U *):]
((U *) *) /\ q1 is set
(((U *) *) /\ q1) \ {{}} is Element of bool (((U *) *) /\ q1)
bool (((U *) *) /\ q1) is non empty set
(U) | ((((U *) *) /\ q1) \ {{}}) is Relation-like (U *) * -defined (((U *) *) /\ q1) \ {{}} -defined (U *) * -defined U * -valued Function-like Function-yielding V159() Element of bool [:((U *) *),(U *):]
q1 /\ (((U *) *) \ {{}}) is functional FinSequence-membered Element of bool ((U *) *)
(U) | (q1 /\ (((U *) *) \ {{}})) is Relation-like (U *) * -defined q1 /\ (((U *) *) \ {{}}) -defined (U *) * -defined U * -valued Function-like Function-yielding V159() Element of bool [:((U *) *),(U *):]
(U) | (((U *) *) \ {{}}) is Relation-like (U *) * -defined ((U *) *) \ {{}} -defined (U *) * -defined U * -valued Function-like Function-yielding V159() Element of bool [:((U *) *),(U *):]
((U) | (((U *) *) \ {{}})) | q1 is Relation-like (U *) * -defined q1 -defined (U *) * -defined U * -valued Function-like Function-yielding V159() Element of bool [:((U *) *),(U *):]
U is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
[:(U *),(U *):] is Relation-like non empty set
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
((U *),(U -concatenation)) is Relation-like ((U *) *) \ {{}} -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(((U *) *) \ {{}}),(U *):]
(U *) * is functional non empty FinSequence-membered FinSequenceSet of U *
((U *) *) \ {{}} is functional non empty FinSequence-membered Element of bool ((U *) *)
bool ((U *) *) is non empty set
[:(((U *) *) \ {{}}),(U *):] is Relation-like non empty set
bool [:(((U *) *) \ {{}}),(U *):] is non empty set
dom ({} .--> {}) is functional non empty trivial finite finite-membered 1 -element empty-membered with_common_domain countable Element of bool {{}}
bool {{}} is non empty finite finite-membered countable set
dom ((U *),(U -concatenation)) is functional non empty FinSequence-membered Element of bool (((U *) *) \ {{}})
bool (((U *) *) \ {{}}) is non empty set
(dom ((U *),(U -concatenation))) /\ (dom ({} .--> {})) is functional trivial finite finite-membered empty-membered with_common_domain countable Element of bool {{}}
f is set
({} .--> {}) . f is Relation-like Function-like set
((U *),(U -concatenation)) . f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U is non empty set
(U) is Relation-like (U *) * -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:((U *) *),(U *):]
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) * is functional non empty FinSequence-membered FinSequenceSet of U *
[:((U *) *),(U *):] is Relation-like non empty set
bool [:((U *) *),(U *):] is non empty set
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
[:(U *),(U *):] is Relation-like non empty set
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
((U *),(U -concatenation)) is Relation-like ((U *) *) \ {{}} -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(((U *) *) \ {{}}),(U *):]
((U *) *) \ {{}} is functional non empty FinSequence-membered Element of bool ((U *) *)
bool ((U *) *) is non empty set
[:(((U *) *) \ {{}}),(U *):] is Relation-like non empty set
bool [:(((U *) *) \ {{}}),(U *):] is non empty set
({} .--> {}) +* ((U *),(U -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
q1 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
(U) . q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
dom ({} .--> {}) is functional non empty trivial finite finite-membered 1 -element empty-membered with_common_domain countable Element of bool {{}}
bool {{}} is non empty finite finite-membered countable set
dom ((U *),(U -concatenation)) is functional non empty FinSequence-membered Element of bool (((U *) *) \ {{}})
bool (((U *) *) \ {{}}) is non empty set
(dom ((U *),(U -concatenation))) \/ (dom ({} .--> {})) is non empty set
((U *),(U -concatenation)) +* ({} .--> {}) is Relation-like Function-like non empty Function-yielding V159() set
(U) . {} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
({} .--> {}) . {} is Relation-like Function-like set
q11 is set
U is non empty set
q1 is set
q2 is set
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
U * is functional non empty FinSequence-membered FinSequenceSet of U
[:(U *),(U *):] is Relation-like non empty set
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
U is non empty set
1 -tuples_on U is functional non empty FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of U
bool (1 -tuples_on U) is non empty set
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
U * is functional non empty FinSequence-membered FinSequenceSet of U
[:(U *),(U *):] is Relation-like non empty set
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
f is functional FinSequence-membered Element of bool (1 -tuples_on U)
q11 is set
f /\ (U *) is functional FinSequence-membered Element of bool (1 -tuples_on U)
F is set
p is set
C is set
y1 is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on U
x is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on U
q1 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
x1 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
p2 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
len p2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
q2 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
len q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
p2 . 1 is set
<*(p2 . 1)*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support set
[1,(p2 . 1)] is non empty V15() set
{[1,(p2 . 1)]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
q2 . 1 is set
<*(q2 . 1)*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support set
[1,(q2 . 1)] is non empty V15() set
{[1,(q2 . 1)]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
(U -concatenation) . (q11,p) is set
[q11,p] is non empty V15() set
(U -concatenation) . [q11,p] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
x2 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
p2 ^ x2 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
(U -concatenation) . (F,C) is set
[F,C] is non empty V15() set
(U -concatenation) . [F,C] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
p1 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
q2 ^ p1 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
(p2 ^ x2) . 1 is set
U is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) * is functional non empty FinSequence-membered FinSequenceSet of U *
(U) is Relation-like (U *) * -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:((U *) *),(U *):]
[:((U *) *),(U *):] is Relation-like non empty set
bool [:((U *) *),(U *):] is non empty set
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
[:(U *),(U *):] is Relation-like non empty set
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
((U *),(U -concatenation)) is Relation-like ((U *) *) \ {{}} -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(((U *) *) \ {{}}),(U *):]
((U *) *) \ {{}} is functional non empty FinSequence-membered Element of bool ((U *) *)
bool ((U *) *) is non empty set
[:(((U *) *) \ {{}}),(U *):] is Relation-like non empty set
bool [:(((U *) *) \ {{}}),(U *):] is non empty set
({} .--> {}) +* ((U *),(U -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
q1 is set
q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 -tuples_on q1 is functional FinSequence-membered FinSequenceSet of q1
(U) .: (q2 -tuples_on q1) is functional FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
dom (U) is functional non empty FinSequence-membered Element of bool ((U *) *)
[:NAT,q1:] is Relation-like set
bool [:NAT,q1:] is non empty set
<*> q1 is Relation-like non-empty empty-yielding NAT -defined q1 -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support FinSequence of q1
{(<*> q1)} is functional non empty trivial finite finite-membered 1 -element empty-membered with_common_domain countable Element of bool (bool [:NAT,q1:])
bool (bool [:NAT,q1:]) is non empty set
(<*> q1) * is functional non empty FinSequence-membered FinSequenceSet of <*> q1
{(<*> q1)} is functional non empty trivial finite finite-membered 1 -element empty-membered with_common_domain countable set
(U) .: {(<*> q1)} is functional finite FinSequence-membered countable Element of bool (U *)
Im ((U),{}) is set
(U) .: {{}} is finite countable set
(U) . {} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
{((U) . {})} is functional non empty trivial finite finite-membered 1 -element empty-membered with_common_domain countable set
((U) . {}) * is functional non empty FinSequence-membered FinSequenceSet of (U) . {}
((U) .: (q2 -tuples_on q1)) /\ (U *) is functional FinSequence-membered Element of bool (U *)
f is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
p is set
C is set
y1 is set
x is set
f . (p,y1) is set
[p,y1] is non empty V15() set
f . [p,y1] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f . (C,x) is set
[C,x] is non empty V15() set
f . [C,x] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
y is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
y ^ q1 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
pb is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
x1 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
f . (pb,x1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
[pb,x1] is non empty V15() set
f . [pb,x1] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
{} ^ x1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
p is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
p + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(p + 1) -tuples_on q1 is functional FinSequence-membered FinSequenceSet of q1
{} -tuples_on q1 is functional FinSequence-membered empty-membered FinSequenceSet of q1
((p + 1) -tuples_on q1) \ {{}} is functional FinSequence-membered Element of bool ((p + 1) -tuples_on q1)
bool ((p + 1) -tuples_on q1) is non empty set
f is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
((U *),f) is Relation-like ((U *) *) \ {{}} -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(((U *) *) \ {{}}),(U *):]
((U *),f) .: ((p + 1) -tuples_on q1) is functional FinSequence-membered Element of bool (U *)
(U) .: ((p + 1) -tuples_on q1) is functional FinSequence-membered Element of bool (U *)
(U) | (((p + 1) -tuples_on q1) \ {{}}) is Relation-like (U *) * -defined ((p + 1) -tuples_on q1) \ {{}} -defined (U *) * -defined U * -valued Function-like Function-yielding V159() Element of bool [:((U *) *),(U *):]
((U) | (((p + 1) -tuples_on q1) \ {{}})) .: (((p + 1) -tuples_on q1) \ {{}}) is functional FinSequence-membered Element of bool (U *)
((U *),f) | ((p + 1) -tuples_on q1) is Relation-like ((U *) *) \ {{}} -defined (p + 1) -tuples_on q1 -defined ((U *) *) \ {{}} -defined U * -valued Function-like Function-yielding V159() Element of bool [:(((U *) *) \ {{}}),(U *):]
(((U *),f) | ((p + 1) -tuples_on q1)) .: ((p + 1) -tuples_on q1) is functional FinSequence-membered Element of bool (U *)
U is non empty set
(U) is Relation-like (U *) * -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:((U *) *),(U *):]
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) * is functional non empty FinSequence-membered FinSequenceSet of U *
[:((U *) *),(U *):] is Relation-like non empty set
bool [:((U *) *),(U *):] is non empty set
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
[:(U *),(U *):] is Relation-like non empty set
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
((U *),(U -concatenation)) is Relation-like ((U *) *) \ {{}} -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(((U *) *) \ {{}}),(U *):]
((U *) *) \ {{}} is functional non empty FinSequence-membered Element of bool ((U *) *)
bool ((U *) *) is non empty set
[:(((U *) *) \ {{}}),(U *):] is Relation-like non empty set
bool [:(((U *) *) \ {{}}),(U *):] is non empty set
({} .--> {}) +* ((U *),(U -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
q1 is set
q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 -tuples_on q1 is functional FinSequence-membered FinSequenceSet of q1
Seg {} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= {} ) } is set
Funcs ((Seg {}),q1) is functional set
(U) | (q2 -tuples_on q1) is Relation-like (U *) * -defined q2 -tuples_on q1 -defined (U *) * -defined U * -valued Function-like Function-yielding V159() Element of bool [:((U *) *),(U *):]
p is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
p + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
C is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
C -tuples_on q1 is functional FinSequence-membered FinSequenceSet of q1
((U *),(U -concatenation)) | (C -tuples_on q1) is Relation-like ((U *) *) \ {{}} -defined C -tuples_on q1 -defined ((U *) *) \ {{}} -defined U * -valued Function-like Function-yielding V159() Element of bool [:(((U *) *) \ {{}}),(U *):]
len {} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of NAT
(C -tuples_on q1) \ {{}} is functional FinSequence-membered Element of bool (C -tuples_on q1)
bool (C -tuples_on q1) is non empty set
(U) | (q2 -tuples_on q1) is Relation-like (U *) * -defined q2 -tuples_on q1 -defined (U *) * -defined U * -valued Function-like Function-yielding V159() Element of bool [:((U *) *),(U *):]
U is set
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) \ {{}} is functional FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q1 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(q1 + 1) -tuples_on U is functional FinSequence-membered FinSequenceSet of U
{} -tuples_on U is functional FinSequence-membered empty-membered FinSequenceSet of U
f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
f -tuples_on U is functional FinSequence-membered FinSequenceSet of U
(U *) \ ({} -tuples_on U) is functional FinSequence-membered Element of bool (U *)
q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
U is set
q1 -tuples_on U is functional FinSequence-membered FinSequenceSet of U
q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
U is set
q1 -tuples_on U is functional FinSequence-membered FinSequenceSet of U
Seg q1 is finite q1 -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= q1 ) } is set
Funcs ((Seg q1),U) is functional set
U is set
q1 is set
q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 -tuples_on q1 is functional FinSequence-membered FinSequenceSet of q1
f is Relation-like NAT -defined Function-like finite q2 -element FinSequence-like FinSubsequence-like countable finite-support set
Seg q2 is finite q2 -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= q2 ) } is set
Funcs ((Seg q2),q1) is functional set
q11 is Relation-like Function-like set
proj1 q11 is set
proj2 q11 is set
U is set
q1 is set
chi (U,q1) is Relation-like Function-like set
[:q1,BOOLEAN:] is Relation-like set
bool [:q1,BOOLEAN:] is non empty set
chi (U,q1) is Relation-like q1 -defined {{},1} -valued Function-like total quasi_total Element of bool [:q1,{{},1}:]
[:q1,{{},1}:] is Relation-like set
bool [:q1,{{},1}:] is non empty set
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
f is non empty set
[:f,f:] is Relation-like non empty set
[:[:f,f:],f:] is Relation-like non empty set
bool [:[:f,f:],f:] is non empty set
q2 is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
(U,q2) is Relation-like (U *) \ {{}} -defined U -valued Function-like non empty total quasi_total Element of bool [:((U *) \ {{}}),U:]
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) \ {{}} is functional non empty FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
[:((U *) \ {{}}),U:] is Relation-like non empty set
bool [:((U *) \ {{}}),U:] is non empty set
q1 is Element of U
<*q1*> is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
[1,q1] is non empty V15() set
{[1,q1]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
(U,q2) . <*q1*> is set
F is Relation-like [:f,f:] -defined f -valued Function-like non empty total quasi_total Element of bool [:[:f,f:],f:]
(f,F) is Relation-like (f *) \ {{}} -defined f -valued Function-like non empty total quasi_total Element of bool [:((f *) \ {{}}),f:]
f * is functional non empty FinSequence-membered FinSequenceSet of f
(f *) \ {{}} is functional non empty FinSequence-membered Element of bool (f *)
bool (f *) is non empty set
[:((f *) \ {{}}),f:] is Relation-like non empty set
bool [:((f *) \ {{}}),f:] is non empty set
p is Relation-like NAT -defined f -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of f
q11 is Element of f
<*q11*> is Relation-like NAT -defined f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of f
[1,q11] is non empty V15() set
{[1,q11]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
p ^ <*q11*> is Relation-like NAT -defined f -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support Element of f *
(f,F) . (p ^ <*q11*>) is set
(f,F) . p is set
F . (((f,F) . p),q11) is set
[((f,F) . p),q11] is non empty V15() set
F . [((f,F) . p),q11] is set
U is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) * is functional non empty FinSequence-membered FinSequenceSet of U *
(U) is Relation-like (U *) * -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:((U *) *),(U *):]
[:((U *) *),(U *):] is Relation-like non empty set
bool [:((U *) *),(U *):] is non empty set
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
[:(U *),(U *):] is Relation-like non empty set
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
((U *),(U -concatenation)) is Relation-like ((U *) *) \ {{}} -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(((U *) *) \ {{}}),(U *):]
((U *) *) \ {{}} is functional non empty FinSequence-membered Element of bool ((U *) *)
bool ((U *) *) is non empty set
[:(((U *) *) \ {{}}),(U *):] is Relation-like non empty set
bool [:(((U *) *) \ {{}}),(U *):] is non empty set
({} .--> {}) +* ((U *),(U -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
q1 is Relation-like NAT -defined U * -valued Function-like non empty finite FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support Element of (U *) *
(U) . q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
((U *),(U -concatenation)) . q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U) | (((U *) *) \ {{}}) is Relation-like (U *) * -defined ((U *) *) \ {{}} -defined (U *) * -defined U * -valued Function-like Function-yielding V159() Element of bool [:((U *) *),(U *):]
((U) | (((U *) *) \ {{}})) . q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U) is Relation-like (U *) * -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:((U *) *),(U *):]
(U *) * is functional non empty FinSequence-membered FinSequenceSet of U *
[:((U *) *),(U *):] is Relation-like non empty set
bool [:((U *) *),(U *):] is non empty set
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
[:(U *),(U *):] is Relation-like non empty set
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
((U *),(U -concatenation)) is Relation-like ((U *) *) \ {{}} -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(((U *) *) \ {{}}),(U *):]
((U *) *) \ {{}} is functional non empty FinSequence-membered Element of bool ((U *) *)
bool ((U *) *) is non empty set
[:(((U *) *) \ {{}}),(U *):] is Relation-like non empty set
bool [:(((U *) *) \ {{}}),(U *):] is non empty set
({} .--> {}) +* ((U *),(U -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
q1 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
q2 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
<*q1,q2*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable finite-support set
<*q1*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support set
[1,q1] is non empty V15() set
{[1,q1]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
<*q2*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support set
[1,q2] is non empty V15() set
{[1,q2]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
<*q1*> ^ <*q2*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
1 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
(U) . <*q1,q2*> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 ^ q2 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
<*q1*> is Relation-like NAT -defined U * -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support FinSequence of U *
<*q2*> is Relation-like NAT -defined U * -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support FinSequence of U *
<*q1*> ^ <*q2*> is Relation-like NAT -defined U * -valued Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support Element of (U *) *
p is Relation-like NAT -defined U * -valued Function-like non empty finite FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support Element of (U *) *
(U) . p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
((U *),(U -concatenation)) . p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((U *),(U -concatenation)) . <*q1*> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U -concatenation) . ((((U *),(U -concatenation)) . <*q1*>),q2) is set
[(((U *),(U -concatenation)) . <*q1*>),q2] is non empty V15() set
(U -concatenation) . [(((U *),(U -concatenation)) . <*q1*>),q2] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U -concatenation) . (q1,q2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
[q1,q2] is non empty V15() set
(U -concatenation) . [q1,q2] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
<:U,q1:> is Relation-like Function-like set
len U is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
len q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
min ((len U),(len q1)) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
proj1 <:U,q1:> is set
Seg (min ((len U),(len q1))) is finite min ((len U),(len q1)) -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= min ((len U),(len q1)) ) } is set
U is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q1 is Relation-like NAT -defined Function-like finite U -element FinSequence-like FinSubsequence-like countable finite-support set
q2 is Relation-like NAT -defined Function-like finite U -element FinSequence-like FinSubsequence-like countable finite-support set
<:q1,q2:> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
len q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
len q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
min ((len q1),(len q2)) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q11 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
dom q11 is finite countable Element of bool NAT
F is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
Seg F is finite F -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
len q11 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
U is set
q1 is set
q2 is Relation-like U -defined Function-like set
f is Relation-like q1 -defined Function-like set
<:q2,f:> is Relation-like Function-like set
U /\ q1 is set
bool U is non empty set
dom q2 is Element of bool U
bool q1 is non empty set
dom f is Element of bool q1
proj1 <:q2,f:> is set
F is Element of bool q1
q11 is Element of bool U
F /\ q11 is Element of bool U
(proj1 <:q2,f:>) /\ (proj1 <:q2,f:>) is set
C is Relation-like Function-like set
U is set
q1 is Relation-like U -defined Function-like set
q2 is Relation-like U -defined Function-like set
<:q1,q2:> is Relation-like U /\ U -defined Function-like set
U /\ U is set
f is Relation-like Function-like set
U is set
q1 is set
U /\ q1 is set
q2 is Relation-like U -defined Function-like total set
f is Relation-like q1 -defined Function-like total set
<:q2,f:> is Relation-like U /\ q1 -defined Function-like set
dom q2 is Element of bool U
bool U is non empty set
dom f is Element of bool q1
bool q1 is non empty set
q11 is Relation-like U /\ q1 -defined Function-like set
dom q11 is Element of bool (U /\ q1)
bool (U /\ q1) is non empty set
F is Relation-like U /\ q1 -defined Function-like set
U is set
q1 is Relation-like U -defined Function-like total set
q2 is Relation-like U -defined Function-like total set
<:q1,q2:> is Relation-like U -defined U /\ U -defined Function-like total set
U /\ U is set
f is Relation-like U -defined Function-like set
U is set
q1 is set
q2 is Relation-like U -valued Function-like set
f is Relation-like q1 -valued Function-like set
<:q2,f:> is Relation-like Function-like set
[:U,q1:] is Relation-like set
proj2 <:q2,f:> is set
rng q2 is Element of bool U
bool U is non empty set
rng f is Element of bool q1
bool q1 is non empty set
[:(rng q2),(rng f):] is Relation-like U -defined q1 -valued Element of bool [:U,q1:]
bool [:U,q1:] is non empty set
F is Relation-like Function-like set
U is non empty set
the Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
U is non empty set
q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
the Relation-like NAT -defined U -valued Function-like finite q1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U is Relation-like NAT -defined U -valued Function-like finite q1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
U is non empty set
q1 is non empty set
[:U,q1:] is Relation-like non empty set
bool [:U,q1:] is non empty set
f is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q2 is Relation-like U -defined q1 -valued Function-like non empty total quasi_total Element of bool [:U,q1:]
f * q2 is Relation-like NAT -defined q1 -valued Function-like finite countable finite-support set
rng f is finite countable Element of bool U
bool U is non empty set
q11 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
q2 * q11 is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
U is non empty set
q1 is non empty set
[:U,q1:] is Relation-like non empty set
bool [:U,q1:] is non empty set
q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q11 is Relation-like NAT -defined U -valued Function-like finite q2 -element FinSequence-like FinSubsequence-like countable finite-support set
f is Relation-like U -defined q1 -valued Function-like non empty total quasi_total Element of bool [:U,q1:]
q11 * f is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
rng q11 is finite countable Element of bool U
bool U is non empty set
dom f is non empty Element of bool U
dom (q11 * f) is finite countable Element of bool NAT
dom q11 is finite q2 -element countable Element of bool NAT
len q11 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
Seg (len q11) is finite len q11 -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= len q11 ) } is set
F is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
Seg F is finite F -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
len (q11 * f) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
q2 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
f is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
<:q2,f:> is Relation-like NAT -defined NAT /\ NAT -defined [:U,U:] -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
NAT /\ NAT is set
q1 is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
<:q2,f:> * q1 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
rng (<:q2,f:> * q1) is finite countable Element of bool U
bool U is non empty set
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
U * is functional non empty FinSequence-membered FinSequenceSet of U
q1 is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
f is Relation-like NAT -defined U -valued Function-like finite q2 -element FinSequence-like FinSubsequence-like countable finite-support Element of U *
q11 is Relation-like NAT -defined U -valued Function-like finite q2 -element FinSequence-like FinSubsequence-like countable finite-support Element of U *
(U,q1,f,q11) is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
<:f,q11:> is Relation-like NAT -defined NAT /\ NAT -defined [:U,U:] -valued Function-like finite q2 -element FinSequence-like FinSubsequence-like countable finite-support set
<:f,q11:> * q1 is Relation-like NAT -defined U -valued Function-like finite q2 -element FinSequence-like FinSubsequence-like countable finite-support set
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
[:{{}},NAT:] is Relation-like non empty non trivial non finite non empty-membered set
[:{{}},NAT:] \ {[{},{}]} is Relation-like {{}} -defined NAT -valued Element of bool [:{{}},NAT:]
bool [:{{}},NAT:] is non empty non trivial non finite non empty-membered set
NAT \/ ([:{{}},NAT:] \ {[{},{}]}) is non empty set
NAT \ {[{},{}]} is Element of bool REAL
(NAT \ {[{},{}]}) \/ ([:{{}},NAT:] \ {[{},{}]}) is set
U is set
q1 is set
U is set
q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q1 -tuples_on U is functional FinSequence-membered FinSequenceSet of U
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
proj2 f is finite countable set
len f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
U is set
q1 is set
U /\ q1 is set
bool U is non empty set
bool q1 is non empty set
U is set
q1 is set
U /\ q1 is set
(U,q1) is Element of bool U
bool U is non empty set
(NAT,NAT) is countable Element of bool NAT
(U,q1) is Element of bool q1
bool q1 is non empty set
(NAT,NAT) is countable Element of bool NAT
q1 is set
U is set
bool U is non empty set
q1 is Element of bool U
U /\ q1 is Element of bool U
(U,q1) is Element of bool U
U /\ q1 is set
(U,q1) is Element of bool q1
bool q1 is non empty set
(U,q1) is set
q1 is set
U is set
q1 \ U is Element of bool q1
bool q1 is non empty set
q2 is set
U /\ q2 is set
(U,q2) is Element of bool U
bool U is non empty set
(U,q2) is Element of bool q2
bool q2 is non empty set
(q1 \ U) /\ (U /\ q2) is Element of bool q1
((q1 \ U),(U /\ q2)) is Element of bool (q1 \ U)
bool (q1 \ U) is non empty set
(q1 \ U) /\ (U /\ q2) is set
((q1 \ U),(U /\ q2)) is Element of bool (U /\ q2)
bool (U /\ q2) is non empty set
F is set
U is set
q1 is set
U \ q1 is Element of bool U
bool U is non empty set
U is set
q1 is set
U \ q1 is Element of bool U
bool U is non empty set
(U,q1) is Element of bool U
((omega \/ [:{{}},omega:]),{[{},{}]}) is Element of bool (omega \/ [:{{}},omega:])
([:{{}},NAT:],{[{},{}]}) is Relation-like {{}} -defined NAT -valued Element of bool [:{{}},NAT:]
U is set
q1 is set
U \/ q1 is set
bool (U \/ q1) is non empty set
U is set
q1 is set
(U,q1) is Element of bool (U \/ q1)
U \/ q1 is set
bool (U \/ q1) is non empty set
(q1,U) is set
U is set
bool U is non empty set
q1 is Element of bool U
U \/ q1 is set
(q1,U) is set
(U,q1) is Element of bool (U \/ q1)
bool (U \/ q1) is non empty set
U is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q1 is Relation-like Function-like set
iter (q1,U) is Relation-like Function-like set
q2 is Relation-like Function-like set
iter (q2,U) is Relation-like Function-like set
iter (q2,{}) is Relation-like Function-like set
iter (q1,{}) is Relation-like Function-like set
field q2 is set
proj1 q2 is set
proj2 q2 is set
(proj1 q2) \/ (proj2 q2) is set
id (field q2) is Relation-like field q2 -defined field q2 -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:(field q2),(field q2):]
[:(field q2),(field q2):] is Relation-like set
bool [:(field q2),(field q2):] is non empty set
field q1 is set
proj1 q1 is set
proj2 q1 is set
(proj1 q1) \/ (proj2 q1) is set
id (field q1) is Relation-like field q1 -defined field q1 -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:(field q1),(field q1):]
[:(field q1),(field q1):] is Relation-like set
bool [:(field q1),(field q1):] is non empty set
f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
iter (q2,f) is Relation-like Function-like set
iter (q1,f) is Relation-like Function-like set
f + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
iter (q2,(f + 1)) is Relation-like Function-like set
iter (q1,(f + 1)) is Relation-like Function-like set
(iter (q2,f)) * q2 is Relation-like Function-like set
(iter (q1,f)) * q1 is Relation-like Function-like set
U is Relation-like set
U [*] is Relation-like set
field U is set
proj1 U is set
proj2 U is set
(proj1 U) \/ (proj2 U) is set
f is set
q11 is set
F is set
[f,q11] is non empty V15() set
[q11,F] is non empty V15() set
p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
len p is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
p . 1 is set
p . (len p) is set
C is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
C + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
y1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
len y1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
y1 . 1 is set
y1 . (len y1) is set
dom y1 is finite countable Element of bool NAT
Seg C is finite C -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= C ) } is set
p | (Seg C) is Relation-like NAT -defined Seg C -defined NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
pb is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
pb ^ y1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
C + {} is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
len pb is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
{} + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
y is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
C + y is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
x1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
C + x1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
(pb ^ y1) . (C + x1) is set
y1 . x1 is set
p2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
Seg (len y1) is finite len y1 -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= len y1 ) } is set
(pb ^ y1) . 1 is set
dom pb is finite countable Element of bool NAT
pb . 1 is set
Seg y is non empty finite y -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= y ) } is set
(len pb) + (len y1) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
(pb ^ y1) . ((len pb) + (len y1)) is set
len (pb ^ y1) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
x1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
(pb ^ y1) . x1 is set
x1 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(pb ^ y1) . (x1 + 1) is set
[((pb ^ y1) . x1),((pb ^ y1) . (x1 + 1))] is non empty V15() set
x is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
dom pb is finite countable Element of bool NAT
pb . x1 is set
pb . (x1 + 1) is set
p . x1 is set
p . (x1 + 1) is set
dom pb is finite countable Element of bool NAT
(pb ^ y1) . C is set
pb . C is set
p . C is set
(pb ^ y1) . (C + 1) is set
p . (C + 1) is set
p2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
C + p2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
1 + {} is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
p2 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
y1 . p2 is set
(len pb) + (p2 + 1) is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(pb ^ y1) . ((len pb) + (p2 + 1)) is set
y1 . (p2 + 1) is set
(pb ^ y1) . (len (pb ^ y1)) is set
x1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
(pb ^ y1) . x1 is set
x1 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(pb ^ y1) . (x1 + 1) is set
[((pb ^ y1) . x1),((pb ^ y1) . (x1 + 1))] is non empty V15() set
[f,F] is non empty V15() set
U is Relation-like set
U [*] is Relation-like set
field (U [*]) is set
proj1 (U [*]) is set
proj2 (U [*]) is set
(proj1 (U [*])) \/ (proj2 (U [*])) is set
field U is set
proj1 U is set
proj2 U is set
(proj1 U) \/ (proj2 U) is set
q11 is set
F is set
[q11,F] is non empty V15() set
F is set
[F,q11] is non empty V15() set
U is Relation-like set
U [*] is Relation-like set
field U is set
proj1 U is set
proj2 U is set
(proj1 U) \/ (proj2 U) is set
f is set
<*f*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support set
[1,f] is non empty V15() set
{[1,f]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
q11 is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support set
len q11 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
q11 . 1 is set
q11 . (len q11) is set
F is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q11 . F is set
F + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
q11 . (F + 1) is set
[(q11 . F),(q11 . (F + 1))] is non empty V15() set
[f,f] is non empty V15() set
U is Relation-like set
U [*] is Relation-like set
field (U [*]) is set
proj1 (U [*]) is set
proj2 (U [*]) is set
(proj1 (U [*])) \/ (proj2 (U [*])) is set
field U is set
proj1 U is set
proj2 U is set
(proj1 U) \/ (proj2 U) is set
U is Relation-like set
U [*] is Relation-like set
field U is set
proj1 U is set
proj2 U is set
(proj1 U) \/ (proj2 U) is set
field (U [*]) is set
proj1 (U [*]) is set
proj2 (U [*]) is set
(proj1 (U [*])) \/ (proj2 (U [*])) is set
q1 is Relation-like set
field U is set
proj1 U is set
proj2 U is set
(proj1 U) \/ (proj2 U) is set
field (U [*]) is set
proj1 (U [*]) is set
proj2 (U [*]) is set
(proj1 (U [*])) \/ (proj2 (U [*])) is set
q1 is Relation-like set
U is Relation-like Function-like set
iter (U,{}) is Relation-like Function-like set
U [*] is Relation-like reflexive transitive set
field U is set
proj1 U is set
proj2 U is set
(proj1 U) \/ (proj2 U) is set
id (field U) is Relation-like field U -defined field U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:(field U),(field U):]
[:(field U),(field U):] is Relation-like set
bool [:(field U),(field U):] is non empty set
field (U [*]) is set
proj1 (U [*]) is set
proj2 (U [*]) is set
(proj1 (U [*])) \/ (proj2 (U [*])) is set
id (field (U [*])) is Relation-like field (U [*]) -defined field (U [*]) -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:(field (U [*])),(field (U [*])):]
[:(field (U [*])),(field (U [*])):] is Relation-like set
bool [:(field (U [*])),(field (U [*])):] is non empty set
U is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
U + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
q1 is Relation-like Function-like set
iter (q1,(U + 1)) is Relation-like Function-like set
q1 [*] is Relation-like reflexive transitive set
{} + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
iter (q1,({} + 1)) is Relation-like Function-like set
iter (q1,1) is Relation-like Function-like set
f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
f + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
iter (q1,(f + 1)) is Relation-like Function-like set
(f + 1) + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
iter (q1,((f + 1) + 1)) is Relation-like Function-like set
q1 * (iter (q1,(f + 1))) is Relation-like Function-like set
(q1 [*]) * (q1 [*]) is Relation-like set
U is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q1 is Relation-like Function-like set
iter (q1,U) is Relation-like Function-like set
q1 [*] is Relation-like reflexive transitive set
q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
U is set
q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 is Relation-like Function-like set
q2 . {} is set
q2 . q1 is set
f is Relation-like Function-like set
proj2 f is set
proj1 f is set
iter (f,q1) is Relation-like Function-like set
(iter (f,q1)) . U is set
(proj1 f) \/ (proj2 f) is set
iter (f,{}) is Relation-like Function-like set
(iter (f,{})) . U is set
field f is set
id (field f) is Relation-like field f -defined field f -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:(field f),(field f):]
[:(field f),(field f):] is Relation-like set
bool [:(field f),(field f):] is non empty set
q11 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 . q11 is set
iter (f,q11) is Relation-like Function-like set
(iter (f,q11)) . U is set
q11 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
q2 . (q11 + 1) is set
iter (f,(q11 + 1)) is Relation-like Function-like set
(iter (f,(q11 + 1))) . U is set
F is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
F + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
q2 . (F + 1) is set
q2 . F is set
f . (q2 . F) is set
F + {} is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
proj1 (iter (f,q11)) is set
q11 + {} is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
f . (q2 . q11) is set
(iter (f,q11)) * f is Relation-like Function-like set
((iter (f,q11)) * f) . U is set
F is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
F + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
q2 . (F + 1) is set
q2 . F is set
f . (q2 . F) is set
[:COMPLEX,COMPLEX:] is Relation-like non empty non trivial non finite non empty-membered set
bool [:COMPLEX,COMPLEX:] is non empty non trivial non finite non empty-membered set
U is complex Element of COMPLEX
q1 is complex set
q1 + 1 is complex set
q2 is complex Element of COMPLEX
f is complex set
f + 1 is complex set
U is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total Element of bool [:COMPLEX,COMPLEX:]
q1 is complex set
q2 is complex Element of COMPLEX
U . q2 is complex Element of COMPLEX
f is complex set
f + 1 is complex set
U . q1 is set
q1 + 1 is complex set
q1 is complex set
U . q1 is set
q1 + 1 is complex set
U is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total Element of bool [:COMPLEX,COMPLEX:]
q1 is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total Element of bool [:COMPLEX,COMPLEX:]
q2 is complex Element of COMPLEX
U . q2 is complex Element of COMPLEX
q2 + 1 is complex set
q1 . q2 is complex Element of COMPLEX
() is Relation-like COMPLEX -defined COMPLEX -valued Function-like non empty total quasi_total Element of bool [:COMPLEX,COMPLEX:]
U is set
q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q1 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
q2 is Relation-like Function-like set
proj2 q2 is set
proj1 q2 is set
iter (q2,q1) is Relation-like Function-like set
(iter (q2,q1)) . U is set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f . 1 is set
f . (q1 + 1) is set
dom () is non empty Element of bool COMPLEX
bool COMPLEX is non empty non trivial non finite non empty-membered set
() * f is Relation-like COMPLEX -defined Function-like set
F is Relation-like Function-like set
p is complex set
F . p is set
p + 1 is complex set
f . (p + 1) is set
C is Element of dom ()
() . C is complex Element of COMPLEX
f . (() . C) is set
{} + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
f . ({} + 1) is set
F . {} is set
p is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
p + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(p + 1) + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
f . ((p + 1) + 1) is set
f . (p + 1) is set
q2 . (f . (p + 1)) is set
F . p is set
q2 . (F . p) is set
F . (p + 1) is set
F . q1 is set
U is set
q1 is Relation-like Function-like set
q1 [*] is Relation-like reflexive transitive set
proj2 q1 is set
proj1 q1 is set
f is set
q11 is set
[f,q11] is non empty V15() set
F is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
len F is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
F . 1 is set
F . (len F) is set
field q1 is set
(proj1 q1) \/ (proj2 q1) is set
p is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
p + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
iter (q1,p) is Relation-like Function-like set
C is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
F . C is set
C + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
F . (C + 1) is set
q1 . (F . C) is set
[(F . C),(F . (C + 1))] is non empty V15() set
F . (p + 1) is set
C is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
C + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
F . (C + 1) is set
F . C is set
q1 . (F . C) is set
proj1 (iter (q1,p)) is set
(iter (q1,p)) . f is set
U is Relation-like Function-like set
proj2 U is set
proj1 U is set
U [*] is Relation-like reflexive transitive set
{ (iter (U,b₁)) where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : verum } is set
union { (iter (U,b₁)) where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : verum } is set
q11 is set
F is set
p is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
iter (U,p) is Relation-like Function-like set
q11 is set
F is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
iter (U,F) is Relation-like Function-like set
p is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
iter (U,p) is Relation-like Function-like set
U is Relation-like Function-like set
proj2 U is set
proj1 U is set
U [*] is Relation-like reflexive transitive set
{ (iter (U,b₁)) where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : verum } is set
union { (iter (U,b₁)) where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : verum } is set
q2 is Relation-like Function-like set
q1 is Relation-like Function-like set
U is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
iter (q2,U) is Relation-like Function-like set
iter (q1,U) is Relation-like Function-like set
U is functional set
union U is set
q1 is set
q2 is set
U is set
q1 is set
q2 is set
Funcs (q1,q2) is functional set
union U is set
[:q1,q2:] is Relation-like set
U is set
U \ U is Element of bool U
bool U is non empty set
(U,U) is Element of bool U
q1 is set
U is non empty set
id U is Relation-like U -defined U -valued Function-like one-to-one non empty total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:U,U:]
[:U,U:] is Relation-like non empty set
bool [:U,U:] is non empty set
q1 is Element of U
(id U) . q1 is Element of U
{((id U) . q1)} is non empty trivial finite 1 -element countable Element of bool U
bool U is non empty set
{q1} is non empty trivial finite 1 -element countable Element of bool U
{((id U) . q1)} \ {q1} is finite countable Element of bool U
({((id U) . q1)},{q1}) is trivial finite countable Element of bool {((id U) . q1)}
bool {((id U) . q1)} is non empty finite finite-membered countable set
{((id U) . q1)} \ {q1} is trivial finite countable Element of bool {((id U) . q1)}
q2 is set
U is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
U ^ q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1,U) is set
(U,q1) is Relation-like NAT -defined finite countable Element of bool (U \/ q1)
U \/ q1 is Relation-like NAT -defined finite countable set
bool (U \/ q1) is non empty finite finite-membered countable set
q1 ^ U is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U is set
q1 is Relation-like U -defined set
q1 | U is Relation-like U -defined U -defined set
(U,q1) is set
(q1,U) is Element of bool (q1 \/ U)
q1 \/ U is set
bool (q1 \/ U) is non empty set
U is Relation-like Function-like set
proj1 U is set
{ [b₁,(U . b₁)] where b₁ is Element of proj1 U : b₁ in proj1 U } is set
q2 is set
f is set
q11 is set
[f,q11] is non empty V15() set
F is Element of proj1 U
U . F is set
[F,(U . F)] is non empty V15() set
q2 is set
f is Element of proj1 U
U . f is set
[f,(U . f)] is non empty V15() set
U is set
id U is Relation-like U -defined U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:U,U:]
[:U,U:] is Relation-like set
bool [:U,U:] is non empty set
q2 is Relation-like U -defined total set
q2 ~ is Relation-like set
q2 * (q2 ~) is Relation-like U -defined set
f is Relation-like Function-like set
proj1 f is set
{ [b₁,(f . b₁)] where b₁ is Element of proj1 f : b₁ in proj1 f } is set
q11 is set
dom (id U) is Element of bool U
bool U is non empty set
F is Element of proj1 f
(id U) . F is set
[F,((id U) . F)] is non empty V15() set
[F,F] is non empty V15() set
dom q2 is Element of bool U
p is set
[F,p] is non empty V15() set
[p,F] is non empty V15() set
U is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
[:(U *),(U *):] is Relation-like non empty set
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q1 -tuples_on U is functional non empty FinSequence-membered FinSequenceSet of U
q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q1 + q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
(q1 + q2) -tuples_on U is functional non empty FinSequence-membered FinSequenceSet of U
q2 -tuples_on U is functional non empty FinSequence-membered FinSequenceSet of U
[:(q1 -tuples_on U),(q2 -tuples_on U):] is Relation-like non empty set
(U -concatenation) .: [:(q1 -tuples_on U),(q2 -tuples_on U):] is functional FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
q11 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
f + q11 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
(f + q11) -tuples_on U is functional non empty FinSequence-membered FinSequenceSet of U
f -tuples_on U is functional non empty FinSequence-membered FinSequenceSet of U
q11 -tuples_on U is functional non empty FinSequence-membered FinSequenceSet of U
[:(f -tuples_on U),(q11 -tuples_on U):] is Relation-like non empty set
(U -concatenation) .: [:(f -tuples_on U),(q11 -tuples_on U):] is functional FinSequence-membered Element of bool (U *)
{ (b₁ ^ b₂) where b₁ is Relation-like NAT -defined U -valued Function-like finite f -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U, b₂ is Relation-like NAT -defined U -valued Function-like finite q11 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U : verum } is set
dom (U -concatenation) is Relation-like U * -defined U * -valued non empty Element of bool [:(U *),(U *):]
bool [:(U *),(U *):] is non empty set
pb is set
q1 is Relation-like NAT -defined U -valued Function-like finite f -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
x1 is Relation-like NAT -defined U -valued Function-like finite q11 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
q1 ^ x1 is Relation-like NAT -defined U -valued Function-like finite f + q11 -element FinSequence-like FinSubsequence-like countable finite-support Element of U *
f + q11 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
p2 is Relation-like NAT -defined U -valued Function-like finite f -element FinSequence-like FinSubsequence-like countable finite-support Element of f -tuples_on U
q2 is Relation-like NAT -defined U -valued Function-like finite q11 -element FinSequence-like FinSubsequence-like countable finite-support Element of q11 -tuples_on U
[p2,q2] is non empty V15() Element of [:(f -tuples_on U),(q11 -tuples_on U):]
x2 is Element of [:(f -tuples_on U),(q11 -tuples_on U):]
{x2} is Relation-like f -tuples_on U -defined q11 -tuples_on U -valued non empty trivial finite 1 -element countable Element of bool [:(f -tuples_on U),(q11 -tuples_on U):]
bool [:(f -tuples_on U),(q11 -tuples_on U):] is non empty set
(U -concatenation) .: {x2} is functional finite FinSequence-membered countable Element of bool (U *)
(U -concatenation) . (q1,x1) is set
[q1,x1] is non empty V15() set
(U -concatenation) . [q1,x1] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U -concatenation) . x2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
p1 is Element of dom (U -concatenation)
(U -concatenation) . p1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
{((U -concatenation) . p1)} is functional non empty trivial finite finite-membered 1 -element FinSequence-membered with_common_domain countable Element of bool (U *)
Im ((U -concatenation),p1) is set
{p1} is non empty trivial finite 1 -element countable set
(U -concatenation) .: {p1} is finite countable set
pb is set
q1 is set
(U -concatenation) . q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
x1 is set
p2 is set
[x1,p2] is non empty V15() set
q2 is Relation-like NAT -defined U -valued Function-like finite f -element FinSequence-like FinSubsequence-like countable finite-support Element of f -tuples_on U
x2 is Relation-like NAT -defined U -valued Function-like finite q11 -element FinSequence-like FinSubsequence-like countable finite-support Element of q11 -tuples_on U
p1 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
p2 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
(U -concatenation) . (p1,p2) is set
[p1,p2] is non empty V15() set
(U -concatenation) . [p1,p2] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
u1 is Relation-like NAT -defined U -valued Function-like finite f -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
u2 is Relation-like NAT -defined U -valued Function-like finite q11 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
u1 ^ u2 is Relation-like NAT -defined U -valued Function-like finite f + q11 -element FinSequence-like FinSubsequence-like countable finite-support Element of U *
U is set
q1 is Relation-like set
q2 is Relation-like set
q1 \/ q2 is Relation-like set
(q1 \/ q2) " U is set
q1 " U is set
q2 " U is set
(q1 " U) \/ (q2 " U) is set
bool (q1 \/ q2) is non empty set
(q2,q1) is set
(q1,q2) is Relation-like Element of bool (q1 \/ q2)
(q1,q2) is set
(q2,q1) is Relation-like Element of bool (q2 \/ q1)
q2 \/ q1 is Relation-like set
bool (q2 \/ q1) is non empty set
y1 is set
x is set
[y1,x] is non empty V15() set
bool ((q1 \/ q2) " U) is non empty set
p is Relation-like Element of bool (q1 \/ q2)
p " U is set
C is Relation-like Element of bool (q1 \/ q2)
C " U is set
y1 is Element of bool ((q1 \/ q2) " U)
x is Element of bool ((q1 \/ q2) " U)
y1 \/ x is Element of bool ((q1 \/ q2) " U)
U is set
q1 is set
(U,q1) is Relation-like q1 -defined BOOLEAN -valued Function-like quasi_total Element of bool [:q1,BOOLEAN:]
[:q1,BOOLEAN:] is Relation-like set
bool [:q1,BOOLEAN:] is non empty set
q1 --> {} is Relation-like q1 -defined {{}} -valued Function-like constant total quasi_total Function-yielding V159() Cardinal-yielding Element of bool [:q1,{{}}:]
[:q1,{{}}:] is Relation-like set
bool [:q1,{{}}:] is non empty set
U /\ q1 is set
(U,q1) is Element of bool U
bool U is non empty set
(U,q1) is Element of bool q1
bool q1 is non empty set
(U /\ q1) --> 1 is Relation-like non-empty U /\ q1 -defined NAT -valued Function-like constant total quasi_total Cardinal-yielding Element of bool [:(U /\ q1),NAT:]
[:(U /\ q1),NAT:] is Relation-like set
bool [:(U /\ q1),NAT:] is non empty set
{1} is non empty trivial finite finite-membered 1 -element with_non-empty_elements non empty-membered countable set
[:(U /\ q1),{1}:] is Relation-like set
(q1 --> {}) +* ((U /\ q1) --> 1) is Relation-like Function-like set
dom (q1 --> {}) is Element of bool q1
dom ((U /\ q1) --> 1) is Element of bool (U /\ q1)
bool (U /\ q1) is non empty set
proj1 ((q1 --> {}) +* ((U /\ q1) --> 1)) is set
(dom (q1 --> {})) \/ (dom ((U /\ q1) --> 1)) is set
F is set
((q1 --> {}) +* ((U /\ q1) --> 1)) . F is set
((U /\ q1) --> 1) . F is set
(q1 --> {}) . F is Relation-like Function-like set
U is set
q1 is set
(U,q1) is Relation-like q1 -defined BOOLEAN -valued Function-like quasi_total Element of bool [:q1,BOOLEAN:]
[:q1,BOOLEAN:] is Relation-like set
bool [:q1,BOOLEAN:] is non empty set
q1 \ U is Element of bool q1
bool q1 is non empty set
(q1,U) is Element of bool q1
(q1 \ U) --> {} is Relation-like q1 \ U -defined {{}} -valued Function-like constant total quasi_total Function-yielding V159() Cardinal-yielding Element of bool [:(q1 \ U),{{}}:]
[:(q1 \ U),{{}}:] is Relation-like set
bool [:(q1 \ U),{{}}:] is non empty set
U /\ q1 is set
(U,q1) is Element of bool U
bool U is non empty set
(U,q1) is Element of bool q1
(U /\ q1) --> 1 is Relation-like non-empty U /\ q1 -defined NAT -valued Function-like constant total quasi_total Cardinal-yielding Element of bool [:(U /\ q1),NAT:]
[:(U /\ q1),NAT:] is Relation-like set
bool [:(U /\ q1),NAT:] is non empty set
{1} is non empty trivial finite finite-membered 1 -element with_non-empty_elements non empty-membered countable set
[:(U /\ q1),{1}:] is Relation-like set
((q1 \ U) --> {}) +* ((U /\ q1) --> 1) is Relation-like Function-like set
q1 --> {} is Relation-like q1 -defined {{}} -valued Function-like constant total quasi_total Function-yielding V159() Cardinal-yielding Element of bool [:q1,{{}}:]
[:q1,{{}}:] is Relation-like set
bool [:q1,{{}}:] is non empty set
q1 /\ q1 is set
(q1,q1) is Element of bool q1
(q1,q1) is Element of bool q1
bool (U /\ q1) is non empty set
(U /\ q1) /\ (U /\ q1) is set
((U /\ q1),(U /\ q1)) is Element of bool (U /\ q1)
((U /\ q1),(U /\ q1)) is Element of bool (U /\ q1)
(U /\ q1) \/ (q1 \ U) is set
dom (U,q1) is Element of bool q1
C is Element of bool q1
y1 is Element of bool q1
q1 /\ y1 is Element of bool q1
(q1,y1) is Element of bool q1
q1 /\ y1 is set
(q1,y1) is Element of bool y1
bool y1 is non empty set
(q1,y1) is set
(y1,q1) is Element of bool (y1 \/ q1)
y1 \/ q1 is set
bool (y1 \/ q1) is non empty set
(q1 \ U) /\ (U /\ q1) is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of bool q1
((q1 \ U),(U /\ q1)) is Element of bool (q1 \ U)
bool (q1 \ U) is non empty set
(q1 \ U) /\ (U /\ q1) is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
((q1 \ U),(U /\ q1)) is Element of bool (U /\ q1)
x is Element of bool q1
q1 /\ x is Element of bool q1
(q1,x) is Element of bool q1
q1 /\ x is set
(q1,x) is Element of bool x
bool x is non empty set
(q1,x) is set
(x,q1) is Element of bool (x \/ q1)
x \/ q1 is set
bool (x \/ q1) is non empty set
(q1 --> {}) +* ((U /\ q1) --> 1) is Relation-like Function-like set
((q1 --> {}) +* ((U /\ q1) --> 1)) | (q1 \ U) is Relation-like Function-like set
(q1 --> {}) | (q1 \ U) is Relation-like q1 -defined q1 \ U -defined q1 -defined {{}} -valued Function-like constant Function-yielding V159() Cardinal-yielding Element of bool [:q1,{{}}:]
((U /\ q1) --> 1) | (q1 \ U) is Relation-like q1 \ U -defined U /\ q1 -defined NAT -valued Function-like constant Cardinal-yielding Element of bool [:(U /\ q1),NAT:]
((q1 --> {}) | (q1 \ U)) +* (((U /\ q1) --> 1) | (q1 \ U)) is Relation-like q1 \ U -defined Function-like set
((q1 --> {}) +* ((U /\ q1) --> 1)) | (U /\ q1) is Relation-like Function-like set
(q1 --> {}) | (U /\ q1) is Relation-like q1 -defined U /\ q1 -defined q1 -defined {{}} -valued Function-like constant Function-yielding V159() Cardinal-yielding Element of bool [:q1,{{}}:]
((U /\ q1) --> 1) | (U /\ q1) is Relation-like U /\ q1 -defined U /\ q1 -defined NAT -valued Function-like constant Cardinal-yielding Element of bool [:(U /\ q1),NAT:]
((U /\ q1),((U /\ q1) --> 1)) is set
(((U /\ q1) --> 1),(U /\ q1)) is Element of bool (((U /\ q1) --> 1) \/ (U /\ q1))
((U /\ q1) --> 1) \/ (U /\ q1) is set
bool (((U /\ q1) --> 1) \/ (U /\ q1)) is non empty set
((U /\ q1) --> 1) | (U /\ q1) is Relation-like U /\ q1 -defined U /\ q1 -defined NAT -valued Function-like constant Cardinal-yielding set
((q1 --> {}) | (U /\ q1)) +* (((U /\ q1) --> 1) | (U /\ q1)) is Relation-like U /\ q1 -defined Function-like set
q1 /\ (q1 \ U) is Element of bool q1
(q1,(q1 \ U)) is Element of bool q1
q1 /\ (q1 \ U) is set
(q1,(q1 \ U)) is Element of bool (q1 \ U)
(q1,(q1 \ U)) is set
((q1 \ U),q1) is Element of bool ((q1 \ U) \/ q1)
(q1 \ U) \/ q1 is set
bool ((q1 \ U) \/ q1) is non empty set
(q1 /\ (q1 \ U)) --> {} is Relation-like q1 /\ (q1 \ U) -defined {{}} -valued Function-like constant total quasi_total Function-yielding V159() Cardinal-yielding Element of bool [:(q1 /\ (q1 \ U)),{{}}:]
[:(q1 /\ (q1 \ U)),{{}}:] is Relation-like set
bool [:(q1 /\ (q1 \ U)),{{}}:] is non empty set
{} --> 1 is Relation-like non-empty empty-yielding {} -defined NAT -valued Function-like one-to-one constant functional empty trivial non proper total quasi_total complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of bool [:{},NAT:]
[:{},NAT:] is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
bool [:{},NAT:] is non empty finite finite-membered countable set
[:{},{1}:] is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
y is Element of bool (U /\ q1)
y --> {} is Relation-like y -defined {{}} -valued Function-like constant total quasi_total Function-yielding V159() Cardinal-yielding Element of bool [:y,{{}}:]
[:y,{{}}:] is Relation-like set
bool [:y,{{}}:] is non empty set
dom ((q1 --> {}) | (U /\ q1)) is Element of bool q1
dom (((U /\ q1) --> 1) | (U /\ q1)) is Element of bool (U /\ q1)
(U,q1) | (q1 \ U) is Relation-like q1 -defined q1 \ U -defined q1 -defined BOOLEAN -valued Function-like Element of bool [:q1,BOOLEAN:]
(U,q1) | (U /\ q1) is Relation-like q1 -defined U /\ q1 -defined q1 -defined BOOLEAN -valued Function-like Element of bool [:q1,BOOLEAN:]
((U,q1) | (q1 \ U)) +* ((U,q1) | (U /\ q1)) is Relation-like q1 -defined BOOLEAN -valued Function-like Element of bool [:q1,BOOLEAN:]
(((q1 --> {}) +* ((U /\ q1) --> 1)) | (q1 \ U)) +* ((U,q1) | (U /\ q1)) is Relation-like Function-like set
((q1 /\ (q1 \ U)) --> {}) +* {} is Relation-like Function-like Function-yielding V159() set
(((q1 /\ (q1 \ U)) --> {}) +* {}) +* (((U /\ q1) --> 1) | (U /\ q1)) is Relation-like Function-like set
U is set
q1 is set
(U,q1) is Relation-like q1 -defined BOOLEAN -valued Function-like quasi_total Element of bool [:q1,BOOLEAN:]
[:q1,BOOLEAN:] is Relation-like set
bool [:q1,BOOLEAN:] is non empty set
q1 \ U is Element of bool q1
bool q1 is non empty set
(q1,U) is Element of bool q1
(q1 \ U) --> {} is Relation-like q1 \ U -defined {{}} -valued Function-like constant total quasi_total Function-yielding V159() Cardinal-yielding Element of bool [:(q1 \ U),{{}}:]
[:(q1 \ U),{{}}:] is Relation-like set
bool [:(q1 \ U),{{}}:] is non empty set
U /\ q1 is set
(U,q1) is Element of bool U
bool U is non empty set
(U,q1) is Element of bool q1
(U /\ q1) --> 1 is Relation-like non-empty U /\ q1 -defined NAT -valued Function-like constant total quasi_total Cardinal-yielding Element of bool [:(U /\ q1),NAT:]
[:(U /\ q1),NAT:] is Relation-like set
bool [:(U /\ q1),NAT:] is non empty set
{1} is non empty trivial finite finite-membered 1 -element with_non-empty_elements non empty-membered countable set
[:(U /\ q1),{1}:] is Relation-like set
((q1 \ U) --> {}) \/ ((U /\ q1) --> 1) is Relation-like set
(q1 \ U) /\ (U /\ q1) is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of bool q1
((q1 \ U),(U /\ q1)) is Element of bool (q1 \ U)
bool (q1 \ U) is non empty set
(q1 \ U) /\ (U /\ q1) is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
((q1 \ U),(U /\ q1)) is Element of bool (U /\ q1)
bool (U /\ q1) is non empty set
((q1 \ U) --> {}) +* ((U /\ q1) --> 1) is Relation-like Function-like set
{1} is non empty trivial finite finite-membered 1 -element with_non-empty_elements non empty-membered countable Element of bool NAT
U is set
q1 is set
(U,q1) is Relation-like q1 -defined BOOLEAN -valued Function-like quasi_total Element of bool [:q1,BOOLEAN:]
[:q1,BOOLEAN:] is Relation-like set
bool [:q1,BOOLEAN:] is non empty set
(U,q1) " {{}} is Element of bool q1
bool q1 is non empty set
q1 \ U is Element of bool q1
(q1,U) is Element of bool q1
(U,q1) " {1} is Element of bool q1
U /\ q1 is set
(U,q1) is Element of bool U
bool U is non empty set
(U,q1) is Element of bool q1
(q1 \ U) --> {} is Relation-like q1 \ U -defined {{}} -valued Function-like constant total quasi_total Function-yielding V159() Cardinal-yielding Element of bool [:(q1 \ U),{{}}:]
[:(q1 \ U),{{}}:] is Relation-like set
bool [:(q1 \ U),{{}}:] is non empty set
(U /\ q1) --> 1 is Relation-like non-empty U /\ q1 -defined NAT -valued Function-like constant total quasi_total Cardinal-yielding Element of bool [:(U /\ q1),NAT:]
[:(U /\ q1),NAT:] is Relation-like set
bool [:(U /\ q1),NAT:] is non empty set
{1} is non empty trivial finite finite-membered 1 -element with_non-empty_elements non empty-membered countable set
[:(U /\ q1),{1}:] is Relation-like set
((q1 \ U) --> {}) " {1} is Element of bool (q1 \ U)
bool (q1 \ U) is non empty set
((U /\ q1) --> 1) " {{}} is Element of bool (U /\ q1)
bool (U /\ q1) is non empty set
((q1 \ U) --> {}) \/ ((U /\ q1) --> 1) is Relation-like set
(((q1 \ U) --> {}) \/ ((U /\ q1) --> 1)) " {{}} is set
((q1 \ U) --> {}) " {{}} is Element of bool (q1 \ U)
(((q1 \ U) --> {}) " {{}}) \/ (((U /\ q1) --> 1) " {{}}) is set
(((q1 \ U) --> {}) \/ ((U /\ q1) --> 1)) " {1} is set
((U /\ q1) --> 1) " {1} is Element of bool (U /\ q1)
(((q1 \ U) --> {}) " {1}) \/ (((U /\ q1) --> 1) " {1}) is set
U is set
q1 is Relation-like Function-like set
q1 . U is set
q2 is non empty set
{q2} is non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable set
q1 " {q2} is set
proj1 q1 is set
proj1 q1 is set
U is set
q1 is Relation-like Function-like set
U is set
bool U is non empty set
q1 is Element of bool U
q2 is Relation-like set
proj2 q2 is set
U is set
q2 is Relation-like U -defined total set
proj2 q2 is set
[:U,(proj2 q2):] is Relation-like set
bool [:U,(proj2 q2):] is non empty set
dom q2 is Element of bool U
bool U is non empty set
f is set
f is Relation-like Function-like set
proj1 f is set
{ [b₁,(f . b₁)] where b₁ is Element of proj1 f : b₁ in proj1 f } is set
q11 is set
F is Element of proj1 f
f . F is set
[F,(f . F)] is non empty V15() set
proj2 f is set
q11 is Relation-like U -defined proj2 q2 -valued Function-like quasi_total Element of bool [:U,(proj2 q2):]
dom q11 is Element of bool U
U is Relation-like set
proj1 U is set
q1 is Relation-like Function-like set
proj1 q1 is set
f is Relation-like proj1 q1 -defined set
q11 is Relation-like proj1 q1 -defined total set
proj2 q11 is set
[:(proj1 q1),(proj2 q11):] is Relation-like set
bool [:(proj1 q1),(proj2 q11):] is non empty set
F is Relation-like proj1 q1 -defined proj2 q11 -valued Function-like quasi_total Element of bool [:(proj1 q1),(proj2 q11):]
dom F is Element of bool (proj1 q1)
bool (proj1 q1) is non empty set
U is set
q1 is Relation-like set
proj1 q1 is set
q2 is Relation-like set
proj2 q2 is set
q2 * q1 is Relation-like set
f is Relation-like U -defined set
q2 * f is Relation-like set
f ~ is Relation-like set
(q2 * f) * (f ~) is Relation-like set
((q2 * f) * (f ~)) * q1 is Relation-like set
q11 is Relation-like U -defined total set
q11 ~ is Relation-like set
(q2 * f) * (q11 ~) is Relation-like set
((q2 * f) * (q11 ~)) * q1 is Relation-like set
C is Relation-like Function-like set
(q11 ~) * q1 is Relation-like set
(q2 * f) * ((q11 ~) * q1) is Relation-like set
f * ((q11 ~) * q1) is Relation-like U -defined set
q2 * (f * ((q11 ~) * q1)) is Relation-like set
f * (q11 ~) is Relation-like U -defined set
p is Relation-like U -defined set
(f * (q11 ~)) * p is Relation-like U -defined set
q2 * ((f * (q11 ~)) * p) is Relation-like set
id U is Relation-like U -defined U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:U,U:]
[:U,U:] is Relation-like set
bool [:U,U:] is non empty set
(id U) * p is Relation-like U -defined set
p | U is Relation-like U -defined U -defined set
(U,p) is set
(p,U) is Element of bool (p \/ U)
p \/ U is set
bool (p \/ U) is non empty set
proj1 (q2 * q1) is set
proj1 q2 is set
q2 * (f * (q11 ~)) is Relation-like set
proj1 (q2 * (f * (q11 ~))) is set
proj1 (((q2 * f) * (q11 ~)) * q1) is set
proj1 ((q2 * f) * (q11 ~)) is set
proj1 C is set
U is set
q1 is set
[:q1,U:] is Relation-like set
bool [:q1,U:] is non empty set
q2 is non empty set
[:U,q2:] is Relation-like set
bool [:U,q2:] is non empty set
f is non empty set
[:U,f:] is Relation-like set
bool [:U,f:] is non empty set
q11 is Relation-like U -defined q2 -valued total quasi_total Element of bool [:U,q2:]
q11 ~ is Relation-like q2 -defined U -valued Element of bool [:q2,U:]
[:q2,U:] is Relation-like set
bool [:q2,U:] is non empty set
F is Relation-like U -defined f -valued total quasi_total Element of bool [:U,f:]
p is Relation-like q1 -defined U -valued Element of bool [:q1,U:]
p * q11 is Relation-like q1 -defined q2 -valued Element of bool [:q1,q2:]
[:q1,q2:] is Relation-like set
bool [:q1,q2:] is non empty set
(p * q11) * (q11 ~) is Relation-like q1 -defined U -valued Element of bool [:q1,U:]
((p * q11) * (q11 ~)) * F is Relation-like q1 -defined f -valued Element of bool [:q1,f:]
[:q1,f:] is Relation-like set
bool [:q1,f:] is non empty set
p * F is Relation-like q1 -defined f -valued Element of bool [:q1,f:]
dom F is Element of bool U
bool U is non empty set
rng p is Element of bool U
U is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U ^ q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U ^ q1) . 1 is set
U . 1 is set
q2 is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support set
len q2 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
Seg (len q2) is non empty finite len q2 -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= len q2 ) } is set
dom q2 is non empty finite countable Element of bool NAT
U is non empty set
q1 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q2 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 ^ q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
q11 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
f ^ q11 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
U * is functional non empty FinSequence-membered FinSequenceSet of U
F is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U is non empty set
q1 is set
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
U * is functional non empty FinSequence-membered FinSequenceSet of U
[:(U *),(U *):] is Relation-like non empty set
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
q11 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
p is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
F is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q11 ^ F is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
C is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
p ^ C is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 /\ (U *) is set
(q1,(U *)) is Element of bool q1
bool q1 is non empty set
(q1,(U *)) is functional FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
(U -concatenation) . (q11,F) is set
[q11,F] is non empty V15() set
(U -concatenation) . [q11,F] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U -concatenation) . (p,C) is set
[p,C] is non empty V15() set
(U -concatenation) . [p,C] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q11 is set
q1 /\ (U *) is set
(q1,(U *)) is Element of bool q1
bool q1 is non empty set
(q1,(U *)) is functional FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
F is set
p is set
C is set
(U -concatenation) . (q11,p) is set
[q11,p] is non empty V15() set
(U -concatenation) . [q11,p] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U -concatenation) . (F,C) is set
[F,C] is non empty V15() set
(U -concatenation) . [F,C] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
y1 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
y is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
y1 ^ y is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
x is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
pb is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
(U -concatenation) . (x,pb) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
[x,pb] is non empty V15() set
(U -concatenation) . [x,pb] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
x ^ pb is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
U is set
U * is functional non empty FinSequence-membered FinSequenceSet of U
q1 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
U is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) * is functional non empty FinSequence-membered FinSequenceSet of U *
(U) is Relation-like (U *) * -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:((U *) *),(U *):]
[:((U *) *),(U *):] is Relation-like non empty set
bool [:((U *) *),(U *):] is non empty set
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
[:(U *),(U *):] is Relation-like non empty set
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
((U *),(U -concatenation)) is Relation-like ((U *) *) \ {{}} -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(((U *) *) \ {{}}),(U *):]
((U *) *) \ {{}} is functional non empty FinSequence-membered Element of bool ((U *) *)
bool ((U *) *) is non empty set
(((U *) *),{{}}) is functional FinSequence-membered Element of bool ((U *) *)
[:(((U *) *) \ {{}}),(U *):] is Relation-like non empty set
bool [:(((U *) *) \ {{}}),(U *):] is non empty set
({} .--> {}) +* ((U *),(U -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 is (U) set
q1 -tuples_on q2 is functional FinSequence-membered FinSequenceSet of q2
(U) .: (q1 -tuples_on q2) is functional FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
f is set
U is set
q1 is set
q1 \+\ U is set
q1 \ U is set
(q1,U) is Element of bool q1
bool q1 is non empty set
q1 \ U is Element of bool q1
U \ q1 is set
(U,q1) is Element of bool U
bool U is non empty set
U \ q1 is Element of bool U
(q1 \ U) \/ (U \ q1) is set
U is set
{U} is non empty trivial finite 1 -element countable set
id {U} is Relation-like {U} -defined {U} -valued Function-like one-to-one non empty total quasi_total onto bijective finite reflexive symmetric antisymmetric transitive countable finite-support Element of bool [:{U},{U}:]
[:{U},{U}:] is Relation-like non empty finite countable set
bool [:{U},{U}:] is non empty finite finite-membered countable set
[U,U] is non empty V15() set
{[U,U]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
(id {U}) \+\ {[U,U]} is Relation-like finite countable set
(id {U}) \ {[U,U]} is Relation-like {U} -defined {U} -valued finite countable set
((id {U}),{[U,U]}) is Relation-like {U} -defined {U} -valued Function-like finite countable finite-support Element of bool (id {U})
bool (id {U}) is non empty finite finite-membered countable set
(id {U}) \ {[U,U]} is Relation-like {U} -defined {U} -valued Function-like finite countable finite-support Element of bool (id {U})
{[U,U]} \ (id {U}) is Relation-like finite countable set
({[U,U]},(id {U})) is Relation-like Function-like constant trivial finite countable finite-support Element of bool {[U,U]}
bool {[U,U]} is non empty finite finite-membered countable set
{[U,U]} \ (id {U}) is Relation-like Function-like constant trivial finite countable finite-support Element of bool {[U,U]}
((id {U}) \ {[U,U]}) \/ ({[U,U]} \ (id {U})) is Relation-like finite countable set
q1 is set
U is set
q1 is set
U .--> q1 is Relation-like {U} -defined Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{U} is non empty trivial finite 1 -element countable set
{U} --> q1 is Relation-like {U} -defined {q1} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{U},{q1}:]
{q1} is non empty trivial finite 1 -element countable set
[:{U},{q1}:] is Relation-like non empty finite countable set
bool [:{U},{q1}:] is non empty finite finite-membered countable set
[U,q1] is non empty V15() set
{[U,q1]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
(U .--> q1) \+\ {[U,q1]} is Relation-like finite countable set
(U .--> q1) \ {[U,q1]} is Relation-like {U} -defined finite countable set
((U .--> q1),{[U,q1]}) is Relation-like {U} -defined Function-like constant trivial finite countable finite-support Element of bool (U .--> q1)
bool (U .--> q1) is non empty finite finite-membered countable set
(U .--> q1) \ {[U,q1]} is Relation-like {U} -defined Function-like constant trivial finite countable finite-support Element of bool (U .--> q1)
{[U,q1]} \ (U .--> q1) is Relation-like finite countable set
({[U,q1]},(U .--> q1)) is Relation-like Function-like constant trivial finite countable finite-support Element of bool {[U,q1]}
bool {[U,q1]} is non empty finite finite-membered countable set
{[U,q1]} \ (U .--> q1) is Relation-like Function-like constant trivial finite countable finite-support Element of bool {[U,q1]}
((U .--> q1) \ {[U,q1]}) \/ ({[U,q1]} \ (U .--> q1)) is Relation-like finite countable set
q2 is set
U is set
{U} is non empty trivial finite 1 -element countable set
id {U} is Relation-like {U} -defined {U} -valued Function-like one-to-one non empty total quasi_total onto bijective finite reflexive symmetric antisymmetric transitive countable finite-support Element of bool [:{U},{U}:]
[:{U},{U}:] is Relation-like non empty finite countable set
bool [:{U},{U}:] is non empty finite finite-membered countable set
U .--> U is Relation-like {U} -defined Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{U} --> U is Relation-like {U} -defined {U} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{U},{U}:]
(id {U}) \+\ (U .--> U) is Relation-like finite countable set
(id {U}) \ (U .--> U) is Relation-like {U} -defined {U} -valued finite countable set
((id {U}),(U .--> U)) is Relation-like {U} -defined {U} -valued Function-like finite countable finite-support Element of bool (id {U})
bool (id {U}) is non empty finite finite-membered countable set
(id {U}) \ (U .--> U) is Relation-like {U} -defined {U} -valued Function-like finite countable finite-support Element of bool (id {U})
(U .--> U) \ (id {U}) is Relation-like {U} -defined finite countable set
((U .--> U),(id {U})) is Relation-like {U} -defined Function-like constant trivial finite countable finite-support Element of bool (U .--> U)
bool (U .--> U) is non empty finite finite-membered countable set
(U .--> U) \ (id {U}) is Relation-like {U} -defined Function-like constant trivial finite countable finite-support Element of bool (U .--> U)
((id {U}) \ (U .--> U)) \/ ((U .--> U) \ (id {U})) is Relation-like {U} -defined finite countable set
[U,U] is non empty V15() set
{[U,U]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
(id {U}) \+\ {[U,U]} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
(id {U}) \ {[U,U]} is Relation-like {U} -defined {U} -valued finite countable set
((id {U}),{[U,U]}) is Relation-like {U} -defined {U} -valued Function-like finite countable finite-support Element of bool (id {U})
(id {U}) \ {[U,U]} is Relation-like {U} -defined {U} -valued Function-like finite countable finite-support Element of bool (id {U})
{[U,U]} \ (id {U}) is Relation-like finite countable set
({[U,U]},(id {U})) is Relation-like Function-like constant trivial finite countable finite-support Element of bool {[U,U]}
bool {[U,U]} is non empty finite finite-membered countable set
{[U,U]} \ (id {U}) is Relation-like Function-like constant trivial finite countable finite-support Element of bool {[U,U]}
((id {U}) \ {[U,U]}) \/ ({[U,U]} \ (id {U})) is Relation-like finite countable set
(U .--> U) \+\ {[U,U]} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
(U .--> U) \ {[U,U]} is Relation-like {U} -defined finite countable set
((U .--> U),{[U,U]}) is Relation-like {U} -defined Function-like constant trivial finite countable finite-support Element of bool (U .--> U)
(U .--> U) \ {[U,U]} is Relation-like {U} -defined Function-like constant trivial finite countable finite-support Element of bool (U .--> U)
{[U,U]} \ (U .--> U) is Relation-like finite countable set
({[U,U]},(U .--> U)) is Relation-like Function-like constant trivial finite countable finite-support Element of bool {[U,U]}
{[U,U]} \ (U .--> U) is Relation-like Function-like constant trivial finite countable finite-support Element of bool {[U,U]}
((U .--> U) \ {[U,U]}) \/ ({[U,U]} \ (U .--> U)) is Relation-like finite countable set
q1 is set
U is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) \ {{}} is functional non empty FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
((U *),{{}}) is functional FinSequence-membered Element of bool (U *)
q1 is set
U is non empty set
[:U,U:] is Relation-like non empty set
[:[:U,U:],U:] is Relation-like non empty set
bool [:[:U,U:],U:] is non empty set
q1 is Element of U
<*q1*> is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
[1,q1] is non empty V15() set
{[1,q1]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
q2 is Relation-like [:U,U:] -defined U -valued Function-like non empty total quasi_total Element of bool [:[:U,U:],U:]
(U,q2) is Relation-like (U *) \ {{}} -defined U -valued Function-like non empty total quasi_total Element of bool [:((U *) \ {{}}),U:]
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) \ {{}} is functional non empty FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
((U *),{{}}) is functional FinSequence-membered Element of bool (U *)
[:((U *) \ {{}}),U:] is Relation-like non empty set
bool [:((U *) \ {{}}),U:] is non empty set
(U,q2) . <*q1*> is set
q11 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q11 ^ <*q1*> is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support set
(U,q2) . (q11 ^ <*q1*>) is set
(U,q2) . q11 is set
q2 . (((U,q2) . q11),q1) is set
[((U,q2) . q11),q1] is non empty V15() set
q2 . [((U,q2) . q11),q1] is set
F is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
F ^ <*q1*> is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
(U,q2) . (F ^ <*q1*>) is set
(U,q2) . F is set
q2 . (((U,q2) . F),q1) is set
[((U,q2) . F),q1] is non empty V15() set
q2 . [((U,q2) . F),q1] is set
U is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 is set
q2 is set
U +~ (q1,q2) is Relation-like Function-like set
q1 .--> q2 is Relation-like {q1} -defined Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{q1} is non empty trivial finite 1 -element countable set
{q1} --> q2 is Relation-like {q1} -defined {q2} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{q1},{q2}:]
{q2} is non empty trivial finite 1 -element countable set
[:{q1},{q2}:] is Relation-like non empty finite countable set
bool [:{q1},{q2}:] is non empty finite finite-membered countable set
U * (q1 .--> q2) is Relation-like NAT -defined Function-like finite countable finite-support set
U +* (U * (q1 .--> q2)) is Relation-like NAT -defined Function-like finite countable finite-support set
proj1 (U +~ (q1,q2)) is set
dom U is finite countable Element of bool NAT
len U is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
Seg (len U) is finite len U -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= len U ) } is set
q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U is set
q1 is set
q2 +~ (U,q1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U .--> q1 is Relation-like {U} -defined Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{U} is non empty trivial finite 1 -element countable set
{U} --> q1 is Relation-like {U} -defined {q1} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{U},{q1}:]
{q1} is non empty trivial finite 1 -element countable set
[:{U},{q1}:] is Relation-like non empty finite countable set
bool [:{U},{q1}:] is non empty finite finite-membered countable set
q2 * (U .--> q1) is Relation-like NAT -defined Function-like finite countable finite-support set
q2 +* (q2 * (U .--> q1)) is Relation-like NAT -defined Function-like finite countable finite-support set
q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
U is set
q1 is set
f is Relation-like NAT -defined Function-like finite q2 -element FinSequence-like FinSubsequence-like countable finite-support set
(U,q1,f) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f +~ (U,q1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U .--> q1 is Relation-like {U} -defined Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{U} is non empty trivial finite 1 -element countable set
{U} --> q1 is Relation-like {U} -defined {q1} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{U},{q1}:]
{q1} is non empty trivial finite 1 -element countable set
[:{U},{q1}:] is Relation-like non empty finite countable set
bool [:{U},{q1}:] is non empty finite finite-membered countable set
f * (U .--> q1) is Relation-like NAT -defined Function-like finite countable finite-support set
f +* (f * (U .--> q1)) is Relation-like NAT -defined Function-like finite countable finite-support set
dom (U,q1,f) is finite countable Element of bool NAT
dom f is finite q2 -element countable Element of bool NAT
len f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
Seg (len f) is finite len f -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= len f ) } is set
F is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
Seg F is finite F -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
len (U,q1,f) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 is non empty set
U is set
q2 is Element of q1
f is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U,q2,f) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f +~ (U,q2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U .--> q2 is Relation-like {U} -defined q1 -valued Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{U} is non empty trivial finite 1 -element countable set
{U} --> q2 is Relation-like {U} -defined q1 -valued {q2} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{U},{q2}:]
{q2} is non empty trivial finite 1 -element countable set
[:{U},{q2}:] is Relation-like non empty finite countable set
bool [:{U},{q2}:] is non empty finite finite-membered countable set
f * (U .--> q2) is Relation-like NAT -defined q1 -valued Function-like finite countable finite-support set
f +* (f * (U .--> q2)) is Relation-like NAT -defined q1 -valued Function-like finite countable finite-support set
q11 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U is set
q1 is set
q2 is set
f is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1,q2,f) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f +~ (q1,q2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 .--> q2 is Relation-like {q1} -defined Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{q1} is non empty trivial finite 1 -element countable set
{q1} --> q2 is Relation-like {q1} -defined {q2} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{q1},{q2}:]
{q2} is non empty trivial finite 1 -element countable set
[:{q1},{q2}:] is Relation-like non empty finite countable set
bool [:{q1},{q2}:] is non empty finite finite-membered countable set
f * (q1 .--> q2) is Relation-like NAT -defined Function-like finite countable finite-support set
f +* (f * (q1 .--> q2)) is Relation-like NAT -defined Function-like finite countable finite-support set
id U is Relation-like U -defined U -valued Function-like one-to-one total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:U,U:]
[:U,U:] is Relation-like set
bool [:U,U:] is non empty set
(id U) +* (q1,q2) is Relation-like U -defined Function-like total set
f * ((id U) +* (q1,q2)) is Relation-like NAT -defined Function-like finite countable finite-support set
rng f is finite countable Element of bool U
bool U is non empty set
q11 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
F is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U is non empty set
q1 is set
q2 is Element of U
f is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1,q2,f) is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f +~ (q1,q2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 .--> q2 is Relation-like {q1} -defined U -valued Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{q1} is non empty trivial finite 1 -element countable set
{q1} --> q2 is Relation-like {q1} -defined U -valued {q2} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{q1},{q2}:]
{q2} is non empty trivial finite 1 -element countable set
[:{q1},{q2}:] is Relation-like non empty finite countable set
bool [:{q1},{q2}:] is non empty finite finite-membered countable set
f * (q1 .--> q2) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
f +* (f * (q1 .--> q2)) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
id U is Relation-like U -defined U -valued Function-like one-to-one non empty total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:U,U:]
[:U,U:] is Relation-like non empty set
bool [:U,U:] is non empty set
(id U) +* (q1,q2) is Relation-like U -defined U -valued Function-like total set
f * ((id U) +* (q1,q2)) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
U is set
<*U*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support set
[1,U] is non empty V15() set
{[1,U]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
q1 is non empty set
q2 is Element of q1
<*q2*> is Relation-like NAT -defined q1 -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
[1,q2] is non empty V15() set
{[1,q2]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
f is Element of q1
(q1,f,U,<*q2*>) is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support set
<*q2*> +~ (f,U) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f .--> U is Relation-like q1 -defined {f} -defined Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{f} is non empty trivial finite 1 -element countable set
{f} --> U is Relation-like {f} -defined {U} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{f},{U}:]
{U} is non empty trivial finite 1 -element countable set
[:{f},{U}:] is Relation-like non empty finite countable set
bool [:{f},{U}:] is non empty finite finite-membered countable set
<*q2*> * (f .--> U) is Relation-like NAT -defined Function-like finite countable finite-support set
<*q2*> +* (<*q2*> * (f .--> U)) is Relation-like NAT -defined Function-like non empty finite countable finite-support set
id q1 is Relation-like q1 -defined q1 -valued Function-like one-to-one non empty total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:q1,q1:]
[:q1,q1:] is Relation-like non empty set
bool [:q1,q1:] is non empty set
(id q1) +* (f,U) is Relation-like q1 -defined Function-like total set
<*q2*> * ((id q1) +* (f,U)) is Relation-like NAT -defined Function-like finite countable finite-support set
1 .--> f is Relation-like NAT -defined {1} -defined q1 -valued Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{1} is non empty trivial finite finite-membered 1 -element with_non-empty_elements non empty-membered countable set
{1} --> f is Relation-like {1} -defined q1 -valued {f} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{1},{f}:]
[:{1},{f}:] is Relation-like non empty finite countable set
bool [:{1},{f}:] is non empty finite finite-membered countable set
1 .--> U is Relation-like NAT -defined {1} -defined Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{1} --> U is Relation-like {1} -defined {U} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{1},{U}:]
[:{1},{U}:] is Relation-like non empty finite countable set
bool [:{1},{U}:] is non empty finite finite-membered countable set
1 .--> q2 is Relation-like NAT -defined {1} -defined q1 -valued Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{1} --> q2 is Relation-like {1} -defined q1 -valued {q2} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{1},{q2}:]
{q2} is non empty trivial finite 1 -element countable set
[:{1},{q2}:] is Relation-like non empty finite countable set
bool [:{1},{q2}:] is non empty finite finite-membered countable set
<*f*> is Relation-like NAT -defined q1 -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
[1,f] is non empty V15() set
{[1,f]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
<*q2*> \+\ (1 .--> q2) is Relation-like finite countable set
<*q2*> \ (1 .--> q2) is Relation-like NAT -defined q1 -valued finite countable set
(<*q2*>,(1 .--> q2)) is Relation-like NAT -defined q1 -valued Function-like constant trivial finite countable finite-support Element of bool <*q2*>
bool <*q2*> is non empty finite finite-membered countable set
<*q2*> \ (1 .--> q2) is Relation-like NAT -defined q1 -valued Function-like constant trivial finite countable finite-support Element of bool <*q2*>
(1 .--> q2) \ <*q2*> is Relation-like NAT -defined q1 -valued finite countable set
((1 .--> q2),<*q2*>) is Relation-like NAT -defined q1 -valued Function-like constant trivial finite countable finite-support Element of bool (1 .--> q2)
bool (1 .--> q2) is non empty finite finite-membered countable set
(1 .--> q2) \ <*q2*> is Relation-like NAT -defined q1 -valued Function-like constant trivial finite countable finite-support Element of bool (1 .--> q2)
(<*q2*> \ (1 .--> q2)) \/ ((1 .--> q2) \ <*q2*>) is Relation-like NAT -defined q1 -valued finite countable set
<*U*> \+\ (1 .--> U) is Relation-like finite countable set
<*U*> \ (1 .--> U) is Relation-like NAT -defined finite countable set
(<*U*>,(1 .--> U)) is Relation-like NAT -defined Function-like constant trivial finite countable finite-support Element of bool <*U*>
bool <*U*> is non empty finite finite-membered countable set
<*U*> \ (1 .--> U) is Relation-like NAT -defined Function-like constant trivial finite countable finite-support Element of bool <*U*>
(1 .--> U) \ <*U*> is Relation-like NAT -defined finite countable set
((1 .--> U),<*U*>) is Relation-like NAT -defined Function-like constant trivial finite countable finite-support Element of bool (1 .--> U)
bool (1 .--> U) is non empty finite finite-membered countable set
(1 .--> U) \ <*U*> is Relation-like NAT -defined Function-like constant trivial finite countable finite-support Element of bool (1 .--> U)
(<*U*> \ (1 .--> U)) \/ ((1 .--> U) \ <*U*>) is Relation-like NAT -defined finite countable set
<*f*> \+\ (1 .--> f) is Relation-like finite countable set
<*f*> \ (1 .--> f) is Relation-like NAT -defined q1 -valued finite countable set
(<*f*>,(1 .--> f)) is Relation-like NAT -defined q1 -valued Function-like constant trivial finite countable finite-support Element of bool <*f*>
bool <*f*> is non empty finite finite-membered countable set
<*f*> \ (1 .--> f) is Relation-like NAT -defined q1 -valued Function-like constant trivial finite countable finite-support Element of bool <*f*>
(1 .--> f) \ <*f*> is Relation-like NAT -defined q1 -valued finite countable set
((1 .--> f),<*f*>) is Relation-like NAT -defined q1 -valued Function-like constant trivial finite countable finite-support Element of bool (1 .--> f)
bool (1 .--> f) is non empty finite finite-membered countable set
(1 .--> f) \ <*f*> is Relation-like NAT -defined q1 -valued Function-like constant trivial finite countable finite-support Element of bool (1 .--> f)
(<*f*> \ (1 .--> f)) \/ ((1 .--> f) \ <*f*>) is Relation-like NAT -defined q1 -valued finite countable set
dom (f .--> U) is non empty trivial finite 1 -element countable Element of bool q1
bool q1 is non empty set
{f} is non empty trivial finite 1 -element countable Element of bool q1
dom (1 .--> U) is non empty trivial finite finite-membered 1 -element countable Element of bool {1}
bool {1} is non empty finite finite-membered countable set
dom (1 .--> f) is non empty trivial finite finite-membered 1 -element countable Element of bool {1}
dom (1 .--> q2) is non empty trivial finite finite-membered 1 -element countable Element of bool {1}
rng (1 .--> q2) is non empty trivial finite 1 -element countable Element of bool q1
{q2} is non empty trivial finite 1 -element countable Element of bool q1
(f .--> U) . f is set
(1 .--> q2) * (f .--> U) is Relation-like NAT -defined Function-like one-to-one finite countable finite-support set
<*q2*> +* ((1 .--> q2) * (f .--> U)) is Relation-like NAT -defined Function-like non empty finite countable finite-support set
(1 .--> q2) +* (1 .--> U) is Relation-like NAT -defined Function-like non empty finite countable finite-support set
<*q2*> +* {} is Relation-like NAT -defined Function-like non empty finite countable finite-support set
U is set
q1 is non empty set
q2 is Element of q1
f is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1,U,q2,f) is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
f +~ (U,q2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U .--> q2 is Relation-like {U} -defined q1 -valued Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{U} is non empty trivial finite 1 -element countable set
{U} --> q2 is Relation-like {U} -defined q1 -valued {q2} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{U},{q2}:]
{q2} is non empty trivial finite 1 -element countable set
[:{U},{q2}:] is Relation-like non empty finite countable set
bool [:{U},{q2}:] is non empty finite finite-membered countable set
f * (U .--> q2) is Relation-like NAT -defined q1 -valued Function-like finite countable finite-support set
f +* (f * (U .--> q2)) is Relation-like NAT -defined q1 -valued Function-like finite countable finite-support set
id q1 is Relation-like q1 -defined q1 -valued Function-like one-to-one non empty total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:q1,q1:]
[:q1,q1:] is Relation-like non empty set
bool [:q1,q1:] is non empty set
(id q1) +* (U,q2) is Relation-like q1 -defined q1 -valued Function-like total set
f * ((id q1) +* (U,q2)) is Relation-like NAT -defined q1 -valued Function-like finite countable finite-support set
q11 is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f ^ q11 is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1,U,q2,(f ^ q11)) is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
(f ^ q11) +~ (U,q2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(f ^ q11) * (U .--> q2) is Relation-like NAT -defined q1 -valued Function-like finite countable finite-support set
(f ^ q11) +* ((f ^ q11) * (U .--> q2)) is Relation-like NAT -defined q1 -valued Function-like finite countable finite-support set
(f ^ q11) * ((id q1) +* (U,q2)) is Relation-like NAT -defined q1 -valued Function-like finite countable finite-support set
(q1,U,q2,q11) is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
q11 +~ (U,q2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q11 * (U .--> q2) is Relation-like NAT -defined q1 -valued Function-like finite countable finite-support set
q11 +* (q11 * (U .--> q2)) is Relation-like NAT -defined q1 -valued Function-like finite countable finite-support set
q11 * ((id q1) +* (U,q2)) is Relation-like NAT -defined q1 -valued Function-like finite countable finite-support set
(q1,U,q2,f) ^ (q1,U,q2,q11) is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of q1 *
q1 * is functional non empty FinSequence-membered FinSequenceSet of q1
(id q1) +* (U,q2) is Relation-like q1 -defined q1 -valued Function-like non empty total quasi_total Element of bool [:q1,q1:]
x2 is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
q2 is Relation-like q1 -defined q1 -valued Function-like non empty total quasi_total Element of bool [:q1,q1:]
q2 * x2 is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
p1 is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
q2 * p1 is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
(q2 * x2) ^ (q2 * p1) is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of q1 *
U is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
q1 is set
q2 is Element of U
[:(U *),(U *):] is Relation-like non empty set
bool [:(U *),(U *):] is non empty set
q11 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
(U,q1,q2,q11) is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
q11 +~ (q1,q2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 .--> q2 is Relation-like {q1} -defined U -valued Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{q1} is non empty trivial finite 1 -element countable set
{q1} --> q2 is Relation-like {q1} -defined U -valued {q2} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{q1},{q2}:]
{q2} is non empty trivial finite 1 -element countable set
[:{q1},{q2}:] is Relation-like non empty finite countable set
bool [:{q1},{q2}:] is non empty finite finite-membered countable set
q11 * (q1 .--> q2) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
q11 +* (q11 * (q1 .--> q2)) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
id U is Relation-like U -defined U -valued Function-like one-to-one non empty total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:U,U:]
[:U,U:] is Relation-like non empty set
bool [:U,U:] is non empty set
(id U) +* (q1,q2) is Relation-like U -defined U -valued Function-like total set
q11 * ((id U) +* (q1,q2)) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
q11 is Relation-like U * -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(U *),(U *):]
F is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
p is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
C is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
q11 . C is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
(U,q1,q2,C) is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
C +~ (q1,q2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 .--> q2 is Relation-like {q1} -defined U -valued Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{q1} is non empty trivial finite 1 -element countable set
{q1} --> q2 is Relation-like {q1} -defined U -valued {q2} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{q1},{q2}:]
{q2} is non empty trivial finite 1 -element countable set
[:{q1},{q2}:] is Relation-like non empty finite countable set
bool [:{q1},{q2}:] is non empty finite finite-membered countable set
C * (q1 .--> q2) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
C +* (C * (q1 .--> q2)) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
id U is Relation-like U -defined U -valued Function-like one-to-one non empty total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:U,U:]
[:U,U:] is Relation-like non empty set
bool [:U,U:] is non empty set
(id U) +* (q1,q2) is Relation-like U -defined U -valued Function-like total set
C * ((id U) +* (q1,q2)) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
q11 . F is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U,q1,q2,F) is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
F +~ (q1,q2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
F * (q1 .--> q2) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
F +* (F * (q1 .--> q2)) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
F * ((id U) +* (q1,q2)) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
F is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q11 . F is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U,q1,q2,F) is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
F +~ (q1,q2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
F * (q1 .--> q2) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
F +* (F * (q1 .--> q2)) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
F * ((id U) +* (q1,q2)) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
q11 is Relation-like U * -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(U *),(U *):]
F is Relation-like U * -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(U *),(U *):]
p is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
q11 . p is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
(U,q1,q2,p) is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
p +~ (q1,q2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 .--> q2 is Relation-like {q1} -defined U -valued Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{q1} is non empty trivial finite 1 -element countable set
{q1} --> q2 is Relation-like {q1} -defined U -valued {q2} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{q1},{q2}:]
{q2} is non empty trivial finite 1 -element countable set
[:{q1},{q2}:] is Relation-like non empty finite countable set
bool [:{q1},{q2}:] is non empty finite finite-membered countable set
p * (q1 .--> q2) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
p +* (p * (q1 .--> q2)) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
id U is Relation-like U -defined U -valued Function-like one-to-one non empty total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:U,U:]
[:U,U:] is Relation-like non empty set
bool [:U,U:] is non empty set
(id U) +* (q1,q2) is Relation-like U -defined U -valued Function-like total set
p * ((id U) +* (q1,q2)) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
F . p is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
U is non empty set
q1 is Element of U
<*q1*> is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
[1,q1] is non empty V15() set
{[1,q1]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
q2 is Element of U
f is Element of U
(U,q2,f) is Relation-like U * -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(U *),(U *):]
U * is functional non empty FinSequence-membered FinSequenceSet of U
[:(U *),(U *):] is Relation-like non empty set
bool [:(U *),(U *):] is non empty set
(U,q2,f) . <*q1*> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
<*f*> is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
[1,f] is non empty V15() set
{[1,f]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
(U,q2,f,<*q1*>) is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
<*q1*> +~ (q2,f) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q2 .--> f is Relation-like U -defined {q2} -defined U -valued Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{q2} is non empty trivial finite 1 -element countable set
{q2} --> f is Relation-like {q2} -defined U -valued {f} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{q2},{f}:]
{f} is non empty trivial finite 1 -element countable set
[:{q2},{f}:] is Relation-like non empty finite countable set
bool [:{q2},{f}:] is non empty finite finite-membered countable set
<*q1*> * (q2 .--> f) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
<*q1*> +* (<*q1*> * (q2 .--> f)) is Relation-like NAT -defined U -valued Function-like non empty finite countable finite-support set
id U is Relation-like U -defined U -valued Function-like one-to-one non empty total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:U,U:]
[:U,U:] is Relation-like non empty set
bool [:U,U:] is non empty set
(id U) +* (q2,f) is Relation-like U -defined U -valued Function-like total set
<*q1*> * ((id U) +* (q2,f)) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
U is non empty set
q1 is set
q2 is Element of U
(U,q1,q2) is Relation-like U * -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(U *),(U *):]
U * is functional non empty FinSequence-membered FinSequenceSet of U
[:(U *),(U *):] is Relation-like non empty set
bool [:(U *),(U *):] is non empty set
q11 is set
dom (U,q1,q2) is functional non empty FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
(U,q1,q2) . q11 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q11 is Relation-like Function-like set
U is Relation-like Function-like Function-yielding V159() FinSequence-yielding set
q1 is set
U . q1 is Relation-like Function-like set
proj1 U is set
proj1 U is set
proj1 U is set
U is set
q1 is non empty set
q2 is Element of q1
(q1,U,q2) is Relation-like q1 * -defined q1 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(q1 *),(q1 *):]
q1 * is functional non empty FinSequence-membered FinSequenceSet of q1
[:(q1 *),(q1 *):] is Relation-like non empty set
bool [:(q1 *),(q1 *):] is non empty set
f is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1,U,q2) . f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q11 is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f ^ q11 is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1,U,q2) . (f ^ q11) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1,U,q2) . q11 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((q1,U,q2) . f) ^ ((q1,U,q2) . q11) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1,U,q2,f) is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
f +~ (U,q2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U .--> q2 is Relation-like {U} -defined q1 -valued Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{U} is non empty trivial finite 1 -element countable set
{U} --> q2 is Relation-like {U} -defined q1 -valued {q2} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{U},{q2}:]
{q2} is non empty trivial finite 1 -element countable set
[:{U},{q2}:] is Relation-like non empty finite countable set
bool [:{U},{q2}:] is non empty finite finite-membered countable set
f * (U .--> q2) is Relation-like NAT -defined q1 -valued Function-like finite countable finite-support set
f +* (f * (U .--> q2)) is Relation-like NAT -defined q1 -valued Function-like finite countable finite-support set
id q1 is Relation-like q1 -defined q1 -valued Function-like one-to-one non empty total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:q1,q1:]
[:q1,q1:] is Relation-like non empty set
bool [:q1,q1:] is non empty set
(id q1) +* (U,q2) is Relation-like q1 -defined q1 -valued Function-like total set
f * ((id q1) +* (U,q2)) is Relation-like NAT -defined q1 -valued Function-like finite countable finite-support set
(q1,U,q2,q11) is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
q11 +~ (U,q2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q11 * (U .--> q2) is Relation-like NAT -defined q1 -valued Function-like finite countable finite-support set
q11 +* (q11 * (U .--> q2)) is Relation-like NAT -defined q1 -valued Function-like finite countable finite-support set
q11 * ((id q1) +* (U,q2)) is Relation-like NAT -defined q1 -valued Function-like finite countable finite-support set
(q1,U,q2,(f ^ q11)) is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
(f ^ q11) +~ (U,q2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(f ^ q11) * (U .--> q2) is Relation-like NAT -defined q1 -valued Function-like finite countable finite-support set
(f ^ q11) +* ((f ^ q11) * (U .--> q2)) is Relation-like NAT -defined q1 -valued Function-like finite countable finite-support set
(f ^ q11) * ((id q1) +* (U,q2)) is Relation-like NAT -defined q1 -valued Function-like finite countable finite-support set
U is non empty set
f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q1 is set
q2 is Element of U
(U,q1,q2) is Relation-like U * -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(U *),(U *):]
U * is functional non empty FinSequence-membered FinSequenceSet of U
[:(U *),(U *):] is Relation-like non empty set
bool [:(U *),(U *):] is non empty set
q11 is Relation-like NAT -defined U -valued Function-like finite f -element FinSequence-like FinSubsequence-like countable finite-support set
(U,q1,q2) . q11 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U,q1,q2,q11) is Relation-like NAT -defined U -valued Function-like finite f -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
q11 +~ (q1,q2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 .--> q2 is Relation-like {q1} -defined U -valued Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{q1} is non empty trivial finite 1 -element countable set
{q1} --> q2 is Relation-like {q1} -defined U -valued {q2} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{q1},{q2}:]
{q2} is non empty trivial finite 1 -element countable set
[:{q1},{q2}:] is Relation-like non empty finite countable set
bool [:{q1},{q2}:] is non empty finite finite-membered countable set
q11 * (q1 .--> q2) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
q11 +* (q11 * (q1 .--> q2)) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
id U is Relation-like U -defined U -valued Function-like one-to-one non empty total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:U,U:]
[:U,U:] is Relation-like non empty set
bool [:U,U:] is non empty set
(id U) +* (q1,q2) is Relation-like U -defined U -valued Function-like total set
q11 * ((id U) +* (q1,q2)) is Relation-like NAT -defined U -valued Function-like finite countable finite-support set
F is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U is non empty set
q1 is set
q2 is Element of U
(U,q1,q2) is Relation-like U * -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(U *),(U *):]
U * is functional non empty FinSequence-membered FinSequenceSet of U
[:(U *),(U *):] is Relation-like non empty set
bool [:(U *),(U *):] is non empty set
f is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
(U,q1,q2) . f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
proj2 f is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like with_non-empty_elements empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
U /\ {} is Relation-like finite countable (U) set
(U,{}) is Element of bool U
bool U is non empty set
(U,{}) is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial non proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of bool {}
bool {} is non empty finite finite-membered countable set
q11 is Relation-like non-empty empty-yielding NAT -defined U -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
F is set
(U,F,q2) is Relation-like U * -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(U *),(U *):]
(U,F,q2) . q11 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
F is set
U is non empty set
(U) is Relation-like (U *) * -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:((U *) *),(U *):]
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U *) * is functional non empty FinSequence-membered FinSequenceSet of U *
[:((U *) *),(U *):] is Relation-like non empty set
bool [:((U *) *),(U *):] is non empty set
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
[:(U *),(U *):] is Relation-like non empty set
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
((U *),(U -concatenation)) is Relation-like ((U *) *) \ {{}} -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(((U *) *) \ {{}}),(U *):]
((U *) *) \ {{}} is functional non empty FinSequence-membered Element of bool ((U *) *)
bool ((U *) *) is non empty set
(((U *) *),{{}}) is functional FinSequence-membered Element of bool ((U *) *)
[:(((U *) *) \ {{}}),(U *):] is Relation-like non empty set
bool [:(((U *) *) \ {{}}),(U *):] is non empty set
({} .--> {}) +* ((U *),(U -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
q11 is set
dom (U) is functional non empty FinSequence-membered Element of bool ((U *) *)
(U) . q11 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q11 is Relation-like Function-like set
U is non empty set
the Element of U is Element of U
<* the Element of U*> is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
[1, the Element of U] is non empty V15() set
{[1, the Element of U]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
U is non empty set
q1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q1 + q2 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
f is Relation-like NAT -defined U -valued Function-like finite q1 + q2 -element FinSequence-like FinSubsequence-like countable finite-support set
f . q1 is set
{(f . q1)} is non empty trivial finite 1 -element countable set
{(f . q1)} \ U is trivial finite countable Element of bool {(f . q1)}
bool {(f . q1)} is non empty finite finite-membered countable set
({(f . q1)},U) is trivial finite countable Element of bool {(f . q1)}
q11 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q11 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(q1 + q2) -tuples_on U is functional non empty FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of U
Seg (q1 + q2) is non empty finite q1 + q2 -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= q1 + q2 ) } is set
Funcs ((Seg (q1 + q2)),U) is functional non empty FUNCTION_DOMAIN of Seg (q1 + q2),U
[:(Seg (q1 + q2)),U:] is Relation-like non empty set
bool [:(Seg (q1 + q2)),U:] is non empty set
(q11 + 1) + q2 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
C is Relation-like Seg (q1 + q2) -defined U -valued Function-like non empty total quasi_total finite countable finite-support Element of bool [:(Seg (q1 + q2)),U:]
y1 is Element of Seg (q1 + q2)
C . y1 is Element of U
x is set
q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q1 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
(q1 + 1) + q2 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
U is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
f is Relation-like NAT -defined U -valued Function-like finite (q1 + 1) + q2 -element FinSequence-like FinSubsequence-like countable finite-support Element of U *
f . (q1 + 1) is set
{(f . (q1 + 1))} is non empty trivial finite 1 -element countable set
{(f . (q1 + 1))} \ U is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of bool {(f . (q1 + 1))}
bool {(f . (q1 + 1))} is non empty finite finite-membered countable set
({(f . (q1 + 1))},U) is trivial finite countable Element of bool {(f . (q1 + 1))}
q11 is set
U is set
<*U*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support set
[1,U] is non empty V15() set
{[1,U]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
<*U*> \+\ {[1,U]} is Relation-like finite countable set
<*U*> \ {[1,U]} is Relation-like NAT -defined finite countable set
(<*U*>,{[1,U]}) is Relation-like NAT -defined Function-like constant trivial finite countable finite-support Element of bool <*U*>
bool <*U*> is non empty finite finite-membered countable set
<*U*> \ {[1,U]} is Relation-like NAT -defined Function-like constant trivial finite countable finite-support Element of bool <*U*>
{[1,U]} \ <*U*> is Relation-like finite countable set
({[1,U]},<*U*>) is Relation-like Function-like constant trivial finite countable finite-support Element of bool {[1,U]}
bool {[1,U]} is non empty finite finite-membered countable set
{[1,U]} \ <*U*> is Relation-like Function-like constant trivial finite countable finite-support Element of bool {[1,U]}
(<*U*> \ {[1,U]}) \/ ({[1,U]} \ <*U*>) is Relation-like finite countable set
q1 is set
U is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
U + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
q1 is Relation-like NAT -defined Function-like finite U + 1 -element FinSequence-like FinSubsequence-like countable finite-support set
Seg U is finite U -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= U ) } is set
q1 | (Seg U) is Relation-like NAT -defined Seg U -defined NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 . (U + 1) is set
<*(q1 . (U + 1))*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support set
[1,(q1 . (U + 1))] is non empty V15() set
{[1,(q1 . (U + 1))]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
(q1 | (Seg U)) ^ <*(q1 . (U + 1))*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support set
((q1 | (Seg U)) ^ <*(q1 . (U + 1))*>) \+\ q1 is Relation-like finite countable set
((q1 | (Seg U)) ^ <*(q1 . (U + 1))*>) \ q1 is Relation-like NAT -defined finite countable set
(((q1 | (Seg U)) ^ <*(q1 . (U + 1))*>),q1) is Relation-like NAT -defined Function-like finite countable finite-support Element of bool ((q1 | (Seg U)) ^ <*(q1 . (U + 1))*>)
bool ((q1 | (Seg U)) ^ <*(q1 . (U + 1))*>) is non empty finite finite-membered countable set
((q1 | (Seg U)) ^ <*(q1 . (U + 1))*>) \ q1 is Relation-like NAT -defined Function-like finite countable finite-support Element of bool ((q1 | (Seg U)) ^ <*(q1 . (U + 1))*>)
q1 \ ((q1 | (Seg U)) ^ <*(q1 . (U + 1))*>) is Relation-like NAT -defined finite countable set
(q1,((q1 | (Seg U)) ^ <*(q1 . (U + 1))*>)) is Relation-like NAT -defined Function-like finite countable finite-support Element of bool q1
bool q1 is non empty finite finite-membered countable set
q1 \ ((q1 | (Seg U)) ^ <*(q1 . (U + 1))*>) is Relation-like NAT -defined Function-like finite countable finite-support Element of bool q1
(((q1 | (Seg U)) ^ <*(q1 . (U + 1))*>) \ q1) \/ (q1 \ ((q1 | (Seg U)) ^ <*(q1 . (U + 1))*>)) is Relation-like NAT -defined finite countable set
len q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
f is set
U is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
U + q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 is Relation-like NAT -defined Function-like finite U + q1 -element FinSequence-like FinSubsequence-like countable finite-support set
Seg U is finite U -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= U ) } is set
q2 | (Seg U) is Relation-like NAT -defined Seg U -defined NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U + {} is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
len q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
Seg (U + q1) is finite U + q1 -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= U + q1 ) } is set
dom q2 is finite U + q1 -element countable Element of bool NAT
bool (dom q2) is non empty finite finite-membered countable set
dom (q2 | (Seg U)) is finite countable Element of bool NAT
p is finite countable Element of bool (dom q2)
((dom q2),p) is set
(dom q2) /\ p is finite countable Element of bool (dom q2)
((dom q2),p) is finite countable Element of bool (dom q2)
(dom q2) /\ p is finite countable set
((dom q2),p) is finite countable Element of bool p
bool p is non empty finite finite-membered countable set
(p,(dom q2)) is finite countable Element of bool (p \/ (dom q2))
p \/ (dom q2) is finite countable set
bool (p \/ (dom q2)) is non empty finite finite-membered countable set
f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
Seg f is finite f -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= f ) } is set
len (q2 | (Seg U)) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
C is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U is Relation-like set
proj2 U is set
U is Relation-like set
U is Relation-like set
U is set
q1 is non empty set
(q1) is Relation-like (q1 *) * -defined q1 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:((q1 *) *),(q1 *):]
q1 * is functional non empty FinSequence-membered FinSequenceSet of q1
(q1 *) * is functional non empty FinSequence-membered FinSequenceSet of q1 *
[:((q1 *) *),(q1 *):] is Relation-like non empty set
bool [:((q1 *) *),(q1 *):] is non empty set
q1 -concatenation is Relation-like [:(q1 *),(q1 *):] -defined q1 * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(q1 *),(q1 *):],(q1 *):]
[:(q1 *),(q1 *):] is Relation-like non empty set
[:[:(q1 *),(q1 *):],(q1 *):] is Relation-like non empty set
bool [:[:(q1 *),(q1 *):],(q1 *):] is non empty set
((q1 *),(q1 -concatenation)) is Relation-like ((q1 *) *) \ {{}} -defined q1 * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(((q1 *) *) \ {{}}),(q1 *):]
((q1 *) *) \ {{}} is functional non empty FinSequence-membered Element of bool ((q1 *) *)
bool ((q1 *) *) is non empty set
(((q1 *) *),{{}}) is functional FinSequence-membered Element of bool ((q1 *) *)
[:(((q1 *) *) \ {{}}),(q1 *):] is Relation-like non empty set
bool [:(((q1 *) *) \ {{}}),(q1 *):] is non empty set
({} .--> {}) +* ((q1 *),(q1 -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
(q1) . U is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((q1 *),(q1 -concatenation)) . U is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
dom (q1 -concatenation) is Relation-like q1 * -defined q1 * -valued non empty Element of bool [:(q1 *),(q1 *):]
bool [:(q1 *),(q1 *):] is non empty set
dom ((q1 *),(q1 -concatenation)) is functional non empty FinSequence-membered Element of bool (((q1 *) *) \ {{}})
bool (((q1 *) *) \ {{}}) is non empty set
dom (q1) is functional non empty FinSequence-membered Element of bool ((q1 *) *)
bool (dom (q1)) is non empty set
p is Relation-like empty-yielding {{}} -valued Function-like Function-yielding V159() set
p . U is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
U is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
(U) is Relation-like (U *) * -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:((U *) *),(U *):]
(U *) * is functional non empty FinSequence-membered FinSequenceSet of U *
[:((U *) *),(U *):] is Relation-like non empty set
bool [:((U *) *),(U *):] is non empty set
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
[:(U *),(U *):] is Relation-like non empty set
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
((U *),(U -concatenation)) is Relation-like ((U *) *) \ {{}} -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(((U *) *) \ {{}}),(U *):]
((U *) *) \ {{}} is functional non empty FinSequence-membered Element of bool ((U *) *)
bool ((U *) *) is non empty set
(((U *) *),{{}}) is functional FinSequence-membered Element of bool ((U *) *)
[:(((U *) *) \ {{}}),(U *):] is Relation-like non empty set
bool [:(((U *) *) \ {{}}),(U *):] is non empty set
({} .--> {}) +* ((U *),(U -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U) . q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q2 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
<*q2*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support set
[1,q2] is non empty V15() set
{[1,q2]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
q1 ^ <*q2*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support set
(U) . (q1 ^ <*q2*>) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((U) . q1) ^ q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
C is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
(U) . C is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
((U) . C) ^ q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(((U) . C),q2) is set
(q2,((U) . C)) is Relation-like NAT -defined finite countable Element of bool (q2 \/ ((U) . C))
q2 \/ ((U) . C) is Relation-like NAT -defined finite countable set
bool (q2 \/ ((U) . C)) is non empty finite finite-membered countable set
q2 ^ ((U) . C) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
C ^ <*q2*> is Relation-like NAT -defined Function-like non empty finite {} + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
{} + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
(C,<*q2*>) is set
(<*q2*>,C) is Relation-like NAT -defined finite countable Element of bool (<*q2*> \/ C)
<*q2*> \/ C is Relation-like NAT -defined non empty finite countable set
bool (<*q2*> \/ C) is non empty finite finite-membered countable set
<*q2*> ^ C is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
(U) . (C ^ <*q2*>) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U) . <*q2*> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
p is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
<*p*> is Relation-like NAT -defined U * -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support FinSequence of U *
[1,p] is non empty V15() set
{[1,p]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
((U *),(U -concatenation)) . <*p*> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
C is Relation-like NAT -defined U * -valued Function-like non empty finite FinSequence-like FinSubsequence-like Function-yielding V159() countable finite-support set
C ^ <*q2*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like Function-yielding V159() countable finite-support set
(U) . (C ^ <*q2*>) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
p is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
<*p*> is Relation-like NAT -defined U * -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support FinSequence of U *
[1,p] is non empty V15() set
{[1,p]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
C ^ <*p*> is Relation-like NAT -defined U * -valued Function-like non empty finite FinSequence-like FinSubsequence-like Function-yielding V159() countable finite-support set
((U *),(U -concatenation)) . (C ^ <*p*>) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((U *),(U -concatenation)) . C is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U -concatenation) . ((((U *),(U -concatenation)) . C),p) is set
[(((U *),(U -concatenation)) . C),p] is non empty V15() set
(U -concatenation) . [(((U *),(U -concatenation)) . C),p] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
y1 is Relation-like NAT -defined U * -valued Function-like non empty finite FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support Element of (U *) *
(U) . y1 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
(U -concatenation) . (((U) . y1),q2) is set
[((U) . y1),q2] is non empty V15() set
(U -concatenation) . [((U) . y1),q2] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U is set
q1 is non empty set
q1 * is functional non empty FinSequence-membered FinSequenceSet of q1
(q1) is Relation-like (q1 *) * -defined q1 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:((q1 *) *),(q1 *):]
(q1 *) * is functional non empty FinSequence-membered FinSequenceSet of q1 *
[:((q1 *) *),(q1 *):] is Relation-like non empty set
bool [:((q1 *) *),(q1 *):] is non empty set
q1 -concatenation is Relation-like [:(q1 *),(q1 *):] -defined q1 * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(q1 *),(q1 *):],(q1 *):]
[:(q1 *),(q1 *):] is Relation-like non empty set
[:[:(q1 *),(q1 *):],(q1 *):] is Relation-like non empty set
bool [:[:(q1 *),(q1 *):],(q1 *):] is non empty set
((q1 *),(q1 -concatenation)) is Relation-like ((q1 *) *) \ {{}} -defined q1 * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(((q1 *) *) \ {{}}),(q1 *):]
((q1 *) *) \ {{}} is functional non empty FinSequence-membered Element of bool ((q1 *) *)
bool ((q1 *) *) is non empty set
(((q1 *) *),{{}}) is functional FinSequence-membered Element of bool ((q1 *) *)
[:(((q1 *) *) \ {{}}),(q1 *):] is Relation-like non empty set
bool [:(((q1 *) *) \ {{}}),(q1 *):] is non empty set
({} .--> {}) +* ((q1 *),(q1 -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
q2 is Element of q1
(q1,U,q2) is Relation-like q1 * -defined q1 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(q1 *),(q1 *):]
bool [:(q1 *),(q1 *):] is non empty set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1) . f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1,U,q2) . ((q1) . f) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f * (q1,U,q2) is Relation-like NAT -defined q1 * -valued Function-like finite Function-yielding V159() countable finite-support set
(q1) . (f * (q1,U,q2)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
len f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
(q1) is Relation-like (q1 *) \ {{}} -defined q1 -valued Function-like non empty total quasi_total Element of bool [:((q1 *) \ {{}}),q1:]
(q1 *) \ {{}} is functional non empty FinSequence-membered Element of bool (q1 *)
bool (q1 *) is non empty set
((q1 *),{{}}) is functional FinSequence-membered Element of bool (q1 *)
[:((q1 *) \ {{}}),q1:] is Relation-like non empty set
bool [:((q1 *) \ {{}}),q1:] is non empty set
(q1) is Relation-like [:q1,q1:] -defined q1 -valued Function-like non empty total quasi_total associative Element of bool [:[:q1,q1:],q1:]
[:q1,q1:] is Relation-like non empty set
[:[:q1,q1:],q1:] is Relation-like non empty set
bool [:[:q1,q1:],q1:] is non empty set
pr1 (q1,q1) is Relation-like [:q1,q1:] -defined q1 -valued Function-like non empty total quasi_total Element of bool [:[:q1,q1:],q1:]
(q1,(q1)) is Relation-like (q1 *) \ {{}} -defined q1 -valued Function-like non empty total quasi_total Element of bool [:((q1 *) \ {{}}),q1:]
((q1 *)) is Relation-like ((q1 *) *) \ {{}} -defined q1 * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(((q1 *) *) \ {{}}),(q1 *):]
((q1 *)) is Relation-like [:(q1 *),(q1 *):] -defined q1 * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(q1 *),(q1 *):],(q1 *):]
pr1 ((q1 *),(q1 *)) is Relation-like [:(q1 *),(q1 *):] -defined q1 * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:[:(q1 *),(q1 *):],(q1 *):]
((q1 *),((q1 *))) is Relation-like ((q1 *) *) \ {{}} -defined q1 * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(((q1 *) *) \ {{}}),(q1 *):]
p2 is Relation-like non-empty empty-yielding NAT -defined q1 * -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
(q1) . p2 is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
(q1,U,q2) . ((q1) . p2) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
p2 * (q1,U,q2) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued q1 * -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
(q1) . (p2 * (q1,U,q2)) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
p2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
p2 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
x2 is Relation-like NAT -defined q1 * -valued Function-like finite p2 + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable finite-support set
(q1) . x2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1,U,q2) . ((q1) . x2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
x2 * (q1,U,q2) is Relation-like NAT -defined q1 * -valued Function-like finite p2 + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable finite-support set
(q1) . (x2 * (q1,U,q2)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
Seg p2 is finite p2 -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= p2 ) } is set
x2 | (Seg p2) is Relation-like NAT -defined Seg p2 -defined NAT -defined q1 * -valued Function-like finite p2 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable finite-support set
p1 is Relation-like NAT -defined q1 * -valued Function-like finite p2 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable finite-support set
(p2 + 1) + {} is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
x2 . (p2 + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
{(x2 . (p2 + 1))} is functional non empty trivial finite finite-membered 1 -element with_common_domain countable set
{(x2 . (p2 + 1))} \ (q1 *) is functional trivial finite finite-membered with_common_domain countable Element of bool {(x2 . (p2 + 1))}
bool {(x2 . (p2 + 1))} is non empty finite finite-membered countable set
({(x2 . (p2 + 1))},(q1 *)) is functional trivial finite finite-membered with_common_domain countable Element of bool {(x2 . (p2 + 1))}
u1 is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of q1 *
(q1,U,q2) . u1 is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of q1 *
<*u1*> is Relation-like NAT -defined q1 * -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support FinSequence of q1 *
[1,u1] is non empty V15() set
{[1,u1]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
p1 ^ <*u1*> is Relation-like NAT -defined q1 * -valued Function-like non empty finite p2 + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable finite-support set
p2 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
(p1 ^ <*u1*>) \+\ x2 is Relation-like finite countable set
(p1 ^ <*u1*>) \ x2 is Relation-like NAT -defined q1 * -valued finite countable set
((p1 ^ <*u1*>),x2) is Relation-like NAT -defined q1 * -valued Function-like finite Function-yielding V159() countable finite-support Element of bool (p1 ^ <*u1*>)
bool (p1 ^ <*u1*>) is non empty finite finite-membered countable set
(p1 ^ <*u1*>) \ x2 is Relation-like NAT -defined q1 * -valued Function-like finite Function-yielding V159() countable finite-support Element of bool (p1 ^ <*u1*>)
x2 \ (p1 ^ <*u1*>) is Relation-like NAT -defined q1 * -valued finite countable set
(x2,(p1 ^ <*u1*>)) is Relation-like NAT -defined q1 * -valued Function-like finite Function-yielding V159() countable finite-support Element of bool x2
bool x2 is non empty finite finite-membered countable set
x2 \ (p1 ^ <*u1*>) is Relation-like NAT -defined q1 * -valued Function-like finite Function-yielding V159() countable finite-support Element of bool x2
((p1 ^ <*u1*>) \ x2) \/ (x2 \ (p1 ^ <*u1*>)) is Relation-like NAT -defined q1 * -valued finite countable set
p2 is Relation-like NAT -defined q1 * -valued Function-like finite p2 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support Element of (q1 *) *
(q1,U,q2) * p2 is Relation-like NAT -defined q1 * -valued Function-like finite p2 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support FinSequence of q1 *
u2 is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of q1 *
<*u2*> is Relation-like NAT -defined q1 * -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support FinSequence of q1 *
[1,u2] is non empty V15() set
{[1,u2]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
((q1,U,q2) * p2) ^ <*u2*> is Relation-like NAT -defined q1 * -valued Function-like non empty finite p2 + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support Element of (q1 *) *
(q1) . (((q1,U,q2) * p2) ^ <*u2*>) is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of q1 *
(q1) . ((q1,U,q2) * p2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((q1) . ((q1,U,q2) * p2)) ^ u2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1) . p2 is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of q1 *
(q1,U,q2) . ((q1) . p2) is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of q1 *
((q1,U,q2) . ((q1) . p2)) ^ u2 is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((q1) . p2) ^ u1 is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1,U,q2) . (((q1) . p2) ^ u1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
p2 is Relation-like NAT -defined q1 * -valued Function-like finite len f -element FinSequence-like FinSubsequence-like Function-yielding V159() countable finite-support set
(q1) . p2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1,U,q2) . ((q1) . p2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
p2 * (q1,U,q2) is Relation-like NAT -defined q1 * -valued Function-like finite len f -element FinSequence-like FinSubsequence-like Function-yielding V159() countable finite-support set
(q1) . (p2 * (q1,U,q2)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U is set
bool U is non empty set
q1 is Element of bool U
q2 is Relation-like U -defined total set
q2 | q1 is Relation-like q1 -defined U -defined set
dom q2 is Element of bool U
dom (q2 | q1) is Element of bool q1
bool q1 is non empty set
(U,q1) is set
U /\ q1 is Element of bool U
(U,q1) is Element of bool U
U /\ q1 is set
(U,q1) is Element of bool q1
(q1,U) is Element of bool (q1 \/ U)
q1 \/ U is set
bool (q1 \/ U) is non empty set
F is Relation-like q1 -defined set
q1 is non empty set
F is non empty set
q2 is Element of q1
f is Element of q1
U is set
<*q2*> is Relation-like NAT -defined q1 -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of q1
[1,q2] is non empty V15() set
{[1,q2]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
(q1,f,U,<*q2*>) is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support set
<*q2*> +~ (f,U) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f .--> U is Relation-like q1 -defined {f} -defined Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{f} is non empty trivial finite 1 -element countable set
{f} --> U is Relation-like {f} -defined {U} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{f},{U}:]
{U} is non empty trivial finite 1 -element countable set
[:{f},{U}:] is Relation-like non empty finite countable set
bool [:{f},{U}:] is non empty finite finite-membered countable set
<*q2*> * (f .--> U) is Relation-like NAT -defined Function-like finite countable finite-support set
<*q2*> +* (<*q2*> * (f .--> U)) is Relation-like NAT -defined Function-like non empty finite countable finite-support set
id q1 is Relation-like q1 -defined q1 -valued Function-like one-to-one non empty total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:q1,q1:]
[:q1,q1:] is Relation-like non empty set
bool [:q1,q1:] is non empty set
(id q1) +* (f,U) is Relation-like q1 -defined Function-like total set
<*q2*> * ((id q1) +* (f,U)) is Relation-like NAT -defined Function-like finite countable finite-support set
<*U*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support set
[1,U] is non empty V15() set
{[1,U]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
p is Element of F
C is Element of F
q11 is set
<*p*> is Relation-like NAT -defined F -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of F
[1,p] is non empty V15() set
{[1,p]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
(F,C,q11,<*p*>) is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support set
<*p*> +~ (C,q11) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
C .--> q11 is Relation-like F -defined {C} -defined Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{C} is non empty trivial finite 1 -element countable set
{C} --> q11 is Relation-like {C} -defined {q11} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{C},{q11}:]
{q11} is non empty trivial finite 1 -element countable set
[:{C},{q11}:] is Relation-like non empty finite countable set
bool [:{C},{q11}:] is non empty finite finite-membered countable set
<*p*> * (C .--> q11) is Relation-like NAT -defined Function-like finite countable finite-support set
<*p*> +* (<*p*> * (C .--> q11)) is Relation-like NAT -defined Function-like non empty finite countable finite-support set
id F is Relation-like F -defined F -valued Function-like one-to-one non empty total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:F,F:]
[:F,F:] is Relation-like non empty set
bool [:F,F:] is non empty set
(id F) +* (C,q11) is Relation-like F -defined Function-like total set
<*p*> * ((id F) +* (C,q11)) is Relation-like NAT -defined Function-like finite countable finite-support set
U is non empty set
q11 is non empty set
q1 is Element of U
q2 is Element of U
f is Element of U
(U,q2,f) is Relation-like U * -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(U *),(U *):]
U * is functional non empty FinSequence-membered FinSequenceSet of U
[:(U *),(U *):] is Relation-like non empty set
bool [:(U *),(U *):] is non empty set
<*q1*> is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
[1,q1] is non empty V15() set
{[1,q1]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
(U,q2,f) . <*q1*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support set
<*f*> is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
[1,f] is non empty V15() set
{[1,f]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
F is Element of q11
p is Element of q11
C is Element of q11
(q11,p,C) is Relation-like q11 * -defined q11 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(q11 *),(q11 *):]
q11 * is functional non empty FinSequence-membered FinSequenceSet of q11
[:(q11 *),(q11 *):] is Relation-like non empty set
bool [:(q11 *),(q11 *):] is non empty set
<*F*> is Relation-like NAT -defined q11 -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of q11
[1,F] is non empty V15() set
{[1,F]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
(q11,p,C) . <*F*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support set
q1 is non empty set
U is set
q2 is Element of q1
(q1,U,q2) is Relation-like q1 * -defined q1 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(q1 *),(q1 *):]
q1 * is functional non empty FinSequence-membered FinSequenceSet of q1
[:(q1 *),(q1 *):] is Relation-like non empty set
bool [:(q1 *),(q1 *):] is non empty set
f is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q11 is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f ^ q11 is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1,U,q2) . (f ^ q11) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1,U,q2) . f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1,U,q2) . q11 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((q1,U,q2) . f) ^ ((q1,U,q2) . q11) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 is non empty set
q1 * is functional non empty FinSequence-membered FinSequenceSet of q1
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U is set
q2 is Element of q1
(q1,U,q2) is Relation-like q1 * -defined q1 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(q1 *),(q1 *):]
[:(q1 *),(q1 *):] is Relation-like non empty set
bool [:(q1 *),(q1 *):] is non empty set
(q1) is Relation-like (q1 *) * -defined q1 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:((q1 *) *),(q1 *):]
(q1 *) * is functional non empty FinSequence-membered FinSequenceSet of q1 *
[:((q1 *) *),(q1 *):] is Relation-like non empty set
bool [:((q1 *) *),(q1 *):] is non empty set
q1 -concatenation is Relation-like [:(q1 *),(q1 *):] -defined q1 * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(q1 *),(q1 *):],(q1 *):]
[:[:(q1 *),(q1 *):],(q1 *):] is Relation-like non empty set
bool [:[:(q1 *),(q1 *):],(q1 *):] is non empty set
((q1 *),(q1 -concatenation)) is Relation-like ((q1 *) *) \ {{}} -defined q1 * -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:(((q1 *) *) \ {{}}),(q1 *):]
((q1 *) *) \ {{}} is functional non empty FinSequence-membered Element of bool ((q1 *) *)
bool ((q1 *) *) is non empty set
(((q1 *) *),{{}}) is functional FinSequence-membered Element of bool ((q1 *) *)
[:(((q1 *) *) \ {{}}),(q1 *):] is Relation-like non empty set
bool [:(((q1 *) *) \ {{}}),(q1 *):] is non empty set
({} .--> {}) +* ((q1 *),(q1 -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
(q1) . f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1,U,q2) . ((q1) . f) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f * (q1,U,q2) is Relation-like NAT -defined q1 * -valued Function-like finite Function-yielding V159() countable finite-support set
(q1) . (f * (q1,U,q2)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U is non empty set
U * is functional non empty FinSequence-membered FinSequenceSet of U
[:(U *),(U *):] is Relation-like non empty set
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total associative Function-yielding V159() Element of bool [:[:(U *),(U *):],(U *):]
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
1 -tuples_on U is functional non empty FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of U
id (1 -tuples_on U) is Relation-like non-empty 1 -tuples_on U -defined 1 -tuples_on U -valued Function-like one-to-one non empty total quasi_total onto bijective Function-yielding V159() reflexive symmetric antisymmetric transitive Element of bool [:(1 -tuples_on U),(1 -tuples_on U):]
[:(1 -tuples_on U),(1 -tuples_on U):] is Relation-like non empty set
bool [:(1 -tuples_on U),(1 -tuples_on U):] is non empty set
(U -concatenation) .: (id (1 -tuples_on U)) is functional FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
{ <*b₁,b₁*> where b₁ is Element of U : verum } is set
2 -tuples_on U is functional non empty FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of U
bool [:(U *),(U *):] is non empty set
{ <*b₁*> where b₁ is Element of U : verum } is set
dom (id (1 -tuples_on U)) is functional non empty FinSequence-membered (U) Element of bool (1 -tuples_on U)
bool (1 -tuples_on U) is non empty set
dom (U -concatenation) is Relation-like U * -defined U * -valued non empty Element of bool [:(U *),(U *):]
{ [b₁,((id (1 -tuples_on U)) . b₁)] where b₁ is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on U : b₁ in 1 -tuples_on U } is set
y1 is set
x is set
(U -concatenation) . x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
y is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on U
(id (1 -tuples_on U)) . y is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on U
[y,((id (1 -tuples_on U)) . y)] is non empty V15() Element of [:(1 -tuples_on U),(1 -tuples_on U):]
pb is Element of U
<*pb*> is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
[1,pb] is non empty V15() set
{[1,pb]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
{((id (1 -tuples_on U)) . y)} is functional non empty trivial finite finite-membered 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (U) Element of bool (1 -tuples_on U)
{y} is functional non empty trivial finite finite-membered 1 -element FinSequence-membered with_non-empty_elements non empty-membered with_common_domain countable (U) Element of bool (1 -tuples_on U)
{((id (1 -tuples_on U)) . y)} \ {y} is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support (U) Element of bool (1 -tuples_on U)
({((id (1 -tuples_on U)) . y)},{y}) is functional trivial finite finite-membered FinSequence-membered with_common_domain countable Element of bool {((id (1 -tuples_on U)) . y)}
bool {((id (1 -tuples_on U)) . y)} is non empty finite finite-membered countable set
{((id (1 -tuples_on U)) . y)} \ {y} is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable FinSequence-yielding finite-support Element of bool {((id (1 -tuples_on U)) . y)}
q1 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
(U -concatenation) . (q1,q1) is set
[q1,q1] is non empty V15() set
(U -concatenation) . [q1,q1] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
<*pb,pb*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable finite-support set
<*pb*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support set
<*pb*> ^ <*pb*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like countable finite-support set
1 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
y1 is set
x is Element of U
<*x,x*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like countable finite-support set
<*x*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support set
[1,x] is non empty V15() set
{[1,x]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
<*x*> ^ <*x*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like countable finite-support set
<*x*> is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
y is Relation-like NAT -defined U -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on U
(id (1 -tuples_on U)) . y is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of 1 -tuples_on U
[y,((id (1 -tuples_on U)) . y)] is non empty V15() Element of [:(1 -tuples_on U),(1 -tuples_on U):]
[y,y] is non empty V15() Element of [:(1 -tuples_on U),(1 -tuples_on U):]
q1 is Element of id (1 -tuples_on U)
C is Relation-like U * -defined U * -valued Element of bool [:(U *),(U *):]
([:(U *),(U *):],C) is set
[:(U *),(U *):] /\ C is Relation-like U * -defined U * -valued Element of bool [:(U *),(U *):]
([:(U *),(U *):],C) is Relation-like U * -defined U * -valued Element of bool [:(U *),(U *):]
[:(U *),(U *):] /\ C is Relation-like U * -defined U * -valued set
([:(U *),(U *):],C) is Relation-like U * -defined U * -valued Element of bool C
bool C is non empty set
(C,[:(U *),(U *):]) is Relation-like Element of bool (C \/ [:(U *),(U *):])
C \/ [:(U *),(U *):] is Relation-like non empty set
bool (C \/ [:(U *),(U *):]) is non empty set
pb is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of U
(U -concatenation) . (pb,pb) is set
[pb,pb] is non empty V15() set
(U -concatenation) . [pb,pb] is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U -concatenation) . q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 is non empty set
U is Relation-like Function-like set
U | q1 is Relation-like Function-like set
q2 is Element of q1
(U | q1) . q2 is set
U . q2 is set
((U | q1) . q2) \+\ (U . q2) is set
((U | q1) . q2) \ (U . q2) is set
(((U | q1) . q2),(U . q2)) is Element of bool ((U | q1) . q2)
bool ((U | q1) . q2) is non empty set
((U | q1) . q2) \ (U . q2) is Element of bool ((U | q1) . q2)
(U . q2) \ ((U | q1) . q2) is set
((U . q2),((U | q1) . q2)) is Element of bool (U . q2)
bool (U . q2) is non empty set
(U . q2) \ ((U | q1) . q2) is Element of bool (U . q2)
(((U | q1) . q2) \ (U . q2)) \/ ((U . q2) \ ((U | q1) . q2)) is set
f is set
q1 is non empty set
q2 is non empty set
[:q1,q2:] is Relation-like non empty set
bool [:q1,q2:] is non empty set
q11 is Relation-like q1 -defined q2 -valued Function-like non empty total quasi_total Element of bool [:q1,q2:]
U is Relation-like Function-like set
q11 * U is Relation-like q1 -defined Function-like set
f is Element of q1
(q11 * U) . f is set
q11 . f is Element of q2
U . (q11 . f) is set
((q11 * U) . f) \+\ (U . (q11 . f)) is set
((q11 * U) . f) \ (U . (q11 . f)) is set
(((q11 * U) . f),(U . (q11 . f))) is Element of bool ((q11 * U) . f)
bool ((q11 * U) . f) is non empty set
((q11 * U) . f) \ (U . (q11 . f)) is Element of bool ((q11 * U) . f)
(U . (q11 . f)) \ ((q11 * U) . f) is set
((U . (q11 . f)),((q11 * U) . f)) is Element of bool (U . (q11 . f))
bool (U . (q11 . f)) is non empty set
(U . (q11 . f)) \ ((q11 * U) . f) is Element of bool (U . (q11 . f))
(((q11 * U) . f) \ (U . (q11 . f))) \/ ((U . (q11 . f)) \ ((q11 * U) . f)) is set
dom q11 is non empty Element of bool q1
bool q1 is non empty set
F is set
U is complex real integer finite ext-real countable set
U is complex real ext-real set
q1 is complex real ext-real set
max (U,q1) is complex real ext-real set
(max (U,q1)) - U is complex real ext-real set
- U is complex real ext-real set
U + (- U) is complex real ext-real set
(max (U,q1)) + (- U) is complex real ext-real set
f is ext-real set
U is set
U is set
bool U is non empty set
q1 is Element of bool U
q1 \ U is Element of bool U
(q1,U) is Element of bool q1
bool q1 is non empty set
q1 \ U is Element of bool q1
q2 is set
U is set
{U} is non empty trivial finite 1 -element countable set
q1 is set
{U,q1} is non empty finite countable set
{U} \ {U,q1} is trivial finite countable Element of bool {U}
bool {U} is non empty finite finite-membered countable set
({U},{U,q1}) is trivial finite countable Element of bool {U}
q2 is set
[U,q1] is non empty V15() set
[U,q1] `1 is set
([U,q1] `1) \+\ U is set
([U,q1] `1) \ U is set
(([U,q1] `1),U) is Element of bool ([U,q1] `1)
bool ([U,q1] `1) is non empty set
([U,q1] `1) \ U is Element of bool ([U,q1] `1)
U \ ([U,q1] `1) is set
(U,([U,q1] `1)) is Element of bool U
bool U is non empty set
U \ ([U,q1] `1) is Element of bool U
(([U,q1] `1) \ U) \/ (U \ ([U,q1] `1)) is set
q2 is set
U is set
q1 is set
[U,q1] is non empty V15() set
[U,q1] `2 is set
([U,q1] `2) \+\ q1 is set
([U,q1] `2) \ q1 is set
(([U,q1] `2),q1) is Element of bool ([U,q1] `2)
bool ([U,q1] `2) is non empty set
([U,q1] `2) \ q1 is Element of bool ([U,q1] `2)
q1 \ ([U,q1] `2) is set
(q1,([U,q1] `2)) is Element of bool q1
bool q1 is non empty set
q1 \ ([U,q1] `2) is Element of bool q1
(([U,q1] `2) \ q1) \/ (q1 \ ([U,q1] `2)) is set
q2 is set
q1 is non empty set
q1 * is functional non empty FinSequence-membered FinSequenceSet of q1
(q1 *) \ {{}} is functional non empty FinSequence-membered Element of bool (q1 *)
bool (q1 *) is non empty set
((q1 *),{{}}) is functional FinSequence-membered Element of bool (q1 *)
U is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(q2 + 1) -tuples_on q1 is functional non empty FinSequence-membered with_non-empty_elements non empty-membered FinSequenceSet of q1
the Relation-like NAT -defined q1 -valued Function-like non empty finite q2 + 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of (q2 + 1) -tuples_on q1 is Relation-like NAT -defined q1 -valued Function-like non empty finite q2 + 1 -element FinSequence-like FinSubsequence-like countable finite-support Element of (q2 + 1) -tuples_on q1
q11 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
q11 -tuples_on q1 is functional non empty FinSequence-membered FinSequenceSet of q1
F is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of (q1 *) \ {{}}
U is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
U + {} is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
len q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
q1 is set
U is Relation-like set
(q1,U) is set
(U,q1) is Element of bool (U \/ q1)
U \/ q1 is set
bool (U \/ q1) is non empty set
q2 is set
q1 is set
U is Function-like set
(q1,U) is set
(U,q1) is Element of bool (U \/ q1)
U \/ q1 is set
bool (U \/ q1) is non empty set
q2 is set
q1 is set
U is Relation-like FinSequence-like set
(q1,U) is Relation-like set
(U,q1) is Element of bool (U \/ q1)
U \/ q1 is set
bool (U \/ q1) is non empty set
q2 is Relation-like set
q1 is set
U is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1,U) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U,q1) is Element of bool (U \/ q1)
U \/ q1 is set
bool (U \/ q1) is non empty set
len U is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support set
len U is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
q1 is set
U is Relation-like set
q1 is set
U | q1 is Relation-like set
proj1 (U | q1) is set
q2 is Relation-like set
U is set
q1 is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
(U,q1) is Relation-like NAT -defined Function-like finite len q1 -element FinSequence-like FinSubsequence-like countable finite-support set
len q1 is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of NAT
(q1,U) is Element of bool (q1 \/ U)
q1 \/ U is set
bool (q1 \/ U) is non empty set
q2 is set
U is set
q1 is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
(U,q1) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element len q1 -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
len q1 is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of NAT
(q1,U) is Element of bool (q1 \/ U)
q1 \/ U is set
bool (q1 \/ U) is non empty set
rng q1 is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like with_non-empty_elements empty-membered Cardinal-yielding with_common_domain countable FinSequence-yielding finite-support Element of bool {{}}
bool {{}} is non empty finite finite-membered countable set
(rng q1) /\ U is Relation-like functional trivial finite finite-membered empty-membered with_common_domain countable Element of bool {{}}
((rng q1),U) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial non proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable FinSequence-yielding finite-support Element of bool (rng q1)
bool (rng q1) is non empty finite finite-membered countable set
(rng q1) /\ U is Relation-like finite countable set
((rng q1),U) is Element of bool U
bool U is non empty set
q2 is Relation-like set
U is functional non empty FinSequence-membered set
q1 is Relation-like Function-like set
proj2 q1 is set
q2 is set
proj1 q1 is set
f is non empty set
[:f,U:] is Relation-like non empty set
bool [:f,U:] is non empty set
F is Relation-like f -defined U -valued Function-like non empty total quasi_total Function-yielding V159() Element of bool [:f,U:]
q11 is Element of f
F . q11 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U
q1 . q2 is set
U is set
q1 is set
q1 * is functional non empty FinSequence-membered FinSequenceSet of q1
Funcs (U,(q1 *)) is functional non empty FUNCTION_DOMAIN of U,q1 *
q2 is Relation-like U -defined q1 * -valued Function-like total quasi_total Function-yielding V159() FinSequence-yielding Element of Funcs (U,(q1 *))
U is set
U * is functional non empty FinSequence-membered FinSequenceSet of U
q1 is set
q2 is Relation-like Function-like set
q2 . q1 is set
proj2 q2 is set
proj1 q2 is set
f is non empty set
[:f,(U *):] is Relation-like non empty set
bool [:f,(U *):] is non empty set
F is Relation-like f -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:f,(U *):]
q11 is Element of f
F . q11 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
proj1 q2 is set
proj1 q2 is set
U is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 is Relation-like NAT -defined Function-like finite U -element FinSequence-like FinSubsequence-like countable finite-support set
(q1,q2) is Relation-like NAT -defined Function-like finite len q2 -element FinSequence-like FinSubsequence-like countable finite-support set
len q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
(q2,q1) is finite countable Element of bool (q2 \/ q1)
q2 \/ q1 is finite countable set
bool (q2 \/ q1) is non empty finite finite-membered countable set
U + q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
Seg (U + q1) is finite U + q1 -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= U + q1 ) } is set
dom q2 is finite U -element countable Element of bool NAT
Seg (len q2) is finite len q2 -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= len q2 ) } is set
U + {} is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
Seg U is finite U -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= U ) } is set
f is Relation-like set
U is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 ^ q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q11 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f ^ q11 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
len q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
Seg (len q1) is finite len q1 -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= len q1 ) } is set
dom q1 is finite countable Element of bool NAT
len f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
Seg (len f) is finite len f -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= len f ) } is set
dom f is finite countable Element of bool NAT
C is Relation-like NAT -defined Function-like finite U -element FinSequence-like FinSubsequence-like countable finite-support set
dom C is finite U -element countable Element of bool NAT
Seg U is finite U -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= U ) } is set
y1 is Relation-like NAT -defined Function-like finite U -element FinSequence-like FinSubsequence-like countable finite-support set
dom y1 is finite U -element countable Element of bool NAT
U + {} is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
Seg (U + {}) is finite U + {} -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= U + {} ) } is set
({},C) is Relation-like NAT -defined Seg (U + {}) -defined Function-like finite len C -element FinSequence-like FinSubsequence-like countable finite-support set
len C is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
(C,{}) is Relation-like NAT -defined finite countable Element of bool (C \/ {})
C \/ {} is Relation-like NAT -defined finite countable set
bool (C \/ {}) is non empty finite finite-membered countable set
C ^ {} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
{} ^ C is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
({},y1) is Relation-like NAT -defined Seg (U + {}) -defined Function-like finite len y1 -element FinSequence-like FinSubsequence-like countable finite-support set
len y1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
(y1,{}) is Relation-like NAT -defined finite countable Element of bool (y1 \/ {})
y1 \/ {} is Relation-like NAT -defined finite countable set
bool (y1 \/ {}) is non empty finite finite-membered countable set
y1 ^ {} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
{} ^ y1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
x is Relation-like NAT -defined Seg U -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((Seg U),x) is Relation-like NAT -defined Function-like finite len x -element FinSequence-like FinSubsequence-like countable finite-support set
len x is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
(x,(Seg U)) is finite countable Element of bool (x \/ (Seg U))
x \/ (Seg U) is finite countable set
bool (x \/ (Seg U)) is non empty finite finite-membered countable set
x | (Seg U) is Relation-like NAT -defined Seg U -defined NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
y is Relation-like NAT -defined Seg U -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
y ^ q11 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(y ^ q11) | (Seg U) is Relation-like NAT -defined Seg U -defined NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((Seg U),y) is Relation-like NAT -defined Function-like finite len y -element FinSequence-like FinSubsequence-like countable finite-support set
len y is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
(y,(Seg U)) is finite countable Element of bool (y \/ (Seg U))
y \/ (Seg U) is finite countable set
bool (y \/ (Seg U)) is non empty finite finite-membered countable set
y | (Seg U) is Relation-like NAT -defined Seg U -defined NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 is Relation-like NAT -defined Function-like finite U -element FinSequence-like FinSubsequence-like countable finite-support set
f is Relation-like NAT -defined Function-like finite q1 -element FinSequence-like FinSubsequence-like countable finite-support set
q2 ^ f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U + q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q11 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
F is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
q11 + F is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
p is Relation-like NAT -defined Function-like finite q11 -element FinSequence-like FinSubsequence-like countable finite-support set
C is Relation-like NAT -defined Function-like finite F -element FinSequence-like FinSubsequence-like countable finite-support set
p ^ C is Relation-like NAT -defined Function-like finite q11 + F -element FinSequence-like FinSubsequence-like countable finite-support set
q11 + F is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
y1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 ^ q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q11 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f ^ q11 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q2 ^ q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q11 ^ f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
len q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
len q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
len f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
len q11 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
(q2,q2) is Relation-like NAT -defined Function-like finite len q2 -element FinSequence-like FinSubsequence-like countable finite-support set
(q2,q2) is Relation-like NAT -defined finite countable Element of bool (q2 \/ q2)
q2 \/ q2 is Relation-like NAT -defined finite countable set
bool (q2 \/ q2) is non empty finite finite-membered countable set
(q11,q11) is Relation-like NAT -defined Function-like finite len q11 -element FinSequence-like FinSubsequence-like countable finite-support set
(q11,q11) is Relation-like NAT -defined finite countable Element of bool (q11 \/ q11)
q11 \/ q11 is Relation-like NAT -defined finite countable set
bool (q11 \/ q11) is non empty finite finite-membered countable set
x is Relation-like NAT -defined Function-like finite U -element FinSequence-like FinSubsequence-like countable finite-support set
pb is Relation-like NAT -defined Function-like finite len q2 -element FinSequence-like FinSubsequence-like countable finite-support set
x ^ pb is Relation-like NAT -defined Function-like finite U + (len q2) -element U + (len q2) -element FinSequence-like FinSubsequence-like countable finite-support set
U + (len q2) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
U + (len q2) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
pb ^ x is Relation-like NAT -defined Function-like finite (len q2) + U -element FinSequence-like FinSubsequence-like countable finite-support set
(len q2) + U is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
y is Relation-like NAT -defined Function-like finite U -element FinSequence-like FinSubsequence-like countable finite-support set
q1 is Relation-like NAT -defined Function-like finite len q11 -element FinSequence-like FinSubsequence-like countable finite-support set
y ^ q1 is Relation-like NAT -defined Function-like finite U + (len q11) -element U + (len q11) -element FinSequence-like FinSubsequence-like countable finite-support set
U + (len q11) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
U + (len q11) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
q1 ^ y is Relation-like NAT -defined Function-like finite (len q11) + U -element FinSequence-like FinSubsequence-like countable finite-support set
(len q11) + U is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
len (x ^ pb) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
len (pb ^ x) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
len (y ^ q1) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
len (q1 ^ y) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
p1 is Relation-like NAT -defined Function-like finite len q2 -element FinSequence-like FinSubsequence-like countable finite-support set
U is set
q1 is non empty set
(q1) is Relation-like (q1 *) * -defined q1 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:((q1 *) *),(q1 *):]
q1 * is functional non empty FinSequence-membered FinSequenceSet of q1
(q1 *) * is functional non empty FinSequence-membered FinSequenceSet of q1 *
[:((q1 *) *),(q1 *):] is Relation-like non empty set
bool [:((q1 *) *),(q1 *):] is non empty set
q1 -concatenation is Relation-like [:(q1 *),(q1 *):] -defined q1 * -valued Function-like non empty total quasi_total associative Function-yielding V159() FinSequence-yielding Element of bool [:[:(q1 *),(q1 *):],(q1 *):]
[:(q1 *),(q1 *):] is Relation-like non empty set
[:[:(q1 *),(q1 *):],(q1 *):] is Relation-like non empty set
bool [:[:(q1 *),(q1 *):],(q1 *):] is non empty set
((q1 *),(q1 -concatenation)) is Relation-like ((q1 *) *) \ {{}} -defined q1 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(((q1 *) *) \ {{}}),(q1 *):]
((q1 *) *) \ {{}} is functional non empty FinSequence-membered Element of bool ((q1 *) *)
bool ((q1 *) *) is non empty set
(((q1 *) *),{{}}) is functional FinSequence-membered Element of bool ((q1 *) *)
[:(((q1 *) *) \ {{}}),(q1 *):] is Relation-like non empty set
bool [:(((q1 *) *) \ {{}}),(q1 *):] is non empty set
({} .--> {}) +* ((q1 *),(q1 -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
(q1) . U is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q2 is non empty set
q2 * is functional non empty FinSequence-membered FinSequenceSet of q2
((q1 *),{}) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued q1 * -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element len {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
len {} is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of NAT
({},(q1 *)) is Element of bool ({} \/ (q1 *))
{} \/ (q1 *) is non empty set
bool ({} \/ (q1 *)) is non empty set
{} + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
y1 is Relation-like NAT -defined q1 * -valued Function-like finite {} + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
(q1) . y1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
1 + {} is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
x is Relation-like NAT -defined q1 * -valued Function-like non empty finite 1 + {} -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
x . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
{(x . 1)} is functional non empty trivial finite finite-membered 1 -element with_common_domain countable set
{(x . 1)} \ (q1 *) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable FinSequence-yielding finite-support Element of bool {(x . 1)}
bool {(x . 1)} is non empty finite finite-membered countable set
({(x . 1)},(q1 *)) is functional trivial finite finite-membered with_common_domain countable Element of bool {(x . 1)}
y1 . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
len y1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
<*(y1 . 1)*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support set
[1,(y1 . 1)] is non empty V15() set
{[1,(y1 . 1)]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
{} ^ <*(y1 . 1)*> is Relation-like NAT -defined Function-like non empty finite {} + 1 -element {} + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
{} + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
({},<*(y1 . 1)*>) is Relation-like NAT -defined Seg (1 + {}) -defined Function-like finite len <*(y1 . 1)*> -element FinSequence-like FinSubsequence-like countable finite-support set
Seg (1 + {}) is non empty finite 1 + {} -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= 1 + {} ) } is set
len <*(y1 . 1)*> is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
(<*(y1 . 1)*>,{}) is Relation-like NAT -defined finite countable Element of bool (<*(y1 . 1)*> \/ {})
<*(y1 . 1)*> \/ {} is Relation-like NAT -defined non empty finite countable set
bool (<*(y1 . 1)*> \/ {}) is non empty finite finite-membered countable set
<*(y1 . 1)*> ^ {} is Relation-like NAT -defined Function-like non empty finite 1 + {} -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
C is Relation-like NAT -defined q1 * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
(q1) . C is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
y is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of q1 *
((q1) . C) ^ y is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
{} ^ (y1 . 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
({},(y1 . 1)) is Relation-like NAT -defined Function-like finite len (y1 . 1) -element FinSequence-like FinSubsequence-like countable finite-support set
len (y1 . 1) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
((y1 . 1),{}) is Relation-like NAT -defined finite countable Element of bool ((y1 . 1) \/ {})
(y1 . 1) \/ {} is Relation-like NAT -defined finite countable set
bool ((y1 . 1) \/ {}) is non empty finite finite-membered countable set
(y1 . 1) ^ {} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
pb is Relation-like NAT -defined q1 * -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support Element of (q1 *) *
(q1) . pb is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of q1 *
q1 is Relation-like NAT -defined q2 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support FinSequence of q2
x1 is Relation-like NAT -defined q2 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of q2 *
<*x1*> is Relation-like NAT -defined q2 * -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support FinSequence of q2 *
[1,x1] is non empty V15() set
{[1,x1]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
y1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
y1 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(y1 + 1) + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
y is Relation-like NAT -defined q1 * -valued Function-like finite (y1 + 1) + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
(q1) . y is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
y1 + 2 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(y,y) is Relation-like NAT -defined Function-like finite len y -element FinSequence-like FinSubsequence-like countable finite-support set
len y is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
(y,y) is Relation-like NAT -defined q1 * -valued finite countable Element of bool (y \/ y)
y \/ y is Relation-like NAT -defined q1 * -valued finite countable set
bool (y \/ y) is non empty finite finite-membered countable set
x is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
x + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
pb is Relation-like NAT -defined q1 * -valued Function-like finite y1 + 2 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
(x + 1) + {} is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
q1 is Relation-like NAT -defined q1 * -valued Function-like finite x + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
Seg x is non empty finite x -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= x ) } is set
q1 | (Seg x) is Relation-like NAT -defined Seg x -defined NAT -defined q1 * -valued Function-like finite x -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
x1 is Relation-like NAT -defined q1 * -valued Function-like non empty finite (x + 1) + {} -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
x1 . (x + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
{(x1 . (x + 1))} is functional non empty trivial finite finite-membered 1 -element with_common_domain countable set
{(x1 . (x + 1))} \ (q1 *) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable FinSequence-yielding finite-support Element of bool {(x1 . (x + 1))}
bool {(x1 . (x + 1))} is non empty finite finite-membered countable set
({(x1 . (x + 1))},(q1 *)) is functional trivial finite finite-membered with_common_domain countable Element of bool {(x1 . (x + 1))}
q1 . (x + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
p2 is Relation-like NAT -defined q1 * -valued Function-like finite x -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
<*(q1 . (x + 1))*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support set
[1,(q1 . (x + 1))] is non empty V15() set
{[1,(q1 . (x + 1))]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
p2 ^ <*(q1 . (x + 1))*> is Relation-like NAT -defined Function-like non empty finite x + 1 -element x + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
x + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
q1 \+\ (p2 ^ <*(q1 . (x + 1))*>) is Relation-like finite countable set
q1 \ (p2 ^ <*(q1 . (x + 1))*>) is Relation-like NAT -defined q1 * -valued finite countable set
(q1,(p2 ^ <*(q1 . (x + 1))*>)) is Relation-like NAT -defined q1 * -valued Function-like finite Function-yielding V159() countable FinSequence-yielding finite-support Element of bool q1
bool q1 is non empty finite finite-membered countable set
q1 \ (p2 ^ <*(q1 . (x + 1))*>) is Relation-like NAT -defined q1 * -valued Function-like finite Function-yielding V159() countable FinSequence-yielding finite-support Element of bool q1
(p2 ^ <*(q1 . (x + 1))*>) \ q1 is Relation-like NAT -defined finite countable set
((p2 ^ <*(q1 . (x + 1))*>),q1) is Relation-like NAT -defined Function-like finite countable finite-support Element of bool (p2 ^ <*(q1 . (x + 1))*>)
bool (p2 ^ <*(q1 . (x + 1))*>) is non empty finite finite-membered countable set
(p2 ^ <*(q1 . (x + 1))*>) \ q1 is Relation-like NAT -defined Function-like finite countable finite-support Element of bool (p2 ^ <*(q1 . (x + 1))*>)
(q1 \ (p2 ^ <*(q1 . (x + 1))*>)) \/ ((p2 ^ <*(q1 . (x + 1))*>) \ q1) is Relation-like NAT -defined finite countable set
q2 is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of q1 *
<*q2*> is Relation-like NAT -defined q1 * -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support FinSequence of q1 *
[1,q2] is non empty V15() set
{[1,q2]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
p2 ^ <*q2*> is Relation-like NAT -defined q1 * -valued Function-like non empty finite x + 1 -element x + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
(q1) . p2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((q1) . p2) ^ q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
proj2 ((q1) . y) is finite countable set
proj2 ((q1) . p2) is finite countable set
x2 is Relation-like NAT -defined q2 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
rng q2 is finite countable Element of bool q1
bool q1 is non empty set
p1 is Relation-like NAT -defined q2 * -valued Function-like finite x -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
p2 is Relation-like NAT -defined q2 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of q2 *
<*p2*> is Relation-like NAT -defined q2 * -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support FinSequence of q2 *
[1,p2] is non empty V15() set
{[1,p2]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
p1 ^ <*p2*> is Relation-like NAT -defined q2 * -valued Function-like non empty finite x + 1 -element x + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
y1 is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
((q2 *),y1) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued q2 * -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element len y1 -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
len y1 is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of NAT
(y1,(q2 *)) is Element of bool (y1 \/ (q2 *))
y1 \/ (q2 *) is non empty set
bool (y1 \/ (q2 *)) is non empty set
y1 is Relation-like NAT -defined q1 * -valued Function-like non empty finite FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
len y1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
x is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
x + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
({},y1) is Relation-like NAT -defined Function-like finite len y1 -element FinSequence-like FinSubsequence-like countable finite-support set
(y1,{}) is Relation-like NAT -defined finite countable Element of bool (y1 \/ {})
y1 \/ {} is Relation-like NAT -defined non empty finite countable set
bool (y1 \/ {}) is non empty finite finite-membered countable set
y1 ^ {} is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
{} ^ y1 is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
y is Relation-like NAT -defined q1 * -valued Function-like finite x + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
U is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
U + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(U + 1) + {} is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
f is Relation-like NAT -defined Function-like non empty finite (U + 1) + {} -element FinSequence-like FinSubsequence-like countable finite-support set
U is non empty set
id U is Relation-like U -defined U -valued Function-like one-to-one non empty total quasi_total onto bijective reflexive symmetric antisymmetric transitive Element of bool [:U,U:]
[:U,U:] is Relation-like non empty set
bool [:U,U:] is non empty set
q1 is Element of U
(id U) . q1 is Element of U
((id U) . q1) \+\ q1 is set
((id U) . q1) \ q1 is set
(((id U) . q1),q1) is Element of bool ((id U) . q1)
bool ((id U) . q1) is non empty set
((id U) . q1) \ q1 is Element of bool ((id U) . q1)
q1 \ ((id U) . q1) is set
(q1,((id U) . q1)) is Element of bool q1
bool q1 is non empty set
q1 \ ((id U) . q1) is Element of bool q1
(((id U) . q1) \ q1) \/ (q1 \ ((id U) . q1)) is set
{((id U) . q1)} is non empty trivial finite 1 -element countable Element of bool U
bool U is non empty set
{q1} is non empty trivial finite 1 -element countable Element of bool U
{((id U) . q1)} \ {q1} is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of bool U
({((id U) . q1)},{q1}) is trivial finite countable Element of bool {((id U) . q1)}
bool {((id U) . q1)} is non empty finite finite-membered countable set
{((id U) . q1)} \ {q1} is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of bool {((id U) . q1)}
q2 is set
U is non empty set
q1 is Relation-like NAT -defined U -valued Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support set
q1 . 1 is set
{(q1 . 1)} is non empty trivial finite 1 -element countable set
{(q1 . 1)} \ U is trivial finite countable Element of bool {(q1 . 1)}
bool {(q1 . 1)} is non empty finite finite-membered countable set
({(q1 . 1)},U) is trivial finite countable Element of bool {(q1 . 1)}
len q1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q2 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
1 + q2 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
f is Relation-like NAT -defined U -valued Function-like finite 1 + q2 -element FinSequence-like FinSubsequence-like countable finite-support set
f . 1 is set
{(f . 1)} is non empty trivial finite 1 -element countable set
{(f . 1)} \ U is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of bool {(f . 1)}
bool {(f . 1)} is non empty finite finite-membered countable set
({(f . 1)},U) is trivial finite countable Element of bool {(f . 1)}
q11 is set
U is set
q1 is set
q2 is set
U .--> q2 is Relation-like {U} -defined Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{U} is non empty trivial finite 1 -element countable set
{U} --> q2 is Relation-like {U} -defined {q2} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{U},{q2}:]
{q2} is non empty trivial finite 1 -element countable set
[:{U},{q2}:] is Relation-like non empty finite countable set
bool [:{U},{q2}:] is non empty finite finite-membered countable set
f is set
q1 .--> f is Relation-like {q1} -defined Function-like one-to-one constant non empty trivial finite 1 -element countable finite-support set
{q1} is non empty trivial finite 1 -element countable set
{q1} --> f is Relation-like {q1} -defined {f} -valued Function-like constant non empty total quasi_total finite countable finite-support Element of bool [:{q1},{f}:]
{f} is non empty trivial finite 1 -element countable set
[:{q1},{f}:] is Relation-like non empty finite countable set
bool [:{q1},{f}:] is non empty finite finite-membered countable set
q11 is Relation-like Function-like set
q11 +* (U .--> q2) is Relation-like Function-like non empty set
(q11 +* (U .--> q2)) +* (q1 .--> f) is Relation-like Function-like non empty set
q11 +* (q1 .--> f) is Relation-like Function-like non empty set
(q11 +* (q1 .--> f)) +* (U .--> q2) is Relation-like Function-like non empty set
dom (q1 .--> f) is non empty trivial finite 1 -element countable Element of bool {q1}
bool {q1} is non empty finite finite-membered countable set
dom (U .--> q2) is non empty trivial finite 1 -element countable Element of bool {U}
bool {U} is non empty finite finite-membered countable set
(U .--> q2) +* (q1 .--> f) is Relation-like Function-like non empty finite countable finite-support set
q11 +* ((U .--> q2) +* (q1 .--> f)) is Relation-like Function-like non empty set
(q1 .--> f) +* (U .--> q2) is Relation-like Function-like non empty finite countable finite-support set
q11 +* ((q1 .--> f) +* (U .--> q2)) is Relation-like Function-like non empty set
U is set
q1 is non empty set
[:U,q1:] is Relation-like set
bool [:U,q1:] is non empty set
the Relation-like U -defined q1 -valued Function-like total quasi_total Element of bool [:U,q1:] is Relation-like U -defined q1 -valued Function-like total quasi_total Element of bool [:U,q1:]
U is set
q1 is non empty set
q2 is Relation-like U -defined q1 -valued total set
f is Relation-like q1 -defined total set
q2 * f is Relation-like U -defined set
rng q2 is Element of bool q1
bool q1 is non empty set
dom f is Element of bool q1
dom (q2 * f) is Element of bool U
bool U is non empty set
dom q2 is Element of bool U
q11 is Relation-like U -defined set
U is set
q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 ^ q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1 ^ q2) ^ f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
proj2 ((q1 ^ q2) ^ f) is finite countable set
proj2 (q1 ^ q2) is finite countable set
proj2 f is finite countable set
proj2 q1 is finite countable set
proj2 q2 is finite countable set
U is set
q1 is Relation-like set
(U,q1) is Relation-like set
(q1,U) is Element of bool (q1 \/ U)
q1 \/ U is set
bool (q1 \/ U) is non empty set
proj2 q1 is set
U \/ (proj2 q1) is set
(U,(proj2 q1)) is set
((proj2 q1),U) is Element of bool ((proj2 q1) \/ U)
(proj2 q1) \/ U is set
bool ((proj2 q1) \/ U) is non empty set
q2 is Relation-like set
U is functional set
q1 is functional set
U \/ q1 is set
q2 is set
U is set
q1 is set
U is functional set
U \/ {{}} is functional non empty set
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ {{}} : b₁ in U } is set
union { (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ {{}} : b₁ in U } is set
U is functional set
(U) is set
U \/ {{}} is functional non empty set
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ {{}} : b₁ in U } is set
union { (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ {{}} : b₁ in U } is set
F is set
p is Relation-like Function-like Element of U \/ {{}}
proj2 p is set
q11 is finite-membered set
C is finite countable Element of q11
f is finite countable set
F is finite finite-membered countable set
union F is finite countable set
the non empty set is non empty set
the non empty set * is functional non empty finite-membered FinSequence-membered FinSequenceSet of the non empty set
the Relation-like NAT -defined the non empty set -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of the non empty set * is Relation-like NAT -defined the non empty set -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of the non empty set *
{ the Relation-like NAT -defined the non empty set -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of the non empty set * } is functional non empty trivial finite finite-membered 1 -element FinSequence-membered with_common_domain countable Element of bool ( the non empty set *)
bool ( the non empty set *) is non empty set
U is functional finite finite-membered countable set
(U) is set
U \/ {{}} is functional non empty finite finite-membered countable set
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ {{}} : b₁ in U } is set
union { (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ {{}} : b₁ in U } is set
U is functional finite finite-membered FinSequence-membered countable set
(U) is finite countable set
U \/ {{}} is functional non empty finite finite-membered countable set
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ {{}} : b₁ in U } is set
union { (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ {{}} : b₁ in U } is set
U is Relation-like Function-like set
{U} is functional non empty trivial finite 1 -element with_common_domain countable set
({U}) is set
{U} \/ {{}} is functional non empty finite countable set
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of {U} \/ {{}} : b₁ in {U} } is set
union { (proj2 b₁) where b₁ is Relation-like Function-like Element of {U} \/ {{}} : b₁ in {U} } is set
proj2 U is set
({{}},{U}) is set
({U},{{}}) is functional finite countable Element of bool ({U} \/ {{}})
bool ({U} \/ {{}}) is non empty finite finite-membered countable set
p is functional finite countable Element of bool ({U} \/ {{}})
C is Relation-like Function-like Element of p
x is set
y is set
pb is Relation-like Function-like Element of {U} \/ {{}}
proj2 pb is set
x is set
proj2 C is set
y1 is Relation-like Function-like Element of {U} \/ {{}}
proj2 y1 is set
U is non empty complex set
abs U is complex real ext-real Element of REAL
q1 is ext-real set
F₁() is set
F₂() is set
{ F₃(b₁) where b₁ is Element of F₁() : b₁ in F₁() } is set
{ F₃(b₁) where b₁ is Element of F₂() : b₁ in F₁() } is set
q2 is set
f is Element of F₁()
F₃(f) is set
q11 is Element of F₂()
F₃(q11) is set
q2 is set
f is Element of F₂()
F₃(f) is set
U is functional set
(U) is set
U \/ {{}} is functional non empty set
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ {{}} : b₁ in U } is set
union { (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ {{}} : b₁ in U } is set
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of U : b₁ in U } is set
union { (proj2 b₁) where b₁ is Relation-like Function-like Element of U : b₁ in U } is set
({{}},U) is set
(U,{{}}) is functional Element of bool (U \/ {{}})
bool (U \/ {{}}) is non empty set
f is set
q11 is set
U is functional set
bool U is non empty set
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of U : b₁ in U } is set
q1 is functional Element of bool U
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of q1 : b₁ in q1 } is set
q11 is set
F is Relation-like Function-like Element of q1
proj2 F is set
U is functional set
bool U is non empty set
q1 is functional Element of bool U
(q1) is set
q1 \/ {{}} is functional non empty set
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of q1 \/ {{}} : b₁ in q1 } is set
union { (proj2 b₁) where b₁ is Relation-like Function-like Element of q1 \/ {{}} : b₁ in q1 } is set
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of q1 : b₁ in q1 } is set
union { (proj2 b₁) where b₁ is Relation-like Function-like Element of q1 : b₁ in q1 } is set
(U) is set
U \/ {{}} is functional non empty set
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ {{}} : b₁ in U } is set
union { (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ {{}} : b₁ in U } is set
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of U : b₁ in U } is set
union { (proj2 b₁) where b₁ is Relation-like Function-like Element of U : b₁ in U } is set
U is functional set
q1 is functional set
U \/ q1 is functional set
((U \/ q1)) is set
(U \/ q1) \/ {{}} is functional non empty set
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of (U \/ q1) \/ {{}} : b₁ in U \/ q1 } is set
union { (proj2 b₁) where b₁ is Relation-like Function-like Element of (U \/ q1) \/ {{}} : b₁ in U \/ q1 } is set
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ q1 : b₁ in U \/ q1 } is set
union { (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ q1 : b₁ in U \/ q1 } is set
(U) is set
U \/ {{}} is functional non empty set
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ {{}} : b₁ in U } is set
union { (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ {{}} : b₁ in U } is set
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of U : b₁ in U } is set
union { (proj2 b₁) where b₁ is Relation-like Function-like Element of U : b₁ in U } is set
(q1) is set
q1 \/ {{}} is functional non empty set
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of q1 \/ {{}} : b₁ in q1 } is set
union { (proj2 b₁) where b₁ is Relation-like Function-like Element of q1 \/ {{}} : b₁ in q1 } is set
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of q1 : b₁ in q1 } is set
union { (proj2 b₁) where b₁ is Relation-like Function-like Element of q1 : b₁ in q1 } is set
(U) \/ (q1) is set
(q1,U) is set
(U,q1) is functional Element of bool (U \/ q1)
bool (U \/ q1) is non empty set
(U,q1) is set
(q1,U) is functional Element of bool (q1 \/ U)
q1 \/ U is functional set
bool (q1 \/ U) is non empty set
bool { (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ q1 : b₁ in U \/ q1 } is non empty set
F is Element of bool { (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ q1 : b₁ in U \/ q1 }
p is Element of bool { (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ q1 : b₁ in U \/ q1 }
F \/ p is Element of bool { (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ q1 : b₁ in U \/ q1 }
C is set
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ q1 : b₁ in U \/ q1 } \ { (proj2 b₁) where b₁ is Relation-like Function-like Element of q1 : b₁ in q1 } is Element of bool { (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ q1 : b₁ in U \/ q1 }
( { (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ q1 : b₁ in U \/ q1 } , { (proj2 b₁) where b₁ is Relation-like Function-like Element of q1 : b₁ in q1 } ) is Element of bool { (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ q1 : b₁ in U \/ q1 }
y1 is Relation-like Function-like Element of U \/ q1
proj2 y1 is set
({{}},U) is set
(U,{{}}) is functional Element of bool (U \/ {{}})
bool (U \/ {{}}) is non empty set
( { (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ q1 : b₁ in U \/ q1 } \ { (proj2 b₁) where b₁ is Relation-like Function-like Element of q1 : b₁ in q1 } ) \/ { (proj2 b₁) where b₁ is Relation-like Function-like Element of q1 : b₁ in q1 } is set
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of U : b₁ in U } \/ { (proj2 b₁) where b₁ is Relation-like Function-like Element of q1 : b₁ in q1 } is set
(p, { (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ q1 : b₁ in U \/ q1 } ) is set
( { (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ q1 : b₁ in U \/ q1 } ,p) is Element of bool ( { (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ q1 : b₁ in U \/ q1 } \/ p)
{ (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ q1 : b₁ in U \/ q1 } \/ p is set
bool ( { (proj2 b₁) where b₁ is Relation-like Function-like Element of U \/ q1 : b₁ in U \/ q1 } \/ p) is non empty set
U is set
bool U is non empty Element of bool (bool U)
bool U is non empty set
bool (bool U) is non empty set
bool (bool U) is non empty set
q1 is Element of bool (bool U)
union q1 is Element of bool U
(union q1) \ U is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of bool U
((union q1),U) is Element of bool (union q1)
bool (union q1) is non empty set
(union q1) \ U is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of bool (union q1)
q2 is set
U is set
q1 is set
U \ q1 is Element of bool U
bool U is non empty set
(U,q1) is Element of bool U
U /\ q1 is set
(U,q1) is Element of bool U
(U,q1) is Element of bool q1
bool q1 is non empty set
(U \ q1) \/ (U /\ q1) is set
q2 is Element of bool U
U \ q2 is Element of bool U
(U,q2) is Element of bool U
q2 \/ (U \ q2) is Element of bool U
q2 \/ (U /\ q1) is set
q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
U is set
q2 -tuples_on U is functional finite-membered FinSequence-membered FinSequenceSet of U
f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q1 is set
f -tuples_on q1 is functional finite-membered FinSequence-membered FinSequenceSet of q1
U is non empty set
q1 is set
q2 is set
U is Relation-like Function-like set
proj1 U is set
q1 is Relation-like Function-like set
proj1 q1 is set
q2 is set
U . q2 is set
q1 . q2 is set
f is set
q11 is set
U . q11 is set
q1 . q11 is set
q2 is set
U . q2 is set
q1 . q2 is set
f is set
q11 is set
U . q11 is set
q1 . q11 is set
F is set
U . F is set
q1 . F is set
U is non empty set
U * is functional non empty finite-membered FinSequence-membered FinSequenceSet of U
(U *) \ {{}} is functional non empty finite-membered FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
((U *),{{}}) is functional finite-membered FinSequence-membered Element of bool (U *)
(U *) * is functional non empty finite-membered FinSequence-membered FinSequenceSet of U *
((U *),((U *) \ {{}})) is functional non empty finite-membered FinSequence-membered Element of bool ((U *) *)
bool ((U *) *) is non empty set
q2 is Relation-like NAT -defined (U *) \ {{}} -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support Element of ((U *),((U *) \ {{}}))
len q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
f + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
1 + f is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
q11 is Relation-like NAT -defined (U *) \ {{}} -valued Function-like finite 1 + f -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
q11 . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
{(q11 . 1)} is functional non empty trivial finite finite-membered 1 -element with_common_domain countable set
{(q11 . 1)} \ ((U *) \ {{}}) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable FinSequence-yielding finite-support Element of bool {(q11 . 1)}
bool {(q11 . 1)} is non empty finite finite-membered countable set
({(q11 . 1)},((U *) \ {{}})) is functional trivial finite finite-membered with_common_domain countable Element of bool {(q11 . 1)}
q2 . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
U * is functional non empty finite-membered FinSequence-membered FinSequenceSet of U
{U} is functional non empty trivial finite finite-membered 1 -element empty-membered with_common_domain countable set
q1 is Relation-like non-empty empty-yielding NAT -defined U -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of U *
U is set
q1 is non empty set
(q1) is Relation-like (q1 *) * -defined q1 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:((q1 *) *),(q1 *):]
q1 * is functional non empty finite-membered FinSequence-membered FinSequenceSet of q1
(q1 *) * is functional non empty finite-membered FinSequence-membered FinSequenceSet of q1 *
[:((q1 *) *),(q1 *):] is Relation-like non empty set
bool [:((q1 *) *),(q1 *):] is non empty set
q1 -concatenation is Relation-like [:(q1 *),(q1 *):] -defined q1 * -valued Function-like non empty total quasi_total associative Function-yielding V159() FinSequence-yielding Element of bool [:[:(q1 *),(q1 *):],(q1 *):]
[:(q1 *),(q1 *):] is Relation-like non empty set
[:[:(q1 *),(q1 *):],(q1 *):] is Relation-like non empty set
bool [:[:(q1 *),(q1 *):],(q1 *):] is non empty set
((q1 *),(q1 -concatenation)) is Relation-like ((q1 *) *) \ {{}} -defined q1 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(((q1 *) *) \ {{}}),(q1 *):]
((q1 *) *) \ {{}} is functional non empty finite-membered FinSequence-membered Element of bool ((q1 *) *)
bool ((q1 *) *) is non empty set
(((q1 *) *),{{}}) is functional finite-membered FinSequence-membered Element of bool ((q1 *) *)
[:(((q1 *) *) \ {{}}),(q1 *):] is Relation-like non empty set
bool [:(((q1 *) *) \ {{}}),(q1 *):] is non empty set
({} .--> {}) +* ((q1 *),(q1 -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
(q1) . U is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q2 is non empty set
(q2) is Relation-like (q2 *) * -defined q2 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:((q2 *) *),(q2 *):]
q2 * is functional non empty finite-membered FinSequence-membered FinSequenceSet of q2
(q2 *) * is functional non empty finite-membered FinSequence-membered FinSequenceSet of q2 *
[:((q2 *) *),(q2 *):] is Relation-like non empty set
bool [:((q2 *) *),(q2 *):] is non empty set
q2 -concatenation is Relation-like [:(q2 *),(q2 *):] -defined q2 * -valued Function-like non empty total quasi_total associative Function-yielding V159() FinSequence-yielding Element of bool [:[:(q2 *),(q2 *):],(q2 *):]
[:(q2 *),(q2 *):] is Relation-like non empty set
[:[:(q2 *),(q2 *):],(q2 *):] is Relation-like non empty set
bool [:[:(q2 *),(q2 *):],(q2 *):] is non empty set
((q2 *),(q2 -concatenation)) is Relation-like ((q2 *) *) \ {{}} -defined q2 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(((q2 *) *) \ {{}}),(q2 *):]
((q2 *) *) \ {{}} is functional non empty finite-membered FinSequence-membered Element of bool ((q2 *) *)
bool ((q2 *) *) is non empty set
(((q2 *) *),{{}}) is functional finite-membered FinSequence-membered Element of bool ((q2 *) *)
[:(((q2 *) *) \ {{}}),(q2 *):] is Relation-like non empty set
bool [:(((q2 *) *) \ {{}}),(q2 *):] is non empty set
({} .--> {}) +* ((q2 *),(q2 -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
(q2) . U is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1) . f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
{} + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
F is non empty set
(F) is Relation-like (F *) * -defined F * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:((F *) *),(F *):]
F * is functional non empty finite-membered FinSequence-membered FinSequenceSet of F
(F *) * is functional non empty finite-membered FinSequence-membered FinSequenceSet of F *
[:((F *) *),(F *):] is Relation-like non empty set
bool [:((F *) *),(F *):] is non empty set
F -concatenation is Relation-like [:(F *),(F *):] -defined F * -valued Function-like non empty total quasi_total associative Function-yielding V159() FinSequence-yielding Element of bool [:[:(F *),(F *):],(F *):]
[:(F *),(F *):] is Relation-like non empty set
[:[:(F *),(F *):],(F *):] is Relation-like non empty set
bool [:[:(F *),(F *):],(F *):] is non empty set
((F *),(F -concatenation)) is Relation-like ((F *) *) \ {{}} -defined F * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(((F *) *) \ {{}}),(F *):]
((F *) *) \ {{}} is functional non empty finite-membered FinSequence-membered Element of bool ((F *) *)
bool ((F *) *) is non empty set
(((F *) *),{{}}) is functional finite-membered FinSequence-membered Element of bool ((F *) *)
[:(((F *) *) \ {{}}),(F *):] is Relation-like non empty set
bool [:(((F *) *) \ {{}}),(F *):] is non empty set
({} .--> {}) +* ((F *),(F -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
p is non empty set
(p) is Relation-like (p *) * -defined p * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:((p *) *),(p *):]
p * is functional non empty finite-membered FinSequence-membered FinSequenceSet of p
(p *) * is functional non empty finite-membered FinSequence-membered FinSequenceSet of p *
[:((p *) *),(p *):] is Relation-like non empty set
bool [:((p *) *),(p *):] is non empty set
p -concatenation is Relation-like [:(p *),(p *):] -defined p * -valued Function-like non empty total quasi_total associative Function-yielding V159() FinSequence-yielding Element of bool [:[:(p *),(p *):],(p *):]
[:(p *),(p *):] is Relation-like non empty set
[:[:(p *),(p *):],(p *):] is Relation-like non empty set
bool [:[:(p *),(p *):],(p *):] is non empty set
((p *),(p -concatenation)) is Relation-like ((p *) *) \ {{}} -defined p * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(((p *) *) \ {{}}),(p *):]
((p *) *) \ {{}} is functional non empty finite-membered FinSequence-membered Element of bool ((p *) *)
bool ((p *) *) is non empty set
(((p *) *),{{}}) is functional finite-membered FinSequence-membered Element of bool ((p *) *)
[:(((p *) *) \ {{}}),(p *):] is Relation-like non empty set
bool [:(((p *) *) \ {{}}),(p *):] is non empty set
({} .--> {}) +* ((p *),(p -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
C is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(F) . C is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(p) . C is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
dom (F) is functional non empty finite-membered FinSequence-membered Element of bool ((F *) *)
dom (p) is functional non empty finite-membered FinSequence-membered Element of bool ((p *) *)
{} /\ F is Relation-like finite countable (F) set
({},F) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial non proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of bool {}
bool {} is non empty finite finite-membered countable set
({},F) is Element of bool F
bool F is non empty set
{} /\ p is Relation-like finite countable (p) set
({},p) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial non proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of bool {}
({},p) is Element of bool p
bool p is non empty set
bool (p *) is non empty set
pb is Element of bool p
(p,pb) is functional non empty finite-membered FinSequence-membered Element of bool (p *)
q1 is functional non empty finite-membered FinSequence-membered Element of bool (p *)
bool (F *) is non empty set
y is Element of bool F
(F,y) is functional non empty finite-membered FinSequence-membered Element of bool (F *)
p2 is functional non empty finite-membered FinSequence-membered Element of bool (F *)
1 + {} is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
x2 is Relation-like NAT -defined Function-like non empty finite 1 + {} -element FinSequence-like FinSubsequence-like countable finite-support set
len x2 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
C . 1 is set
<*(C . 1)*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support set
[1,(C . 1)] is non empty V15() set
{[1,(C . 1)]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
{} ^ <*(C . 1)*> is Relation-like NAT -defined Function-like non empty finite {} + 1 -element {} + 1 -element FinSequence-like FinSubsequence-like countable finite-support set
{} + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
({},<*(C . 1)*>) is Relation-like NAT -defined Seg (1 + {}) -defined {} \/ (proj2 <*(C . 1)*>) -valued Function-like finite len <*(C . 1)*> -element FinSequence-like FinSubsequence-like countable finite-support set
Seg (1 + {}) is non empty finite 1 + {} -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= 1 + {} ) } is set
proj2 <*(C . 1)*> is non empty trivial finite 1 -element countable set
{} \/ (proj2 <*(C . 1)*>) is non empty finite countable set
len <*(C . 1)*> is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
(<*(C . 1)*>,{}) is Relation-like NAT -defined finite countable Element of bool (<*(C . 1)*> \/ {})
<*(C . 1)*> \/ {} is Relation-like NAT -defined non empty finite countable set
bool (<*(C . 1)*> \/ {}) is non empty finite finite-membered countable set
<*(C . 1)*> ^ {} is Relation-like NAT -defined Function-like non empty finite 1 + {} -element FinSequence-like FinSubsequence-like countable finite-support set
q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of p2
q2 ^ <*(C . 1)*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support set
<*q2*> is Relation-like NAT -defined p2 -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support FinSequence of p2
[1,q2] is non empty V15() set
{[1,q2]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
q2 ^ <*q2*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support set
(F) . q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((F) . q2) ^ q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
{} ^ {} is Relation-like empty-yielding NAT -defined {{}} -valued Function-like finite {} + {} -element FinSequence-like FinSubsequence-like Function-yielding V159() Cardinal-yielding countable FinSequence-yielding finite-support set
{} + {} is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
({},{}) is Relation-like non-empty empty-yielding NAT -defined Seg ({} + {}) -defined {} -valued {{}} -valued {} \/ (proj2 {}) -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element len {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
Seg ({} + {}) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} + {} -element {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= {} + {} ) } is set
proj2 {} is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like with_non-empty_elements empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
{} \/ (proj2 {}) is Relation-like empty-yielding NAT -defined {{}} -valued functional finite finite-membered countable set
len {} is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of NAT
({},{}) is Relation-like empty-yielding NAT -defined {{}} -valued functional finite finite-membered countable Element of bool ({} \/ {})
{} \/ {} is Relation-like empty-yielding NAT -defined {{}} -valued functional finite finite-membered countable set
bool ({} \/ {}) is non empty finite finite-membered countable set
p1 is Relation-like NAT -defined F * -valued Function-like non empty finite FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
p1 . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
{(p1 . 1)} is functional non empty trivial finite finite-membered 1 -element with_common_domain countable set
{(p1 . 1)} \ (F *) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable FinSequence-yielding finite-support Element of bool {(p1 . 1)}
bool {(p1 . 1)} is non empty finite finite-membered countable set
({(p1 . 1)},(F *)) is functional trivial finite finite-membered with_common_domain countable Element of bool {(p1 . 1)}
x2 . 1 is set
p2 is Relation-like NAT -defined F -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of F *
((F) . q2) ^ p2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
{} ^ p2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
({},p2) is Relation-like NAT -defined {} \/ (proj2 p2) -valued Function-like finite len p2 -element FinSequence-like FinSubsequence-like countable finite-support set
proj2 p2 is finite countable set
{} \/ (proj2 p2) is finite countable set
len p2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
(p2,{}) is Relation-like NAT -defined finite countable Element of bool (p2 \/ {})
p2 \/ {} is Relation-like NAT -defined finite countable set
bool (p2 \/ {}) is non empty finite finite-membered countable set
p2 ^ {} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
p1 is Relation-like NAT -defined F * -valued Function-like non empty finite FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
p1 . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
{(p1 . 1)} is functional non empty trivial finite finite-membered 1 -element with_common_domain countable set
{(p1 . 1)} \ (F *) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable FinSequence-yielding finite-support Element of bool {(p1 . 1)}
bool {(p1 . 1)} is non empty finite finite-membered countable set
({(p1 . 1)},(F *)) is functional trivial finite finite-membered with_common_domain countable Element of bool {(p1 . 1)}
p2 is Relation-like NAT -defined p * -valued Function-like non empty finite FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
p2 . 1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
{(p2 . 1)} is functional non empty trivial finite finite-membered 1 -element with_common_domain countable set
{(p2 . 1)} \ (p *) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable FinSequence-yielding finite-support Element of bool {(p2 . 1)}
bool {(p2 . 1)} is non empty finite finite-membered countable set
({(p2 . 1)},(p *)) is functional trivial finite finite-membered with_common_domain countable Element of bool {(p2 . 1)}
u1 is Relation-like NAT -defined F -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of F *
((F) . q2) ^ u1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
{} ^ u1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
({},u1) is Relation-like NAT -defined {} \/ (proj2 u1) -valued Function-like finite len u1 -element FinSequence-like FinSubsequence-like countable finite-support set
proj2 u1 is finite countable set
{} \/ (proj2 u1) is finite countable set
len u1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
(u1,{}) is Relation-like NAT -defined finite countable Element of bool (u1 \/ {})
u1 \/ {} is Relation-like NAT -defined finite countable set
bool (u1 \/ {}) is non empty finite finite-membered countable set
u1 ^ {} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
x1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of q1
(p) . x1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
u2 is Relation-like NAT -defined p -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of p *
((p) . x1) ^ u2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
F is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
F + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
(F + 1) + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
p is non empty set
(p) is Relation-like (p *) * -defined p * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:((p *) *),(p *):]
p * is functional non empty finite-membered FinSequence-membered FinSequenceSet of p
(p *) * is functional non empty finite-membered FinSequence-membered FinSequenceSet of p *
[:((p *) *),(p *):] is Relation-like non empty set
bool [:((p *) *),(p *):] is non empty set
p -concatenation is Relation-like [:(p *),(p *):] -defined p * -valued Function-like non empty total quasi_total associative Function-yielding V159() FinSequence-yielding Element of bool [:[:(p *),(p *):],(p *):]
[:(p *),(p *):] is Relation-like non empty set
[:[:(p *),(p *):],(p *):] is Relation-like non empty set
bool [:[:(p *),(p *):],(p *):] is non empty set
((p *),(p -concatenation)) is Relation-like ((p *) *) \ {{}} -defined p * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(((p *) *) \ {{}}),(p *):]
((p *) *) \ {{}} is functional non empty finite-membered FinSequence-membered Element of bool ((p *) *)
bool ((p *) *) is non empty set
(((p *) *),{{}}) is functional finite-membered FinSequence-membered Element of bool ((p *) *)
[:(((p *) *) \ {{}}),(p *):] is Relation-like non empty set
bool [:(((p *) *) \ {{}}),(p *):] is non empty set
({} .--> {}) +* ((p *),(p -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
C is non empty set
(C) is Relation-like (C *) * -defined C * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:((C *) *),(C *):]
C * is functional non empty finite-membered FinSequence-membered FinSequenceSet of C
(C *) * is functional non empty finite-membered FinSequence-membered FinSequenceSet of C *
[:((C *) *),(C *):] is Relation-like non empty set
bool [:((C *) *),(C *):] is non empty set
C -concatenation is Relation-like [:(C *),(C *):] -defined C * -valued Function-like non empty total quasi_total associative Function-yielding V159() FinSequence-yielding Element of bool [:[:(C *),(C *):],(C *):]
[:(C *),(C *):] is Relation-like non empty set
[:[:(C *),(C *):],(C *):] is Relation-like non empty set
bool [:[:(C *),(C *):],(C *):] is non empty set
((C *),(C -concatenation)) is Relation-like ((C *) *) \ {{}} -defined C * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(((C *) *) \ {{}}),(C *):]
((C *) *) \ {{}} is functional non empty finite-membered FinSequence-membered Element of bool ((C *) *)
bool ((C *) *) is non empty set
(((C *) *),{{}}) is functional finite-membered FinSequence-membered Element of bool ((C *) *)
[:(((C *) *) \ {{}}),(C *):] is Relation-like non empty set
bool [:(((C *) *) \ {{}}),(C *):] is non empty set
({} .--> {}) +* ((C *),(C -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
dom (p) is functional non empty finite-membered FinSequence-membered Element of bool ((p *) *)
dom (C) is functional non empty finite-membered FinSequence-membered Element of bool ((C *) *)
y is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(p) . y is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(C) . y is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
{} /\ p is Relation-like finite countable (p) set
({},p) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial non proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of bool {}
bool {} is non empty finite finite-membered countable set
({},p) is Element of bool p
bool p is non empty set
bool (p *) is non empty set
pb is Element of bool p
(p,pb) is functional non empty finite-membered FinSequence-membered Element of bool (p *)
((F + 1) + 1) + {} is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
q1 is functional non empty finite-membered FinSequence-membered Element of bool (p *)
x1 is Relation-like NAT -defined {} * -valued Function-like non empty finite ((F + 1) + 1) + {} -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
Seg (F + 1) is non empty finite F + 1 -element F + 1 -element countable Element of bool NAT
F + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= F + 1 ) } is set
x1 | (Seg (F + 1)) is Relation-like NAT -defined Seg (F + 1) -defined NAT -defined {} * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
x1 . ((F + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
{(x1 . ((F + 1) + 1))} is functional non empty trivial finite finite-membered 1 -element with_common_domain countable set
{(x1 . ((F + 1) + 1))} \ ({} *) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable FinSequence-yielding finite-support Element of bool {(x1 . ((F + 1) + 1))}
bool {(x1 . ((F + 1) + 1))} is non empty finite finite-membered countable set
({(x1 . ((F + 1) + 1))},({} *)) is functional trivial finite finite-membered with_common_domain countable Element of bool {(x1 . ((F + 1) + 1))}
p2 is Relation-like NAT -defined q1 -valued Function-like non empty finite F + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of q1
<*q2*> is Relation-like NAT -defined q1 -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support FinSequence of q1
[1,q2] is non empty V15() set
{[1,q2]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
p2 ^ <*q2*> is Relation-like NAT -defined q1 -valued Function-like non empty finite (F + 1) + 1 -element (F + 1) + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
(F + 1) + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
x1 \+\ (p2 ^ <*q2*>) is Relation-like finite countable set
x1 \ (p2 ^ <*q2*>) is Relation-like NAT -defined {} * -valued finite countable set
(x1,(p2 ^ <*q2*>)) is Relation-like NAT -defined {} * -valued Function-like finite Function-yielding V159() countable FinSequence-yielding finite-support Element of bool x1
bool x1 is non empty finite finite-membered countable set
x1 \ (p2 ^ <*q2*>) is Relation-like NAT -defined {} * -valued Function-like finite Function-yielding V159() countable FinSequence-yielding finite-support Element of bool x1
(p2 ^ <*q2*>) \ x1 is Relation-like NAT -defined q1 -valued finite countable set
((p2 ^ <*q2*>),x1) is Relation-like NAT -defined q1 -valued Function-like finite Function-yielding V159() countable FinSequence-yielding finite-support Element of bool (p2 ^ <*q2*>)
bool (p2 ^ <*q2*>) is non empty finite finite-membered countable set
(p2 ^ <*q2*>) \ x1 is Relation-like NAT -defined q1 -valued Function-like finite Function-yielding V159() countable FinSequence-yielding finite-support Element of bool (p2 ^ <*q2*>)
(x1 \ (p2 ^ <*q2*>)) \/ ((p2 ^ <*q2*>) \ x1) is Relation-like NAT -defined finite countable set
(p) . x1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(p) . p2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((p) . p2) ^ q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((p) . p2) ^ {} is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
({},((p) . p2)) is Relation-like NAT -defined {} \/ (proj2 ((p) . p2)) -valued Function-like finite len ((p) . p2) -element FinSequence-like FinSubsequence-like countable finite-support set
proj2 ((p) . p2) is finite countable set
{} \/ (proj2 ((p) . p2)) is finite countable set
len ((p) . p2) is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
(((p) . p2),{}) is Relation-like NAT -defined finite countable Element of bool (((p) . p2) \/ {})
((p) . p2) \/ {} is Relation-like NAT -defined finite countable set
bool (((p) . p2) \/ {}) is non empty finite finite-membered countable set
{} ^ ((p) . p2) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((F + 1) + 1) + {} is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
pb is Relation-like NAT -defined p * -valued Function-like non empty finite ((F + 1) + 1) + {} -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
Seg (F + 1) is non empty finite F + 1 -element F + 1 -element countable Element of bool NAT
F + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= F + 1 ) } is set
pb | (Seg (F + 1)) is Relation-like NAT -defined Seg (F + 1) -defined NAT -defined p * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
pb . ((F + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
{(pb . ((F + 1) + 1))} is functional non empty trivial finite finite-membered 1 -element with_common_domain countable set
{(pb . ((F + 1) + 1))} \ (p *) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable FinSequence-yielding finite-support Element of bool {(pb . ((F + 1) + 1))}
bool {(pb . ((F + 1) + 1))} is non empty finite finite-membered countable set
({(pb . ((F + 1) + 1))},(p *)) is functional trivial finite finite-membered with_common_domain countable Element of bool {(pb . ((F + 1) + 1))}
q1 is Relation-like NAT -defined p * -valued Function-like non empty finite F + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
x1 is Relation-like NAT -defined p -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of p *
<*x1*> is Relation-like NAT -defined p * -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support FinSequence of p *
[1,x1] is non empty V15() set
{[1,x1]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
q1 ^ <*x1*> is Relation-like NAT -defined p * -valued Function-like non empty finite (F + 1) + 1 -element (F + 1) + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
(F + 1) + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
pb \+\ (q1 ^ <*x1*>) is Relation-like finite countable set
pb \ (q1 ^ <*x1*>) is Relation-like NAT -defined p * -valued finite countable set
(pb,(q1 ^ <*x1*>)) is Relation-like NAT -defined p * -valued Function-like finite Function-yielding V159() countable FinSequence-yielding finite-support Element of bool pb
bool pb is non empty finite finite-membered countable set
pb \ (q1 ^ <*x1*>) is Relation-like NAT -defined p * -valued Function-like finite Function-yielding V159() countable FinSequence-yielding finite-support Element of bool pb
(q1 ^ <*x1*>) \ pb is Relation-like NAT -defined p * -valued finite countable set
((q1 ^ <*x1*>),pb) is Relation-like NAT -defined p * -valued Function-like finite Function-yielding V159() countable FinSequence-yielding finite-support Element of bool (q1 ^ <*x1*>)
bool (q1 ^ <*x1*>) is non empty finite finite-membered countable set
(q1 ^ <*x1*>) \ pb is Relation-like NAT -defined p * -valued Function-like finite Function-yielding V159() countable FinSequence-yielding finite-support Element of bool (q1 ^ <*x1*>)
(pb \ (q1 ^ <*x1*>)) \/ ((q1 ^ <*x1*>) \ pb) is Relation-like NAT -defined p * -valued finite countable set
(p) . q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((p) . q1) ^ x1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q11 is Relation-like Function-like finite countable finite-support Element of {{}}
<*q11*> is Relation-like empty-yielding NAT -defined {{}} -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable finite-support FinSequence of {{}}
[1,q11] is non empty V15() set
{[1,q11]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
p2 is Relation-like empty-yielding NAT -defined {{}} -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V159() countable finite-support set
q2 is Relation-like empty-yielding NAT -defined {{}} -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V159() countable finite-support set
p2 ^ q2 is Relation-like empty-yielding NAT -defined {{}} -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V159() countable finite-support set
((F + 1) + 1) + {} is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
pb is Relation-like NAT -defined p * -valued Function-like non empty finite ((F + 1) + 1) + {} -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
Seg (F + 1) is non empty finite F + 1 -element F + 1 -element countable Element of bool NAT
F + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= F + 1 ) } is set
pb | (Seg (F + 1)) is Relation-like NAT -defined Seg (F + 1) -defined NAT -defined p * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
pb . ((F + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
{(pb . ((F + 1) + 1))} is functional non empty trivial finite finite-membered 1 -element with_common_domain countable set
{(pb . ((F + 1) + 1))} \ (p *) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable FinSequence-yielding finite-support Element of bool {(pb . ((F + 1) + 1))}
bool {(pb . ((F + 1) + 1))} is non empty finite finite-membered countable set
({(pb . ((F + 1) + 1))},(p *)) is functional trivial finite finite-membered with_common_domain countable Element of bool {(pb . ((F + 1) + 1))}
p2 is Relation-like NAT -defined C * -valued Function-like non empty finite ((F + 1) + 1) + {} -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
p2 | (Seg (F + 1)) is Relation-like NAT -defined Seg (F + 1) -defined NAT -defined C * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
p2 . ((F + 1) + 1) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
{(p2 . ((F + 1) + 1))} is functional non empty trivial finite finite-membered 1 -element with_common_domain countable set
{(p2 . ((F + 1) + 1))} \ (C *) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding with_common_domain countable FinSequence-yielding finite-support Element of bool {(p2 . ((F + 1) + 1))}
bool {(p2 . ((F + 1) + 1))} is non empty finite finite-membered countable set
({(p2 . ((F + 1) + 1))},(C *)) is functional trivial finite finite-membered with_common_domain countable Element of bool {(p2 . ((F + 1) + 1))}
q1 is Relation-like NAT -defined p * -valued Function-like non empty finite F + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
x1 is Relation-like NAT -defined p -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of p *
<*x1*> is Relation-like NAT -defined p * -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support FinSequence of p *
[1,x1] is non empty V15() set
{[1,x1]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
q1 ^ <*x1*> is Relation-like NAT -defined p * -valued Function-like non empty finite (F + 1) + 1 -element (F + 1) + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
(F + 1) + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
pb \+\ (q1 ^ <*x1*>) is Relation-like finite countable set
pb \ (q1 ^ <*x1*>) is Relation-like NAT -defined p * -valued finite countable set
(pb,(q1 ^ <*x1*>)) is Relation-like NAT -defined p * -valued Function-like finite Function-yielding V159() countable FinSequence-yielding finite-support Element of bool pb
bool pb is non empty finite finite-membered countable set
pb \ (q1 ^ <*x1*>) is Relation-like NAT -defined p * -valued Function-like finite Function-yielding V159() countable FinSequence-yielding finite-support Element of bool pb
(q1 ^ <*x1*>) \ pb is Relation-like NAT -defined p * -valued finite countable set
((q1 ^ <*x1*>),pb) is Relation-like NAT -defined p * -valued Function-like finite Function-yielding V159() countable FinSequence-yielding finite-support Element of bool (q1 ^ <*x1*>)
bool (q1 ^ <*x1*>) is non empty finite finite-membered countable set
(q1 ^ <*x1*>) \ pb is Relation-like NAT -defined p * -valued Function-like finite Function-yielding V159() countable FinSequence-yielding finite-support Element of bool (q1 ^ <*x1*>)
(pb \ (q1 ^ <*x1*>)) \/ ((q1 ^ <*x1*>) \ pb) is Relation-like NAT -defined p * -valued finite countable set
q2 is Relation-like NAT -defined C * -valued Function-like non empty finite F + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
x2 is Relation-like NAT -defined C -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of C *
<*x2*> is Relation-like NAT -defined C * -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support FinSequence of C *
[1,x2] is non empty V15() set
{[1,x2]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
q2 ^ <*x2*> is Relation-like NAT -defined C * -valued Function-like non empty finite (F + 1) + 1 -element (F + 1) + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
p2 \+\ (q2 ^ <*x2*>) is Relation-like finite countable set
p2 \ (q2 ^ <*x2*>) is Relation-like NAT -defined C * -valued finite countable set
(p2,(q2 ^ <*x2*>)) is Relation-like NAT -defined C * -valued Function-like finite Function-yielding V159() countable FinSequence-yielding finite-support Element of bool p2
bool p2 is non empty finite finite-membered countable set
p2 \ (q2 ^ <*x2*>) is Relation-like NAT -defined C * -valued Function-like finite Function-yielding V159() countable FinSequence-yielding finite-support Element of bool p2
(q2 ^ <*x2*>) \ p2 is Relation-like NAT -defined C * -valued finite countable set
((q2 ^ <*x2*>),p2) is Relation-like NAT -defined C * -valued Function-like finite Function-yielding V159() countable FinSequence-yielding finite-support Element of bool (q2 ^ <*x2*>)
bool (q2 ^ <*x2*>) is non empty finite finite-membered countable set
(q2 ^ <*x2*>) \ p2 is Relation-like NAT -defined C * -valued Function-like finite Function-yielding V159() countable FinSequence-yielding finite-support Element of bool (q2 ^ <*x2*>)
(p2 \ (q2 ^ <*x2*>)) \/ ((q2 ^ <*x2*>) \ p2) is Relation-like NAT -defined C * -valued finite countable set
(p) . pb is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(p) . q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((p) . q1) ^ x1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(C) . p2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(C) . q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((C) . q2) ^ x2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
dom (q1) is functional non empty finite-membered FinSequence-membered Element of bool ((q1 *) *)
dom (q2) is functional non empty finite-membered FinSequence-membered Element of bool ((q2 *) *)
C is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support set
len C is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
y1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
y1 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
x is Relation-like NAT -defined Function-like non empty finite y1 + 1 -element FinSequence-like FinSubsequence-like countable finite-support set
(q1) . x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q2) . x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
len f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
C is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
C + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
y1 is Relation-like NAT -defined Function-like non empty finite C + 1 -element FinSequence-like FinSubsequence-like countable finite-support set
(q1) . y1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
len f is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
C is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
C + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
y1 is Relation-like NAT -defined Function-like non empty finite C + 1 -element FinSequence-like FinSubsequence-like countable finite-support set
U is non empty set
(U) is Relation-like (U *) * -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:((U *) *),(U *):]
U * is functional non empty finite-membered FinSequence-membered FinSequenceSet of U
(U *) * is functional non empty finite-membered FinSequence-membered FinSequenceSet of U *
[:((U *) *),(U *):] is Relation-like non empty set
bool [:((U *) *),(U *):] is non empty set
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total associative Function-yielding V159() FinSequence-yielding Element of bool [:[:(U *),(U *):],(U *):]
[:(U *),(U *):] is Relation-like non empty set
[:[:(U *),(U *):],(U *):] is Relation-like non empty set
bool [:[:(U *),(U *):],(U *):] is non empty set
((U *),(U -concatenation)) is Relation-like ((U *) *) \ {{}} -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(((U *) *) \ {{}}),(U *):]
((U *) *) \ {{}} is functional non empty finite-membered FinSequence-membered Element of bool ((U *) *)
bool ((U *) *) is non empty set
(((U *) *),{{}}) is functional finite-membered FinSequence-membered Element of bool ((U *) *)
[:(((U *) *) \ {{}}),(U *):] is Relation-like non empty set
bool [:(((U *) *) \ {{}}),(U *):] is non empty set
({} .--> {}) +* ((U *),(U -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
q1 is set
(U) . q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U is set
U is with_non-empty_elements set
q1 is Relation-like U -valued set
rng q1 is Element of bool U
bool U is non empty set
q2 is non empty set
the Element of q2 is Element of q2
U is set
U \ {{}} is Element of bool U
bool U is non empty set
(U,{{}}) is Element of bool U
U is with_non-empty_elements set
bool U is non empty set
q1 is Element of bool U
U is non empty set
U * is functional non empty finite-membered FinSequence-membered FinSequenceSet of U
len (U *) is non empty epsilon-transitive epsilon-connected ordinal cardinal set
q1 is set
U is non empty set
U * is functional non empty non trivial non finite finite-membered FinSequence-membered non empty-membered FinSequenceSet of U
U is non empty non empty-membered set
bool U is non empty set
the non empty Element of U is non empty Element of U
{ the non empty Element of U} is non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable Element of bool U
U is set
q1 is non empty set
q1 * is functional non empty non trivial non finite finite-membered FinSequence-membered non empty-membered FinSequenceSet of q1
(q1) is Relation-like (q1 *) * -defined q1 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:((q1 *) *),(q1 *):]
(q1 *) * is functional non empty non trivial non finite finite-membered FinSequence-membered non empty-membered FinSequenceSet of q1 *
[:((q1 *) *),(q1 *):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:((q1 *) *),(q1 *):] is non empty non trivial non finite non empty-membered set
q1 -concatenation is Relation-like [:(q1 *),(q1 *):] -defined q1 * -valued Function-like non empty total quasi_total associative Function-yielding V159() FinSequence-yielding Element of bool [:[:(q1 *),(q1 *):],(q1 *):]
[:(q1 *),(q1 *):] is Relation-like non empty non trivial non finite non empty-membered set
[:[:(q1 *),(q1 *):],(q1 *):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:[:(q1 *),(q1 *):],(q1 *):] is non empty non trivial non finite non empty-membered set
((q1 *),(q1 -concatenation)) is Relation-like ((q1 *) *) \ {{}} -defined q1 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(((q1 *) *) \ {{}}),(q1 *):]
((q1 *) *) \ {{}} is functional non empty finite-membered FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((q1 *) *)
bool ((q1 *) *) is non empty non trivial non finite non empty-membered set
(((q1 *) *),{{}}) is functional finite-membered FinSequence-membered Element of bool ((q1 *) *)
[:(((q1 *) *) \ {{}}),(q1 *):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:(((q1 *) *) \ {{}}),(q1 *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* ((q1 *),(q1 -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1) . q2 is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
f is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support set
proj2 f is non empty finite countable set
bool (q1 *) is non empty non trivial non finite non empty-membered set
q11 is functional non empty finite-membered FinSequence-membered with_non-empty_elements non empty-membered Element of bool (q1 *)
F is Relation-like non empty-yielding NAT -defined q11 -valued Function-like non empty finite FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
U is set
q1 is non empty set
q1 * is functional non empty non trivial non finite finite-membered FinSequence-membered non empty-membered FinSequenceSet of q1
(q1) is Relation-like (q1 *) * -defined q1 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:((q1 *) *),(q1 *):]
(q1 *) * is functional non empty non trivial non finite finite-membered FinSequence-membered non empty-membered FinSequenceSet of q1 *
[:((q1 *) *),(q1 *):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:((q1 *) *),(q1 *):] is non empty non trivial non finite non empty-membered set
q1 -concatenation is Relation-like [:(q1 *),(q1 *):] -defined q1 * -valued Function-like non empty total quasi_total associative Function-yielding V159() FinSequence-yielding Element of bool [:[:(q1 *),(q1 *):],(q1 *):]
[:(q1 *),(q1 *):] is Relation-like non empty non trivial non finite non empty-membered set
[:[:(q1 *),(q1 *):],(q1 *):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:[:(q1 *),(q1 *):],(q1 *):] is non empty non trivial non finite non empty-membered set
((q1 *),(q1 -concatenation)) is Relation-like ((q1 *) *) \ {{}} -defined q1 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(((q1 *) *) \ {{}}),(q1 *):]
((q1 *) *) \ {{}} is functional non empty finite-membered FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((q1 *) *)
bool ((q1 *) *) is non empty non trivial non finite non empty-membered set
(((q1 *) *),{{}}) is functional finite-membered FinSequence-membered Element of bool ((q1 *) *)
[:(((q1 *) *) \ {{}}),(q1 *):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:(((q1 *) *) \ {{}}),(q1 *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* ((q1 *),(q1 -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
q2 is non empty set
(q2) is Relation-like (q2 *) * -defined q2 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:((q2 *) *),(q2 *):]
q2 * is functional non empty non trivial non finite finite-membered FinSequence-membered non empty-membered FinSequenceSet of q2
(q2 *) * is functional non empty non trivial non finite finite-membered FinSequence-membered non empty-membered FinSequenceSet of q2 *
[:((q2 *) *),(q2 *):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:((q2 *) *),(q2 *):] is non empty non trivial non finite non empty-membered set
q2 -concatenation is Relation-like [:(q2 *),(q2 *):] -defined q2 * -valued Function-like non empty total quasi_total associative Function-yielding V159() FinSequence-yielding Element of bool [:[:(q2 *),(q2 *):],(q2 *):]
[:(q2 *),(q2 *):] is Relation-like non empty non trivial non finite non empty-membered set
[:[:(q2 *),(q2 *):],(q2 *):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:[:(q2 *),(q2 *):],(q2 *):] is non empty non trivial non finite non empty-membered set
((q2 *),(q2 -concatenation)) is Relation-like ((q2 *) *) \ {{}} -defined q2 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(((q2 *) *) \ {{}}),(q2 *):]
((q2 *) *) \ {{}} is functional non empty finite-membered FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((q2 *) *)
bool ((q2 *) *) is non empty non trivial non finite non empty-membered set
(((q2 *) *),{{}}) is functional finite-membered FinSequence-membered Element of bool ((q2 *) *)
[:(((q2 *) *) \ {{}}),(q2 *):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:(((q2 *) *) \ {{}}),(q2 *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* ((q2 *),(q2 -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1) . f is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q2) . f is Relation-like NAT -defined q2 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
bool q2 is non empty set
q11 is non empty Element of bool q2
(q2,q11) is functional non empty non trivial non finite finite-membered FinSequence-membered non empty-membered Element of bool (q2 *)
bool (q2 *) is non empty non trivial non finite non empty-membered set
bool (q2,q11) is non empty non trivial non finite non empty-membered set
F is functional finite-membered FinSequence-membered Element of bool (q2,q11)
p is functional finite-membered FinSequence-membered Element of bool (q2 *)
C is Relation-like NAT -defined F -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V159() countable finite-support set
(q1) . C is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
y1 is Relation-like NAT -defined p -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V159() countable finite-support set
(q2) . y1 is Relation-like NAT -defined q2 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
U is set
q1 is set
q1 * is functional non empty finite-membered FinSequence-membered FinSequenceSet of q1
q2 is non empty set
(q2) is Relation-like (q2 *) * -defined q2 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:((q2 *) *),(q2 *):]
q2 * is functional non empty non trivial non finite finite-membered FinSequence-membered non empty-membered FinSequenceSet of q2
(q2 *) * is functional non empty non trivial non finite finite-membered FinSequence-membered non empty-membered FinSequenceSet of q2 *
[:((q2 *) *),(q2 *):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:((q2 *) *),(q2 *):] is non empty non trivial non finite non empty-membered set
q2 -concatenation is Relation-like [:(q2 *),(q2 *):] -defined q2 * -valued Function-like non empty total quasi_total associative Function-yielding V159() FinSequence-yielding Element of bool [:[:(q2 *),(q2 *):],(q2 *):]
[:(q2 *),(q2 *):] is Relation-like non empty non trivial non finite non empty-membered set
[:[:(q2 *),(q2 *):],(q2 *):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:[:(q2 *),(q2 *):],(q2 *):] is non empty non trivial non finite non empty-membered set
((q2 *),(q2 -concatenation)) is Relation-like ((q2 *) *) \ {{}} -defined q2 * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(((q2 *) *) \ {{}}),(q2 *):]
((q2 *) *) \ {{}} is functional non empty finite-membered FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((q2 *) *)
bool ((q2 *) *) is non empty non trivial non finite non empty-membered set
(((q2 *) *),{{}}) is functional finite-membered FinSequence-membered Element of bool ((q2 *) *)
[:(((q2 *) *) \ {{}}),(q2 *):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:(((q2 *) *) \ {{}}),(q2 *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* ((q2 *),(q2 -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
(q2) . U is Relation-like NAT -defined q2 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
dom (q2) is functional non empty finite-membered FinSequence-membered Element of bool ((q2 *) *)
q11 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q1 *) * is functional non empty non trivial non finite finite-membered FinSequence-membered non empty-membered FinSequenceSet of q1 *
(q2) . q11 is Relation-like NAT -defined q2 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
p is Relation-like NAT -defined q2 * -valued Function-like non empty finite FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support FinSequence of q2 *
C is non empty set
(C) is Relation-like (C *) * -defined C * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:((C *) *),(C *):]
C * is functional non empty non trivial non finite finite-membered FinSequence-membered non empty-membered FinSequenceSet of C
(C *) * is functional non empty non trivial non finite finite-membered FinSequence-membered non empty-membered FinSequenceSet of C *
[:((C *) *),(C *):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:((C *) *),(C *):] is non empty non trivial non finite non empty-membered set
C -concatenation is Relation-like [:(C *),(C *):] -defined C * -valued Function-like non empty total quasi_total associative Function-yielding V159() FinSequence-yielding Element of bool [:[:(C *),(C *):],(C *):]
[:(C *),(C *):] is Relation-like non empty non trivial non finite non empty-membered set
[:[:(C *),(C *):],(C *):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:[:(C *),(C *):],(C *):] is non empty non trivial non finite non empty-membered set
((C *),(C -concatenation)) is Relation-like ((C *) *) \ {{}} -defined C * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(((C *) *) \ {{}}),(C *):]
((C *) *) \ {{}} is functional non empty finite-membered FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((C *) *)
bool ((C *) *) is non empty non trivial non finite non empty-membered set
(((C *) *),{{}}) is functional finite-membered FinSequence-membered Element of bool ((C *) *)
[:(((C *) *) \ {{}}),(C *):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:(((C *) *) \ {{}}),(C *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* ((C *),(C -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
F is Relation-like NAT -defined q1 * -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support Element of (q1 *) *
(C) . p is Relation-like NAT -defined C -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(q2) . q11 is Relation-like NAT -defined q2 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
p is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
rng p is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial proper complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like with_non-empty_elements empty-membered Cardinal-yielding with_common_domain countable FinSequence-yielding finite-support Element of bool {{}}
bool {{}} is non empty finite finite-membered countable set
(q2) . q11 is Relation-like NAT -defined q2 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
U is set
q1 -tuples_on U is functional finite-membered FinSequence-membered FinSequenceSet of U
U * is functional non empty finite-membered FinSequence-membered FinSequenceSet of U
(q1 -tuples_on U) \ (U *) is functional finite-membered FinSequence-membered Element of bool (q1 -tuples_on U)
bool (q1 -tuples_on U) is non empty set
((q1 -tuples_on U),(U *)) is functional finite-membered FinSequence-membered Element of bool (q1 -tuples_on U)
q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
q2 -tuples_on U is functional finite-membered FinSequence-membered FinSequenceSet of U
f is set
U is set
U * is functional non empty finite-membered FinSequence-membered FinSequenceSet of U
q1 is set
U /\ q1 is set
(U,q1) is Element of bool U
bool U is non empty set
(U,q1) is Element of bool q1
bool q1 is non empty set
(U /\ q1) * is functional non empty finite-membered FinSequence-membered FinSequenceSet of U /\ q1
q1 * is functional non empty finite-membered FinSequence-membered FinSequenceSet of q1
(U *) /\ (q1 *) is set
((U *),(q1 *)) is functional finite-membered FinSequence-membered Element of bool (U *)
bool (U *) is non empty set
((U *),(q1 *)) is functional finite-membered FinSequence-membered Element of bool (q1 *)
bool (q1 *) is non empty set
f is Element of bool U
(U,f) is functional non empty finite-membered FinSequence-membered Element of bool (U *)
q11 is Element of bool q1
(q1,q11) is functional non empty finite-membered FinSequence-membered Element of bool (q1 *)
F is set
p is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
len p is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
(len p) -tuples_on U is functional finite-membered FinSequence-membered FinSequenceSet of U
(len p) -tuples_on q1 is functional finite-membered FinSequence-membered FinSequenceSet of q1
(len p) -tuples_on (U /\ q1) is functional finite-membered FinSequence-membered FinSequenceSet of U /\ q1
((len p) -tuples_on (U /\ q1)) \ ((U /\ q1) *) is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support Element of bool ((len p) -tuples_on (U /\ q1))
bool ((len p) -tuples_on (U /\ q1)) is non empty set
(((len p) -tuples_on (U /\ q1)),((U /\ q1) *)) is functional finite-membered FinSequence-membered Element of bool ((len p) -tuples_on (U /\ q1))
pb is Relation-like NAT -defined q1 -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((len p) -tuples_on U) /\ ((len p) -tuples_on q1) is set
(((len p) -tuples_on U),((len p) -tuples_on q1)) is functional finite-membered FinSequence-membered Element of bool ((len p) -tuples_on U)
bool ((len p) -tuples_on U) is non empty set
(((len p) -tuples_on U),((len p) -tuples_on q1)) is functional finite-membered FinSequence-membered Element of bool ((len p) -tuples_on q1)
bool ((len p) -tuples_on q1) is non empty set
U is set
q1 is Relation-like set
q1 | U is Relation-like U -defined set
q2 is Relation-like set
q1 \/ q2 is Relation-like set
(q1 \/ q2) | U is Relation-like U -defined set
q2 | U is Relation-like U -defined set
(q1 | U) \/ (q2 | U) is Relation-like U -defined set
(q2,q1) is Relation-like q2 \/ (proj2 q1) -valued set
proj2 q1 is set
q2 \/ (proj2 q1) is set
(q1,q2) is Relation-like Element of bool (q1 \/ q2)
bool (q1 \/ q2) is non empty set
(q2,q1) | U is Relation-like U -defined q2 \/ (proj2 q1) -valued set
(q1,q2) is Relation-like q1 \/ (proj2 q2) -valued set
proj2 q2 is set
q1 \/ (proj2 q2) is set
(q2,q1) is Relation-like Element of bool (q2 \/ q1)
q2 \/ q1 is Relation-like set
bool (q2 \/ q1) is non empty set
(q1,q2) | U is Relation-like U -defined q1 \/ (proj2 q2) -valued set
y1 is set
x is set
y is set
[x,y] is non empty V15() set
U is set
bool U is non empty set
bool U is non empty Element of bool (bool U)
bool (bool U) is non empty set
(bool U) \ U is Element of bool (bool U)
((bool U),U) is Element of bool (bool U)
bool (bool U) is non empty set
(bool U) \ U is Element of bool (bool U)
q1 is set
U is set
q1 is Relation-like set
(U,q1) is Relation-like U \/ (proj2 q1) -valued set
proj2 q1 is set
U \/ (proj2 q1) is set
(q1,U) is Element of bool (q1 \/ U)
q1 \/ U is set
bool (q1 \/ U) is non empty set
proj1 q1 is set
U \/ (proj1 q1) is set
(U,(proj1 q1)) is set
((proj1 q1),U) is Element of bool ((proj1 q1) \/ U)
(proj1 q1) \/ U is set
bool ((proj1 q1) \/ U) is non empty set
q2 is Relation-like set
U is set
q1 is Relation-like Function-like set
q1 | U is Relation-like U -defined Function-like set
q2 is Relation-like Function-like set
(q1 | U) +* q2 is Relation-like Function-like set
proj1 q2 is set
U \ (proj1 q2) is Element of bool U
bool U is non empty set
(U,(proj1 q2)) is Element of bool U
q1 | (U \ (proj1 q2)) is Relation-like U \ (proj1 q2) -defined Function-like set
(q1 | (U \ (proj1 q2))) \/ q2 is Relation-like set
dom (q1 | (U \ (proj1 q2))) is Element of bool (U \ (proj1 q2))
bool (U \ (proj1 q2)) is non empty set
U /\ (proj1 q2) is set
(U,(proj1 q2)) is Element of bool U
(U,(proj1 q2)) is Element of bool (proj1 q2)
bool (proj1 q2) is non empty set
(U \ (proj1 q2)) \/ (U /\ (proj1 q2)) is set
q1 | ((U \ (proj1 q2)) \/ (U /\ (proj1 q2))) is Relation-like (U \ (proj1 q2)) \/ (U /\ (proj1 q2)) -defined Function-like set
(q1 | ((U \ (proj1 q2)) \/ (U /\ (proj1 q2)))) +* q2 is Relation-like Function-like set
q1 | (U /\ (proj1 q2)) is Relation-like U /\ (proj1 q2) -defined Function-like set
(q1 | (U \ (proj1 q2))) +* (q1 | (U /\ (proj1 q2))) is Relation-like Function-like set
((q1 | (U \ (proj1 q2))) +* (q1 | (U /\ (proj1 q2)))) +* q2 is Relation-like Function-like set
{} \/ (proj1 q2) is set
({},q2) is Relation-like {} \/ (proj1 q2) -defined {} \/ (proj2 q2) -valued Function-like set
proj2 q2 is set
{} \/ (proj2 q2) is set
(q2,{}) is Relation-like Element of bool (q2 \/ {})
q2 \/ {} is Relation-like set
bool (q2 \/ {}) is non empty set
(({} \/ (proj1 q2)),({},q2)) is Relation-like ({} \/ (proj1 q2)) \/ (proj1 ({},q2)) -defined ({} \/ (proj1 q2)) \/ (proj2 ({},q2)) -valued Function-like set
proj1 ({},q2) is set
({} \/ (proj1 q2)) \/ (proj1 ({},q2)) is set
proj2 ({},q2) is set
({} \/ (proj1 q2)) \/ (proj2 ({},q2)) is set
(({},q2),({} \/ (proj1 q2))) is Element of bool (({},q2) \/ ({} \/ (proj1 q2)))
({},q2) \/ ({} \/ (proj1 q2)) is set
bool (({},q2) \/ ({} \/ (proj1 q2))) is non empty set
({},q2) | ({} \/ (proj1 q2)) is Relation-like {} \/ (proj1 q2) -defined {} \/ (proj1 q2) -defined {} \/ (proj2 q2) -valued Function-like set
(q1 | (U /\ (proj1 q2))) +* (({} \/ (proj1 q2)),({},q2)) is Relation-like Function-like set
(q1 | (U \ (proj1 q2))) +* ((q1 | (U /\ (proj1 q2))) +* (({} \/ (proj1 q2)),({},q2))) is Relation-like Function-like set
(q1 | U) | (proj1 q2) is Relation-like proj1 q2 -defined U -defined Function-like set
q2 | (proj1 q2) is Relation-like proj1 q2 -defined Function-like set
((q1 | U) | (proj1 q2)) +* (q2 | (proj1 q2)) is Relation-like proj1 q2 -defined Function-like set
(q1 | (U \ (proj1 q2))) +* (((q1 | U) | (proj1 q2)) +* (q2 | (proj1 q2))) is Relation-like Function-like set
((q1 | U) +* q2) | (proj1 q2) is Relation-like proj1 q2 -defined Function-like set
(q1 | (U \ (proj1 q2))) +* (((q1 | U) +* q2) | (proj1 q2)) is Relation-like Function-like set
(q1 | (U \ (proj1 q2))) +* q2 is Relation-like Function-like set
U is set
q1 is Relation-like U -defined Function-like set
q2 is Relation-like U -defined Function-like total set
q1 +* q2 is Relation-like U -defined Function-like total set
(q1,q2) is Relation-like q1 \/ (proj1 q2) -defined q1 \/ (proj2 q2) -valued Function-like set
proj1 q2 is set
q1 \/ (proj1 q2) is set
proj2 q2 is set
q1 \/ (proj2 q2) is set
(q2,q1) is Relation-like U -defined Element of bool (q2 \/ q1)
q2 \/ q1 is Relation-like U -defined set
bool (q2 \/ q1) is non empty set
dom q2 is Element of bool U
bool U is non empty set
dom q1 is Element of bool U
U is set
{U} is non empty trivial finite 1 -element countable set
q1 is set
proj2 q1 is set
q2 is set
[:q2,{U}:] is Relation-like set
q1 /\ [:q2,{U}:] is Relation-like set
(q1,[:q2,{U}:]) is Element of bool q1
bool q1 is non empty set
(q1,[:q2,{U}:]) is Relation-like q2 -defined {U} -valued Element of bool [:q2,{U}:]
bool [:q2,{U}:] is non empty set
p is set
p `1 is set
p `2 is set
[(p `1),(p `2)] is non empty V15() set
U is set
proj2 U is set
bool (proj2 U) is non empty set
bool (proj2 U) is non empty Element of bool (bool (proj2 U))
bool (bool (proj2 U)) is non empty set
(bool (proj2 U)) \ (proj2 U) is non empty Element of bool (bool (proj2 U))
((bool (proj2 U)),(proj2 U)) is Element of bool (bool (proj2 U))
bool (bool (proj2 U)) is non empty set
(bool (proj2 U)) \ (proj2 U) is non empty Element of bool (bool (proj2 U))
the Element of (bool (proj2 U)) \ (proj2 U) is Element of (bool (proj2 U)) \ (proj2 U)
{ the Element of (bool (proj2 U)) \ (proj2 U)} is non empty trivial finite 1 -element countable Element of bool ((bool (proj2 U)) \ (proj2 U))
bool ((bool (proj2 U)) \ (proj2 U)) is non empty set
[:NAT,{ the Element of (bool (proj2 U)) \ (proj2 U)}:] is Relation-like REAL -defined (bool (proj2 U)) \ (proj2 U) -valued non empty non trivial non finite non empty-membered Element of bool [:REAL,((bool (proj2 U)) \ (proj2 U)):]
[:REAL,((bool (proj2 U)) \ (proj2 U)):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:REAL,((bool (proj2 U)) \ (proj2 U)):] is non empty non trivial non finite non empty-membered set
U is set
(U) is set
proj2 U is set
bool (proj2 U) is non empty set
bool (proj2 U) is non empty Element of bool (bool (proj2 U))
bool (bool (proj2 U)) is non empty set
(bool (proj2 U)) \ (proj2 U) is non empty Element of bool (bool (proj2 U))
((bool (proj2 U)),(proj2 U)) is Element of bool (bool (proj2 U))
bool (bool (proj2 U)) is non empty set
(bool (proj2 U)) \ (proj2 U) is non empty Element of bool (bool (proj2 U))
the Element of (bool (proj2 U)) \ (proj2 U) is Element of (bool (proj2 U)) \ (proj2 U)
{ the Element of (bool (proj2 U)) \ (proj2 U)} is non empty trivial finite 1 -element countable Element of bool ((bool (proj2 U)) \ (proj2 U))
bool ((bool (proj2 U)) \ (proj2 U)) is non empty set
[:NAT,{ the Element of (bool (proj2 U)) \ (proj2 U)}:] is Relation-like REAL -defined (bool (proj2 U)) \ (proj2 U) -valued non empty non trivial non finite non empty-membered Element of bool [:REAL,((bool (proj2 U)) \ (proj2 U)):]
[:REAL,((bool (proj2 U)) \ (proj2 U)):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:REAL,((bool (proj2 U)) \ (proj2 U)):] is non empty non trivial non finite non empty-membered set
(U) /\ U is set
((U),U) is Element of bool (U)
bool (U) is non empty set
((U),U) is Element of bool U
bool U is non empty set
U is set
(U) is set
proj2 U is set
bool (proj2 U) is non empty set
bool (proj2 U) is non empty Element of bool (bool (proj2 U))
bool (bool (proj2 U)) is non empty set
(bool (proj2 U)) \ (proj2 U) is non empty Element of bool (bool (proj2 U))
((bool (proj2 U)),(proj2 U)) is Element of bool (bool (proj2 U))
bool (bool (proj2 U)) is non empty set
(bool (proj2 U)) \ (proj2 U) is non empty Element of bool (bool (proj2 U))
the Element of (bool (proj2 U)) \ (proj2 U) is Element of (bool (proj2 U)) \ (proj2 U)
{ the Element of (bool (proj2 U)) \ (proj2 U)} is non empty trivial finite 1 -element countable Element of bool ((bool (proj2 U)) \ (proj2 U))
bool ((bool (proj2 U)) \ (proj2 U)) is non empty set
[:NAT,{ the Element of (bool (proj2 U)) \ (proj2 U)}:] is Relation-like REAL -defined (bool (proj2 U)) \ (proj2 U) -valued non empty non trivial non finite non empty-membered Element of bool [:REAL,((bool (proj2 U)) \ (proj2 U)):]
[:REAL,((bool (proj2 U)) \ (proj2 U)):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:REAL,((bool (proj2 U)) \ (proj2 U)):] is non empty non trivial non finite non empty-membered set
q1 is set
U is set
(U) is non empty non trivial non finite non empty-membered set
proj2 U is set
bool (proj2 U) is non empty set
bool (proj2 U) is non empty Element of bool (bool (proj2 U))
bool (bool (proj2 U)) is non empty set
(bool (proj2 U)) \ (proj2 U) is non empty Element of bool (bool (proj2 U))
((bool (proj2 U)),(proj2 U)) is Element of bool (bool (proj2 U))
bool (bool (proj2 U)) is non empty set
(bool (proj2 U)) \ (proj2 U) is non empty Element of bool (bool (proj2 U))
the Element of (bool (proj2 U)) \ (proj2 U) is Element of (bool (proj2 U)) \ (proj2 U)
{ the Element of (bool (proj2 U)) \ (proj2 U)} is non empty trivial finite 1 -element countable Element of bool ((bool (proj2 U)) \ (proj2 U))
bool ((bool (proj2 U)) \ (proj2 U)) is non empty set
[:NAT,{ the Element of (bool (proj2 U)) \ (proj2 U)}:] is Relation-like REAL -defined (bool (proj2 U)) \ (proj2 U) -valued non empty non trivial non finite non empty-membered Element of bool [:REAL,((bool (proj2 U)) \ (proj2 U)):]
[:REAL,((bool (proj2 U)) \ (proj2 U)):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:REAL,((bool (proj2 U)) \ (proj2 U)):] is non empty non trivial non finite non empty-membered set
(U) /\ U is set
((U),U) is Element of bool (U)
bool (U) is non empty non trivial non finite non empty-membered set
((U),U) is Element of bool U
bool U is non empty set
U is set
(U) is non empty non trivial non finite non empty-membered set
proj2 U is set
bool (proj2 U) is non empty set
bool (proj2 U) is non empty Element of bool (bool (proj2 U))
bool (bool (proj2 U)) is non empty set
(bool (proj2 U)) \ (proj2 U) is non empty Element of bool (bool (proj2 U))
((bool (proj2 U)),(proj2 U)) is Element of bool (bool (proj2 U))
bool (bool (proj2 U)) is non empty set
(bool (proj2 U)) \ (proj2 U) is non empty Element of bool (bool (proj2 U))
the Element of (bool (proj2 U)) \ (proj2 U) is Element of (bool (proj2 U)) \ (proj2 U)
{ the Element of (bool (proj2 U)) \ (proj2 U)} is non empty trivial finite 1 -element countable Element of bool ((bool (proj2 U)) \ (proj2 U))
bool ((bool (proj2 U)) \ (proj2 U)) is non empty set
[:NAT,{ the Element of (bool (proj2 U)) \ (proj2 U)}:] is Relation-like REAL -defined (bool (proj2 U)) \ (proj2 U) -valued non empty non trivial non finite non empty-membered Element of bool [:REAL,((bool (proj2 U)) \ (proj2 U)):]
[:REAL,((bool (proj2 U)) \ (proj2 U)):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:REAL,((bool (proj2 U)) \ (proj2 U)):] is non empty non trivial non finite non empty-membered set
q1 is set
NAT \ INT is Element of bool REAL
(NAT,INT) is countable Element of bool NAT
NAT \ INT is countable Element of bool NAT
U is set
<*U*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like countable finite-support set
[1,U] is non empty V15() set
{[1,U]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
q1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
<*U*> ^ q1 is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like countable finite-support set
(<*U*> ^ q1) . 1 is set
((<*U*> ^ q1) . 1) \+\ U is set
((<*U*> ^ q1) . 1) \ U is set
(((<*U*> ^ q1) . 1),U) is Element of bool ((<*U*> ^ q1) . 1)
bool ((<*U*> ^ q1) . 1) is non empty set
((<*U*> ^ q1) . 1) \ U is Element of bool ((<*U*> ^ q1) . 1)
U \ ((<*U*> ^ q1) . 1) is set
(U,((<*U*> ^ q1) . 1)) is Element of bool U
bool U is non empty set
U \ ((<*U*> ^ q1) . 1) is Element of bool U
(((<*U*> ^ q1) . 1) \ U) \/ (U \ ((<*U*> ^ q1) . 1)) is set
q2 is set
U is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q1 is Relation-like non-empty empty-yielding NAT -defined {{}} -valued Function-like one-to-one constant functional empty trivial complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural real integer finite finite-yielding finite-membered cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative Function-yielding V159() FuncSeq-like empty-membered Cardinal-yielding countable FinSequence-yielding finite-support set
U + q1 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
Seg (U + q1) is finite U + q1 -element countable Element of bool NAT
{ b₁ where b₁ is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT : ( 1 <= b₁ & b₁ <= U + q1 ) } is set
q2 is Relation-like NAT -defined Function-like finite U -element FinSequence-like FinSubsequence-like countable finite-support set
(q1,q2) is Relation-like NAT -defined q1 \/ (proj1 q2) -defined Seg (U + q1) -defined q1 \/ (proj2 q2) -valued Function-like finite len q2 -element FinSequence-like FinSubsequence-like countable finite-support set
proj1 q2 is finite U -element countable set
q1 \/ (proj1 q2) is finite countable set
proj2 q2 is finite countable set
q1 \/ (proj2 q2) is finite countable set
len q2 is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable Element of NAT
(q2,q1) is Relation-like NAT -defined finite countable Element of bool (q2 \/ q1)
q2 \/ q1 is Relation-like NAT -defined finite countable set
bool (q2 \/ q1) is non empty finite finite-membered countable set
q2 ^ q1 is Relation-like NAT -defined Function-like finite U + {} -element FinSequence-like FinSubsequence-like countable finite-support set
U + {} is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
q1 ^ q2 is Relation-like NAT -defined Function-like finite {} + U -element FinSequence-like FinSubsequence-like countable finite-support set
{} + U is complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real non negative countable set
f is Relation-like Seg (U + q1) -defined set
dom f is finite countable Element of bool (Seg (U + q1))
bool (Seg (U + q1)) is non empty finite finite-membered countable set
U is non empty set
(U) is Relation-like (U *) * -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:((U *) *),(U *):]
U * is functional non empty non trivial non finite finite-membered FinSequence-membered non empty-membered FinSequenceSet of U
(U *) * is functional non empty non trivial non finite finite-membered FinSequence-membered non empty-membered FinSequenceSet of U *
[:((U *) *),(U *):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:((U *) *),(U *):] is non empty non trivial non finite non empty-membered set
U -concatenation is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total associative Function-yielding V159() FinSequence-yielding Element of bool [:[:(U *),(U *):],(U *):]
[:(U *),(U *):] is Relation-like non empty non trivial non finite non empty-membered set
[:[:(U *),(U *):],(U *):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:[:(U *),(U *):],(U *):] is non empty non trivial non finite non empty-membered set
((U *),(U -concatenation)) is Relation-like ((U *) *) \ {{}} -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(((U *) *) \ {{}}),(U *):]
((U *) *) \ {{}} is functional non empty finite-membered FinSequence-membered with_non-empty_elements non empty-membered Element of bool ((U *) *)
bool ((U *) *) is non empty non trivial non finite non empty-membered set
(((U *) *),{{}}) is functional finite-membered FinSequence-membered Element of bool ((U *) *)
[:(((U *) *) \ {{}}),(U *):] is Relation-like non empty non trivial non finite non empty-membered set
bool [:(((U *) *) \ {{}}),(U *):] is non empty non trivial non finite non empty-membered set
({} .--> {}) +* ((U *),(U -concatenation)) is Relation-like Function-like non empty Function-yielding V159() set
q1 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q2 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
<*q1,q2*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable finite-support set
<*q1*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support set
[1,q1] is non empty V15() set
{[1,q1]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
<*q2*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support set
[1,q2] is non empty V15() set
{[1,q2]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
<*q1*> ^ <*q2*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element 1 + 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() countable FinSequence-yielding finite-support set
1 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable set
1 + 1 is non empty complex epsilon-transitive epsilon-connected ordinal natural real integer finite cardinal ext-real positive non negative countable Element of NAT
(U) . <*q1,q2*> is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
q1 ^ q2 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((U) . <*q1,q2*>) \+\ (q1 ^ q2) is Relation-like finite countable set
((U) . <*q1,q2*>) \ (q1 ^ q2) is Relation-like NAT -defined U -valued finite countable set
(((U) . <*q1,q2*>),(q1 ^ q2)) is Relation-like NAT -defined U -valued Function-like finite countable finite-support Element of bool ((U) . <*q1,q2*>)
bool ((U) . <*q1,q2*>) is non empty finite finite-membered countable set
((U) . <*q1,q2*>) \ (q1 ^ q2) is Relation-like NAT -defined U -valued Function-like finite countable finite-support Element of bool ((U) . <*q1,q2*>)
(q1 ^ q2) \ ((U) . <*q1,q2*>) is Relation-like NAT -defined U -valued finite countable set
((q1 ^ q2),((U) . <*q1,q2*>)) is Relation-like NAT -defined U -valued Function-like finite countable finite-support Element of bool (q1 ^ q2)
bool (q1 ^ q2) is non empty finite finite-membered countable set
(q1 ^ q2) \ ((U) . <*q1,q2*>) is Relation-like NAT -defined U -valued Function-like finite countable finite-support Element of bool (q1 ^ q2)
(((U) . <*q1,q2*>) \ (q1 ^ q2)) \/ ((q1 ^ q2) \ ((U) . <*q1,q2*>)) is Relation-like NAT -defined U -valued finite countable set
f is Relation-like [:(U *),(U *):] -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:[:(U *),(U *):],(U *):]
((U *),f) is Relation-like ((U *) *) \ {{}} -defined U * -valued Function-like non empty total quasi_total Function-yielding V159() FinSequence-yielding Element of bool [:(((U *) *) \ {{}}),(U *):]
q11 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support Element of U *
<*q11*> is Relation-like NAT -defined U * -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like Function-yielding V159() FuncSeq-like countable FinSequence-yielding finite-support FinSequence of U *
[1,q11] is non empty V15() set
{[1,q11]} is Relation-like Function-like constant non empty trivial finite 1 -element with_non-empty_elements non empty-membered countable finite-support set
(U) . <*q11*> is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((U) . <*q11*>) ^ q2 is Relation-like NAT -defined U -valued Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
((U *),f) . <*q11*> is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
(((U *),f) . <*q11*>) ^ q2 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like countable finite-support set
y1 is set