:: LATTICE8 semantic presentation

REAL is set
NAT is epsilon-transitive epsilon-connected ordinal non empty V40() V45() V46() Element of bool REAL
bool REAL is non empty set
NAT is epsilon-transitive epsilon-connected ordinal non empty V40() V45() V46() set
bool NAT is non empty V40() V271() set
COMPLEX is set
RAT is set
INT is set
bool NAT is non empty V40() V271() set
{} is epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like functional empty trivial V33() V34() ext-real V38() V40() V45() V47( {} ) FinSequence-membered set
the epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like functional empty trivial V33() V34() ext-real V38() V40() V45() V47( {} ) FinSequence-membered set is epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like functional empty trivial V33() V34() ext-real V38() V40() V45() V47( {} ) FinSequence-membered set
1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() ext-real positive V38() V40() V45() Element of NAT
{{},1} is non empty set
2 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() ext-real positive V38() V40() V45() Element of NAT
[:2,2:] is non empty set
[:[:2,2:],2:] is non empty set
bool [:[:2,2:],2:] is non empty V271() set
3 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() ext-real positive V38() V40() V45() Element of NAT
0 is epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural Function-like functional empty trivial V33() V34() ext-real V38() V40() V45() V47( {} ) FinSequence-membered Element of NAT
4 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() ext-real positive V38() V40() V45() Element of NAT
the non empty finite reflexive transitive antisymmetric lower-bounded upper-bounded V227() distributive with_suprema with_infima V297() modular RelStr is non empty finite reflexive transitive antisymmetric lower-bounded upper-bounded V227() distributive with_suprema with_infima V297() modular RelStr
2 * 0 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() even Element of NAT
(2 * 0) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() ext-real V38() V40() V45() non even Element of NAT
2 * 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() even Element of NAT
L is non empty non trivial set
EqRelLATT L is non empty reflexive transitive antisymmetric lower-bounded upper-bounded V227() with_suprema with_infima V297() RelStr
the carrier of (EqRelLATT L) is non empty set
nabla L is Relation-like L -defined L -valued total V72() V74() V79() Element of bool [:L,L:]
[:L,L:] is non empty set
bool [:L,L:] is non empty V271() set
id L is Relation-like L -defined L -valued Function-like one-to-one non empty total V72() V74() V75() V79() Element of bool [:L,L:]
the Element of L is Element of L
{ the Element of L} is non empty trivial V47(1) Element of bool L
bool L is non empty V271() set
L \ { the Element of L} is non empty Element of bool L
the Element of L \ { the Element of L} is Element of L \ { the Element of L}
A is Element of the carrier of (EqRelLATT L)
D is Element of the carrier of (EqRelLATT L)
{A,D} is non empty Element of bool the carrier of (EqRelLATT L)
bool the carrier of (EqRelLATT L) is non empty V271() set
subrelstr {A,D} is non empty strict reflexive transitive antisymmetric full SubRelStr of EqRelLATT L
the carrier of (subrelstr {A,D}) is non empty set
FD is Element of the carrier of (EqRelLATT L)
f is Element of the carrier of (EqRelLATT L)
{FD,f} is non empty Element of bool the carrier of (EqRelLATT L)
"/\" ({FD,f},(EqRelLATT L)) is Element of the carrier of (EqRelLATT L)
A "/\" A is Element of the carrier of (EqRelLATT L)
A "/\" D is Element of the carrier of (EqRelLATT L)
D "/\" A is Element of the carrier of (EqRelLATT L)
D "/\" D is Element of the carrier of (EqRelLATT L)
FD is set
FD is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() ext-real positive V38() V40() V45() Element of NAT
f is Relation-like L -defined L -valued total V72() V74() V79() Element of bool [:L,L:]
FS is Relation-like L -defined L -valued total V72() V74() V79() Element of bool [:L,L:]
f "\/" FS is Relation-like L -defined L -valued total V72() V74() V79() Element of bool [:L,L:]
f is set
FD is set
[f,FD] is non empty V25() set
{f,FD} is non empty set
{f} is non empty trivial V47(1) set
{{f,FD},{f}} is non empty set
A9 is set
d9 is set
Aq9 is set
[d9,Aq9] is non empty V25() set
{d9,Aq9} is non empty set
{d9} is non empty trivial V47(1) set
{{d9,Aq9},{d9}} is non empty set
<*f,A9,FD*> is Relation-like NAT -defined Function-like non empty V40() V47(3) FinSequence-like FinSubsequence-like set
d9 is Relation-like NAT -defined L -valued Function-like non empty V40() FinSequence-like FinSubsequence-like FinSequence of L
len d9 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() ext-real V38() V40() V45() Element of NAT
d9 . 2 is set
d9 . 1 is set
Aq9 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
d9 . Aq9 is set
Aq9 + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
d9 . (Aq9 + 1) is set
[(d9 . Aq9),(d9 . (Aq9 + 1))] is non empty V25() set
{(d9 . Aq9),(d9 . (Aq9 + 1))} is non empty set
{(d9 . Aq9)} is non empty trivial V47(1) set
{{(d9 . Aq9),(d9 . (Aq9 + 1))},{(d9 . Aq9)}} is non empty set
2 + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
dq9 is set
q is set
[dq9,q] is non empty V25() set
{dq9,q} is non empty set
{dq9} is non empty trivial V47(1) set
{{dq9,q},{dq9}} is non empty set
dq9 is set
q is set
[dq9,q] is non empty V25() set
{dq9,q} is non empty set
{dq9} is non empty trivial V47(1) set
{{dq9,q},{dq9}} is non empty set
D "\/" A is Element of the carrier of (EqRelLATT L)
d9 . 3 is set
d9 . 2 is set
d9 . 3 is set
Aq9 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
d9 . Aq9 is set
Aq9 + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
d9 . (Aq9 + 1) is set
[(d9 . Aq9),(d9 . (Aq9 + 1))] is non empty V25() set
{(d9 . Aq9),(d9 . (Aq9 + 1))} is non empty set
{(d9 . Aq9)} is non empty trivial V47(1) set
{{(d9 . Aq9),(d9 . (Aq9 + 1))},{(d9 . Aq9)}} is non empty set
2 + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A "\/" D is Element of the carrier of (EqRelLATT L)
dq9 is set
q is set
[dq9,q] is non empty V25() set
{dq9,q} is non empty set
{dq9} is non empty trivial V47(1) set
{{dq9,q},{dq9}} is non empty set
dq9 is set
q is set
[dq9,q] is non empty V25() set
{dq9,q} is non empty set
{dq9} is non empty trivial V47(1) set
{{dq9,q},{dq9}} is non empty set
d9 . 1 is set
FD is Element of the carrier of (EqRelLATT L)
f is Element of the carrier of (EqRelLATT L)
{FD,f} is non empty Element of bool the carrier of (EqRelLATT L)
"\/" ({FD,f},(EqRelLATT L)) is Element of the carrier of (EqRelLATT L)
A "\/" A is Element of the carrier of (EqRelLATT L)
A "\/" D is Element of the carrier of (EqRelLATT L)
D "\/" A is Element of the carrier of (EqRelLATT L)
D "\/" D is Element of the carrier of (EqRelLATT L)
FD is Element of the carrier of (subrelstr {A,D})
{FD} is non empty trivial V47(1) Element of bool the carrier of (subrelstr {A,D})
bool the carrier of (subrelstr {A,D}) is non empty V271() set
[ the Element of L, the Element of L \ { the Element of L}] is non empty V25() Element of [:L,(L \ { the Element of L}):]
[:L,(L \ { the Element of L}):] is non empty set
{ the Element of L, the Element of L \ { the Element of L}} is non empty set
{ the Element of L} is non empty trivial V47(1) set
{{ the Element of L, the Element of L \ { the Element of L}},{ the Element of L}} is non empty set
FD is non empty reflexive transitive antisymmetric full meet-inheriting join-inheriting with_suprema with_infima SubRelStr of EqRelLATT L
succ {} is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() ext-real V38() V40() V45() set
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:L,L:], the carrier of A:]
DistEsti D is epsilon-transitive epsilon-connected ordinal V45() set
L is non empty trivial finite 1 -element reflexive transitive antisymmetric lower-bounded upper-bounded V227() with_suprema with_infima V297() RelStr
the carrier of L is non empty trivial V40() V47(1) set
A is Element of the carrier of L
S is Element of the carrier of L
D is Element of the carrier of L
D "/\" S is Element of the carrier of L
A "\/" (D "/\" S) is Element of the carrier of L
A "\/" D is Element of the carrier of L
(A "\/" D) "/\" S is Element of the carrier of L
D "/\" S is Element of the carrier of L
A "\/" (D "/\" S) is Element of the carrier of L
A "\/" D is Element of the carrier of L
(A "\/" D) "/\" S is Element of the carrier of L
L is non empty set
EqRelLATT L is non empty reflexive transitive antisymmetric lower-bounded upper-bounded V227() with_suprema with_infima V297() RelStr
[:L,L:] is non empty set
bool [:L,L:] is non empty V271() set
id L is Relation-like L -defined L -valued Function-like one-to-one non empty total V72() V74() V75() V79() Element of bool [:L,L:]
A is non empty meet-inheriting join-inheriting SubRelStr of EqRelLATT L
the carrier of A is non empty set
D is set
the carrier of (EqRelLATT L) is non empty set
{D} is non empty trivial V47(1) set
FS is set
FS is Relation-like L -defined L -valued total V72() V74() V79() Element of bool [:L,L:]
S is Relation-like L -defined L -valued total V72() V74() V79() Element of bool [:L,L:]
FS is set
D is Relation-like L -defined L -valued total V72() V74() V79() Element of bool [:L,L:]
L is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of L is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[: the carrier of L, the carrier of A:] is non empty set
bool [: the carrier of L, the carrier of A:] is non empty V271() set
D is Relation-like the carrier of L -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier of L, the carrier of A:]
S is Element of the carrier of L
FS is Element of the carrier of L
{S,FS} is non empty Element of bool the carrier of L
bool the carrier of L is non empty V271() set
S is Element of the carrier of L
FS is Element of the carrier of L
{S,FS} is non empty Element of bool the carrier of L
bool the carrier of L is non empty V271() set
L is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
D is Element of the carrier of A
FS is Element of the carrier of A
S is Element of the carrier of A
S "/\" FS is Element of the carrier of A
D "\/" (S "/\" FS) is Element of the carrier of A
D "\/" S is Element of the carrier of A
(D "\/" S) "/\" FS is Element of the carrier of A
the carrier of L is non empty set
[: the carrier of L, the carrier of A:] is non empty set
bool [: the carrier of L, the carrier of A:] is non empty V271() set
FS is Relation-like the carrier of L -defined the carrier of A -valued Function-like quasi_total Element of bool [: the carrier of L, the carrier of A:]
FS " is Relation-like Function-like set
(FS ") . FS is set
(FS ") . D is set
(FS ") . S is set
rng FS is Element of bool the carrier of A
bool the carrier of A is non empty V271() set
FS . ((FS ") . S) is set
dom FS is Element of bool the carrier of L
bool the carrier of L is non empty V271() set
FS . ((FS ") . D) is set
FS . ((FS ") . FS) is set
f is Element of the carrier of L
A9 is Element of the carrier of L
FD is Element of the carrier of L
FD "/\" A9 is Element of the carrier of L
f "\/" (FD "/\" A9) is Element of the carrier of L
f "\/" FD is Element of the carrier of L
(f "\/" FD) "/\" A9 is Element of the carrier of L
S "/\" FS is Element of the carrier of A
D "\/" (S "/\" FS) is Element of the carrier of A
FS . f is Element of the carrier of A
FS . (FD "/\" A9) is Element of the carrier of A
(FS . f) "\/" (FS . (FD "/\" A9)) is Element of the carrier of A
FS . ((f "\/" FD) "/\" A9) is Element of the carrier of A
FS . (f "\/" FD) is Element of the carrier of A
FS . A9 is Element of the carrier of A
(FS . (f "\/" FD)) "/\" (FS . A9) is Element of the carrier of A
D "\/" S is Element of the carrier of A
(D "\/" S) "/\" FS is Element of the carrier of A
L is non empty reflexive transitive antisymmetric lower-bounded RelStr
the carrier of L is non empty set
A is non empty reflexive transitive antisymmetric RelStr
the carrier of A is non empty set
[: the carrier of L, the carrier of A:] is non empty set
bool [: the carrier of L, the carrier of A:] is non empty V271() set
D is Relation-like the carrier of L -defined the carrier of A -valued Function-like quasi_total monotone Element of bool [: the carrier of L, the carrier of A:]
Image D is non empty strict reflexive transitive antisymmetric full SubRelStr of A
rng D is Element of bool the carrier of A
bool the carrier of A is non empty V271() set
subrelstr (rng D) is strict reflexive transitive antisymmetric full SubRelStr of A
S is Element of the carrier of L
dom D is Element of bool the carrier of L
bool the carrier of L is non empty V271() set
D . S is Element of the carrier of A
the carrier of (Image D) is non empty set
FS is Element of the carrier of (Image D)
FS is Element of the carrier of (Image D)
the carrier of (subrelstr (rng D)) is set
FD is set
D . FD is set
FS is Element of the carrier of L
f is Element of the carrier of A
L is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of L is non empty set
A is Element of the carrier of L
D is Element of the carrier of L
S is non empty set
EqRelLATT S is non empty reflexive transitive antisymmetric lower-bounded upper-bounded V227() with_suprema with_infima V297() RelStr
the carrier of (EqRelLATT S) is non empty set
[: the carrier of L, the carrier of (EqRelLATT S):] is non empty set
bool [: the carrier of L, the carrier of (EqRelLATT S):] is non empty V271() set
FS is Relation-like the carrier of L -defined the carrier of (EqRelLATT S) -valued Function-like quasi_total monotone meet-preserving join-preserving Element of bool [: the carrier of L, the carrier of (EqRelLATT S):]
Image FS is non empty strict reflexive transitive antisymmetric full meet-inheriting join-inheriting with_suprema with_infima SubRelStr of EqRelLATT S
rng FS is Element of bool the carrier of (EqRelLATT S)
bool the carrier of (EqRelLATT S) is non empty V271() set
subrelstr (rng FS) is strict reflexive transitive antisymmetric full SubRelStr of EqRelLATT S
the carrier of (Image FS) is non empty set
corestr FS is Relation-like the carrier of L -defined the carrier of (Image FS) -valued Function-like quasi_total onto monotone Element of bool [: the carrier of L, the carrier of (Image FS):]
[: the carrier of L, the carrier of (Image FS):] is non empty set
bool [: the carrier of L, the carrier of (Image FS):] is non empty V271() set
(corestr FS) . A is Element of the carrier of (Image FS)
(corestr FS) . D is Element of the carrier of (Image FS)
FS is Element of the carrier of L
FD is Element of the carrier of L
FS "/\" FD is Element of the carrier of L
(corestr FS) . (FS "/\" FD) is Element of the carrier of (Image FS)
(corestr FS) . FS is Element of the carrier of (Image FS)
(corestr FS) . FD is Element of the carrier of (Image FS)
((corestr FS) . FS) "/\" ((corestr FS) . FD) is Element of the carrier of (Image FS)
FS . FS is Element of the carrier of (EqRelLATT S)
FS . FD is Element of the carrier of (EqRelLATT S)
(FS . FS) "/\" (FS . FD) is Element of the carrier of (EqRelLATT S)
((corestr FS) . D) "/\" ((corestr FS) . A) is Element of the carrier of (Image FS)
A "/\" D is Element of the carrier of L
(corestr FS) . (A "/\" D) is Element of the carrier of (Image FS)
L is non empty non trivial set
EqRelLATT L is non empty reflexive transitive antisymmetric lower-bounded upper-bounded V227() with_suprema with_infima V297() RelStr
[:L,L:] is non empty set
bool [:L,L:] is non empty V271() set
id L is Relation-like L -defined L -valued Function-like one-to-one non empty total V72() V74() V75() V79() Element of bool [:L,L:]
A is non empty reflexive transitive antisymmetric full meet-inheriting join-inheriting with_suprema with_infima () SubRelStr of EqRelLATT L
the carrier of A is non empty set
type_of A is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
D is Relation-like L -defined L -valued total V72() V74() V79() Element of bool [:L,L:]
S is Element of the carrier of A
FS is Element of the carrier of A
FS is Element of the carrier of A
FS "/\" FS is Element of the carrier of A
S "\/" (FS "/\" FS) is Element of the carrier of A
S "\/" FS is Element of the carrier of A
(S "\/" FS) "/\" FS is Element of the carrier of A
the carrier of (EqRelLATT L) is non empty set
FD is Relation-like L -defined L -valued total V72() V74() V79() Element of bool [:L,L:]
f is Relation-like L -defined L -valued total V72() V74() V79() Element of bool [:L,L:]
FS is Relation-like L -defined L -valued total V72() V74() V79() Element of bool [:L,L:]
A9 is Element of the carrier of (EqRelLATT L)
f is Element of the carrier of (EqRelLATT L)
A9 "\/" f is Element of the carrier of (EqRelLATT L)
FD is Element of the carrier of (EqRelLATT L)
(A9 "\/" f) "/\" FD is Element of the carrier of (EqRelLATT L)
(A9 "\/" f) /\ f is Relation-like L -defined L -valued Element of bool [:L,L:]
FS "\/" FD is Relation-like L -defined L -valued total V72() V74() V79() Element of bool [:L,L:]
(FS "\/" FD) /\ f is Relation-like L -defined L -valued total V72() V74() V79() Element of bool [:L,L:]
f "/\" FD is Element of the carrier of (EqRelLATT L)
A9 "\/" (f "/\" FD) is Element of the carrier of (EqRelLATT L)
FD /\ f is Relation-like L -defined L -valued total V72() V74() V79() Element of bool [:L,L:]
FS "\/" (FD /\ f) is Relation-like L -defined L -valued total V72() V74() V79() Element of bool [:L,L:]
d9 is non empty set
[:d9,d9:] is non empty set
bool [:d9,d9:] is non empty V271() set
field D is set
Aq9 is Element of L
dq9 is Element of L
[Aq9,dq9] is non empty V25() set
{Aq9,dq9} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,dq9},{Aq9}} is non empty set
[Aq9,dq9] is non empty V25() Element of [:L,L:]
2 + 2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
q is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
q is Relation-like NAT -defined L -valued Function-like non empty V40() FinSequence-like FinSubsequence-like FinSequence of L
len q is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() ext-real V38() V40() V45() Element of NAT
q . 4 is set
Q is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
2 * Q is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() even Element of NAT
(2 * Q) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() ext-real V38() V40() V45() non even Element of NAT
q . 3 is set
3 + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
q . (3 + 1) is set
[(q . 3),(q . (3 + 1))] is non empty V25() set
{(q . 3),(q . (3 + 1))} is non empty set
{(q . 3)} is non empty trivial V47(1) set
{{(q . 3),(q . (3 + 1))},{(q . 3)}} is non empty set
u is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
2 * u is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() even Element of NAT
q . 2 is set
2 + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
q . (2 + 1) is set
[(q . 2),(q . (2 + 1))] is non empty V25() set
{(q . 2),(q . (2 + 1))} is non empty set
{(q . 2)} is non empty trivial V47(1) set
{{(q . 2),(q . (2 + 1))},{(q . 2)}} is non empty set
q . 1 is set
e is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
2 * e is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() even Element of NAT
(2 * e) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() ext-real V38() V40() V45() non even Element of NAT
1 + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
q . (1 + 1) is set
[(q . 1),(q . (1 + 1))] is non empty V25() set
{(q . 1),(q . (1 + 1))} is non empty set
{(q . 1)} is non empty trivial V47(1) set
{{(q . 1),(q . (1 + 1))},{(q . 1)}} is non empty set
v is Element of the carrier of (EqRelLATT L)
A9 "\/" v is Element of the carrier of (EqRelLATT L)
v "\/" A9 is Element of the carrier of (EqRelLATT L)
[dq9,Aq9] is non empty V25() Element of [:L,L:]
{dq9,Aq9} is non empty set
{dq9} is non empty trivial V47(1) set
{{dq9,Aq9},{dq9}} is non empty set
[(q . 3),Aq9] is non empty V25() set
{(q . 3),Aq9} is non empty set
{{(q . 3),Aq9},{(q . 3)}} is non empty set
[(q . 3),(q . 2)] is non empty V25() set
{(q . 3),(q . 2)} is non empty set
{{(q . 3),(q . 2)},{(q . 3)}} is non empty set
[(q . 2),(q . 3)] is non empty V25() set
{(q . 2),(q . 3)} is non empty set
{{(q . 2),(q . 3)},{(q . 2)}} is non empty set
[Aq9,(q . 3)] is non empty V25() set
{Aq9,(q . 3)} is non empty set
{{Aq9,(q . 3)},{Aq9}} is non empty set
1 + 2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
q is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
q is Relation-like NAT -defined L -valued Function-like non empty V40() FinSequence-like FinSubsequence-like FinSequence of L
len q is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() ext-real V38() V40() V45() Element of NAT
q . 2 is set
u is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
a is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
2 * a is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() even Element of NAT
(2 * a) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() ext-real V38() V40() V45() non even Element of NAT
q . 1 is set
1 + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
q . (1 + 1) is set
[(q . 1),(q . (1 + 1))] is non empty V25() set
{(q . 1),(q . (1 + 1))} is non empty set
{(q . 1)} is non empty trivial V47(1) set
{{(q . 1),(q . (1 + 1))},{(q . 1)}} is non empty set
2 * u is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() even Element of NAT
2 + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
q . (2 + 1) is set
[(q . 2),(q . (2 + 1))] is non empty V25() set
{(q . 2),(q . (2 + 1))} is non empty set
{(q . 2)} is non empty trivial V47(1) set
{{(q . 2),(q . (2 + 1))},{(q . 2)}} is non empty set
v is Element of the carrier of (EqRelLATT L)
A9 "\/" v is Element of the carrier of (EqRelLATT L)
[(q . 2),Aq9] is non empty V25() set
{(q . 2),Aq9} is non empty set
{{(q . 2),Aq9},{(q . 2)}} is non empty set
[(q . 2),dq9] is non empty V25() set
{(q . 2),dq9} is non empty set
{{(q . 2),dq9},{(q . 2)}} is non empty set
v "\/" A9 is Element of the carrier of (EqRelLATT L)
q . 3 is set
0 + 2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
q is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
q is Relation-like NAT -defined L -valued Function-like non empty V40() FinSequence-like FinSubsequence-like FinSequence of L
len q is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() ext-real V38() V40() V45() Element of NAT
u is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
2 * u is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() even Element of NAT
(2 * u) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() ext-real V38() V40() V45() non even Element of NAT
q . 1 is set
1 + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
q . (1 + 1) is set
[(q . 1),(q . (1 + 1))] is non empty V25() set
{(q . 1),(q . (1 + 1))} is non empty set
{(q . 1)} is non empty trivial V47(1) set
{{(q . 1),(q . (1 + 1))},{(q . 1)}} is non empty set
Q is Element of the carrier of (EqRelLATT L)
A9 "\/" Q is Element of the carrier of (EqRelLATT L)
q . 2 is set
S "\/" FS is Element of the carrier of A
(S "\/" FS) "/\" FS is Element of the carrier of A
FS "/\" FS is Element of the carrier of A
S "\/" (FS "/\" FS) is Element of the carrier of A
L is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of L is non empty set
A is non empty non trivial set
EqRelLATT A is non empty reflexive transitive antisymmetric lower-bounded upper-bounded V227() with_suprema with_infima V297() RelStr
the carrier of (EqRelLATT A) is non empty set
[: the carrier of L, the carrier of (EqRelLATT A):] is non empty set
bool [: the carrier of L, the carrier of (EqRelLATT A):] is non empty V271() set
D is Relation-like the carrier of L -defined the carrier of (EqRelLATT A) -valued Function-like quasi_total monotone meet-preserving join-preserving Element of bool [: the carrier of L, the carrier of (EqRelLATT A):]
Image D is non empty strict reflexive transitive antisymmetric full meet-inheriting join-inheriting with_suprema with_infima SubRelStr of EqRelLATT A
rng D is Element of bool the carrier of (EqRelLATT A)
bool the carrier of (EqRelLATT A) is non empty V271() set
subrelstr (rng D) is strict reflexive transitive antisymmetric full SubRelStr of EqRelLATT A
[:A,A:] is non empty set
bool [:A,A:] is non empty V271() set
the carrier of (Image D) is non empty set
id A is Relation-like A -defined A -valued Function-like one-to-one non empty total V72() V74() V75() V79() Element of bool [:A,A:]
type_of (Image D) is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
corestr D is Relation-like the carrier of L -defined the carrier of (Image D) -valued Function-like quasi_total onto monotone Element of bool [: the carrier of L, the carrier of (Image D):]
[: the carrier of L, the carrier of (Image D):] is non empty set
bool [: the carrier of L, the carrier of (Image D):] is non empty V271() set
rng (corestr D) is Element of bool the carrier of (Image D)
bool the carrier of (Image D) is non empty V271() set
S is Element of the carrier of L
FS is Element of the carrier of L
(corestr D) . S is Element of the carrier of (Image D)
(corestr D) . FS is Element of the carrier of (Image D)
S is Element of the carrier of L
(corestr D) . S is Element of the carrier of (Image D)
FS is Element of the carrier of L
(corestr D) . FS is Element of the carrier of (Image D)
S is Relation-like A -defined A -valued total V72() V74() V79() Element of bool [:A,A:]
L is set
{L} is non empty trivial V47(1) set
{{L}} is non empty trivial V47(1) set
{{L},{{L}}} is non empty set
L \/ {{L},{{L}}} is non empty set
L is set
(L) is set
{L} is non empty trivial V47(1) set
{{L}} is non empty trivial V47(1) set
{{L},{{L}}} is non empty set
L \/ {{L},{{L}}} is non empty set
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
[:L,L, the carrier of A, the carrier of A:] is non empty set
(L) is non empty set
{L} is non empty trivial V47(1) set
{{L}} is non empty trivial V47(1) set
{{L},{{L}}} is non empty set
L \/ {{L},{{L}}} is non empty set
[:(L),(L):] is non empty set
[:[:(L),(L):], the carrier of A:] is non empty set
bool [:[:(L),(L):], the carrier of A:] is non empty V271() set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:L,L:], the carrier of A:]
Bottom A is Element of the carrier of A
"\/" ({},A) is Element of the carrier of A
S is Element of [:L,L, the carrier of A, the carrier of A:]
S `1_4 is Element of L
S `1 is set
(S `1) `1 is set
((S `1) `1) `1 is set
S `2_4 is Element of L
((S `1) `1) `2 is set
D . ((S `1_4),(S `2_4)) is Element of the carrier of A
[(S `1_4),(S `2_4)] is non empty V25() set
{(S `1_4),(S `2_4)} is non empty set
{(S `1_4)} is non empty trivial V47(1) set
{{(S `1_4),(S `2_4)},{(S `1_4)}} is non empty set
D . [(S `1_4),(S `2_4)] is set
S `3_4 is Element of the carrier of A
(S `1) `2 is set
(D . ((S `1_4),(S `2_4))) "\/" (S `3_4) is Element of the carrier of A
S `4_4 is Element of the carrier of A
((D . ((S `1_4),(S `2_4))) "\/" (S `3_4)) "/\" (S `4_4) is Element of the carrier of A
FS is Element of the carrier of A
(D . ((S `1_4),(S `2_4))) "\/" FS is Element of the carrier of A
FS is Element of the carrier of A
((D . ((S `1_4),(S `2_4))) "\/" FS) "/\" FS is Element of the carrier of A
FS is Element of (L)
f is Element of (L)
D . (FS,f) is set
[FS,f] is non empty V25() set
{FS,f} is non empty set
{FS} is non empty trivial V47(1) set
{{FS,f},{FS}} is non empty set
D . [FS,f] is set
FD is Element of L
A9 is Element of L
D . (FD,A9) is Element of the carrier of A
[FD,A9] is non empty V25() set
{FD,A9} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,A9},{FD}} is non empty set
D . [FD,A9] is set
FD is Element of L
D . (FD,(S `1_4)) is Element of the carrier of A
[FD,(S `1_4)] is non empty V25() set
{FD,(S `1_4)} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,(S `1_4)},{FD}} is non empty set
D . [FD,(S `1_4)] is set
(D . (FD,(S `1_4))) "\/" FS is Element of the carrier of A
FD is Element of L
D . (FD,(S `2_4)) is Element of the carrier of A
[FD,(S `2_4)] is non empty V25() set
{FD,(S `2_4)} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,(S `2_4)},{FD}} is non empty set
D . [FD,(S `2_4)] is set
(D . (FD,(S `2_4))) "\/" FS is Element of the carrier of A
FD is Element of L
D . (FD,(S `1_4)) is Element of the carrier of A
[FD,(S `1_4)] is non empty V25() set
{FD,(S `1_4)} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,(S `1_4)},{FD}} is non empty set
D . [FD,(S `1_4)] is set
(D . (FD,(S `1_4))) "\/" FS is Element of the carrier of A
FD is Element of L
D . (FD,(S `2_4)) is Element of the carrier of A
[FD,(S `2_4)] is non empty V25() set
{FD,(S `2_4)} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,(S `2_4)},{FD}} is non empty set
D . [FD,(S `2_4)] is set
(D . (FD,(S `2_4))) "\/" FS is Element of the carrier of A
FS is Relation-like [:(L),(L):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L),(L):], the carrier of A:]
f is Relation-like [:(L),(L):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L),(L):], the carrier of A:]
FD is Element of L
f . ({L},FD) is set
[{L},FD] is non empty V25() set
{{L},FD} is non empty set
{{{L},FD},{{L}}} is non empty set
f . [{L},FD] is set
D . (FD,(S `1_4)) is Element of the carrier of A
[FD,(S `1_4)] is non empty V25() set
{FD,(S `1_4)} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,(S `1_4)},{FD}} is non empty set
D . [FD,(S `1_4)] is set
(D . (FD,(S `1_4))) "\/" FS is Element of the carrier of A
f . ({{L}},FD) is set
[{{L}},FD] is non empty V25() set
{{{L}},FD} is non empty set
{{{L}}} is non empty trivial V47(1) set
{{{{L}},FD},{{{L}}}} is non empty set
f . [{{L}},FD] is set
D . (FD,(S `2_4)) is Element of the carrier of A
[FD,(S `2_4)] is non empty V25() set
{FD,(S `2_4)} is non empty set
{{FD,(S `2_4)},{FD}} is non empty set
D . [FD,(S `2_4)] is set
(D . (FD,(S `2_4))) "\/" FS is Element of the carrier of A
A9 is Element of (L)
f . ({L},A9) is set
[{L},A9] is non empty V25() set
{{L},A9} is non empty set
{{{L},A9},{{L}}} is non empty set
f . [{L},A9] is set
d9 is Element of L
D . (d9,(S `1_4)) is Element of the carrier of A
[d9,(S `1_4)] is non empty V25() set
{d9,(S `1_4)} is non empty set
{d9} is non empty trivial V47(1) set
{{d9,(S `1_4)},{d9}} is non empty set
D . [d9,(S `1_4)] is set
(D . (d9,(S `1_4))) "\/" FS is Element of the carrier of A
f . ({{L}},A9) is set
[{{L}},A9] is non empty V25() set
{{{L}},A9} is non empty set
{{{{L}},A9},{{{L}}}} is non empty set
f . [{{L}},A9] is set
d9 is Element of L
D . (d9,(S `2_4)) is Element of the carrier of A
[d9,(S `2_4)] is non empty V25() set
{d9,(S `2_4)} is non empty set
{d9} is non empty trivial V47(1) set
{{d9,(S `2_4)},{d9}} is non empty set
D . [d9,(S `2_4)] is set
(D . (d9,(S `2_4))) "\/" FS is Element of the carrier of A
f . ({L},{L}) is set
[{L},{L}] is non empty V25() set
{{L},{L}} is non empty set
{{{L},{L}},{{L}}} is non empty set
f . [{L},{L}] is set
f . ({{L}},{{L}}) is set
[{{L}},{{L}}] is non empty V25() set
{{{L}},{{L}}} is non empty set
{{{L}}} is non empty trivial V47(1) set
{{{{L}},{{L}}},{{{L}}}} is non empty set
f . [{{L}},{{L}}] is set
f . ({L},{{L}}) is set
[{L},{{L}}] is non empty V25() set
{{{L},{{L}}},{{L}}} is non empty set
f . [{L},{{L}}] is set
f . ({{L}},{L}) is set
[{{L}},{L}] is non empty V25() set
{{{L}},{L}} is non empty set
{{{{L}},{L}},{{{L}}}} is non empty set
f . [{{L}},{L}] is set
FD is Element of L
A9 is Element of L
f . (FD,A9) is set
[FD,A9] is non empty V25() set
{FD,A9} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,A9},{FD}} is non empty set
f . [FD,A9] is set
D . (FD,A9) is Element of the carrier of A
D . [FD,A9] is set
d9 is Element of (L)
Aq9 is Element of (L)
f . (d9,Aq9) is Element of the carrier of A
[d9,Aq9] is non empty V25() set
{d9,Aq9} is non empty set
{d9} is non empty trivial V47(1) set
{{d9,Aq9},{d9}} is non empty set
f . [d9,Aq9] is set
FD is Element of L
f . (FD,{L}) is set
[FD,{L}] is non empty V25() set
{FD,{L}} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,{L}},{FD}} is non empty set
f . [FD,{L}] is set
D . (FD,(S `1_4)) is Element of the carrier of A
[FD,(S `1_4)] is non empty V25() set
{FD,(S `1_4)} is non empty set
{{FD,(S `1_4)},{FD}} is non empty set
D . [FD,(S `1_4)] is set
(D . (FD,(S `1_4))) "\/" FS is Element of the carrier of A
f . (FD,{{L}}) is set
[FD,{{L}}] is non empty V25() set
{FD,{{L}}} is non empty set
{{FD,{{L}}},{FD}} is non empty set
f . [FD,{{L}}] is set
D . (FD,(S `2_4)) is Element of the carrier of A
[FD,(S `2_4)] is non empty V25() set
{FD,(S `2_4)} is non empty set
{{FD,(S `2_4)},{FD}} is non empty set
D . [FD,(S `2_4)] is set
(D . (FD,(S `2_4))) "\/" FS is Element of the carrier of A
A9 is Element of (L)
f . (A9,{L}) is set
[A9,{L}] is non empty V25() set
{A9,{L}} is non empty set
{A9} is non empty trivial V47(1) set
{{A9,{L}},{A9}} is non empty set
f . [A9,{L}] is set
d9 is Element of L
D . (d9,(S `1_4)) is Element of the carrier of A
[d9,(S `1_4)] is non empty V25() set
{d9,(S `1_4)} is non empty set
{d9} is non empty trivial V47(1) set
{{d9,(S `1_4)},{d9}} is non empty set
D . [d9,(S `1_4)] is set
(D . (d9,(S `1_4))) "\/" FS is Element of the carrier of A
f . (A9,{{L}}) is set
[A9,{{L}}] is non empty V25() set
{A9,{{L}}} is non empty set
{{A9,{{L}}},{A9}} is non empty set
f . [A9,{{L}}] is set
d9 is Element of L
D . (d9,(S `2_4)) is Element of the carrier of A
[d9,(S `2_4)] is non empty V25() set
{d9,(S `2_4)} is non empty set
{d9} is non empty trivial V47(1) set
{{d9,(S `2_4)},{d9}} is non empty set
D . [d9,(S `2_4)] is set
(D . (d9,(S `2_4))) "\/" FS is Element of the carrier of A
FD is Element of L
A9 is Element of L
f . (FD,A9) is set
[FD,A9] is non empty V25() set
{FD,A9} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,A9},{FD}} is non empty set
f . [FD,A9] is set
D . (FD,A9) is Element of the carrier of A
D . [FD,A9] is set
d9 is Element of L
f . (d9,{L}) is set
[d9,{L}] is non empty V25() set
{d9,{L}} is non empty set
{d9} is non empty trivial V47(1) set
{{d9,{L}},{d9}} is non empty set
f . [d9,{L}] is set
D . (d9,(S `1_4)) is Element of the carrier of A
[d9,(S `1_4)] is non empty V25() set
{d9,(S `1_4)} is non empty set
{{d9,(S `1_4)},{d9}} is non empty set
D . [d9,(S `1_4)] is set
(D . (d9,(S `1_4))) "\/" (S `3_4) is Element of the carrier of A
Aq9 is Element of L
f . ({L},Aq9) is set
[{L},Aq9] is non empty V25() set
{{L},Aq9} is non empty set
{{{L},Aq9},{{L}}} is non empty set
f . [{L},Aq9] is set
D . (Aq9,(S `1_4)) is Element of the carrier of A
[Aq9,(S `1_4)] is non empty V25() set
{Aq9,(S `1_4)} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,(S `1_4)},{Aq9}} is non empty set
D . [Aq9,(S `1_4)] is set
(D . (Aq9,(S `1_4))) "\/" (S `3_4) is Element of the carrier of A
dq9 is Element of L
f . (dq9,{{L}}) is set
[dq9,{{L}}] is non empty V25() set
{dq9,{{L}}} is non empty set
{dq9} is non empty trivial V47(1) set
{{dq9,{{L}}},{dq9}} is non empty set
f . [dq9,{{L}}] is set
D . (dq9,(S `2_4)) is Element of the carrier of A
[dq9,(S `2_4)] is non empty V25() set
{dq9,(S `2_4)} is non empty set
{{dq9,(S `2_4)},{dq9}} is non empty set
D . [dq9,(S `2_4)] is set
(D . (dq9,(S `2_4))) "\/" (S `3_4) is Element of the carrier of A
q is Element of L
f . ({{L}},q) is set
[{{L}},q] is non empty V25() set
{{{L}},q} is non empty set
{{{{L}},q},{{{L}}}} is non empty set
f . [{{L}},q] is set
D . (q,(S `2_4)) is Element of the carrier of A
[q,(S `2_4)] is non empty V25() set
{q,(S `2_4)} is non empty set
{q} is non empty trivial V47(1) set
{{q,(S `2_4)},{q}} is non empty set
D . [q,(S `2_4)] is set
(D . (q,(S `2_4))) "\/" (S `3_4) is Element of the carrier of A
f is Relation-like [:(L),(L):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L),(L):], the carrier of A:]
f . ({L},{L}) is set
[{L},{L}] is non empty V25() set
{{L},{L}} is non empty set
{{{L},{L}},{{L}}} is non empty set
f . [{L},{L}] is set
f . ({{L}},{{L}}) is set
[{{L}},{{L}}] is non empty V25() set
{{{L}},{{L}}} is non empty set
{{{L}}} is non empty trivial V47(1) set
{{{{L}},{{L}}},{{{L}}}} is non empty set
f . [{{L}},{{L}}] is set
f . ({L},{{L}}) is set
[{L},{{L}}] is non empty V25() set
{{{L},{{L}}},{{L}}} is non empty set
f . [{L},{{L}}] is set
f . ({{L}},{L}) is set
[{{L}},{L}] is non empty V25() set
{{{L}},{L}} is non empty set
{{{{L}},{L}},{{{L}}}} is non empty set
f . [{{L}},{L}] is set
FS is Relation-like [:(L),(L):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L),(L):], the carrier of A:]
FS . ({L},{L}) is set
FS . [{L},{L}] is set
FS . ({{L}},{{L}}) is set
FS . [{{L}},{{L}}] is set
FS . ({L},{{L}}) is set
FS . [{L},{{L}}] is set
FS . ({{L}},{L}) is set
FS . [{{L}},{L}] is set
f is Element of (L)
FD is Element of (L)
f . (f,FD) is Element of the carrier of A
[f,FD] is non empty V25() set
{f,FD} is non empty set
{f} is non empty trivial V47(1) set
{{f,FD},{f}} is non empty set
f . [f,FD] is set
D . (f,FD) is set
D . [f,FD] is set
FS . (f,FD) is Element of the carrier of A
FS . [f,FD] is set
f . (f,FD) is Element of the carrier of A
[f,FD] is non empty V25() set
{f,FD} is non empty set
{f} is non empty trivial V47(1) set
{{f,FD},{f}} is non empty set
f . [f,FD] is set
A9 is Element of L
D . (A9,(S `1_4)) is Element of the carrier of A
[A9,(S `1_4)] is non empty V25() set
{A9,(S `1_4)} is non empty set
{A9} is non empty trivial V47(1) set
{{A9,(S `1_4)},{A9}} is non empty set
D . [A9,(S `1_4)] is set
(D . (A9,(S `1_4))) "\/" (S `3_4) is Element of the carrier of A
FS . (f,FD) is Element of the carrier of A
FS . [f,FD] is set
f . (f,FD) is Element of the carrier of A
[f,FD] is non empty V25() set
{f,FD} is non empty set
{f} is non empty trivial V47(1) set
{{f,FD},{f}} is non empty set
f . [f,FD] is set
A9 is Element of L
D . (A9,(S `2_4)) is Element of the carrier of A
[A9,(S `2_4)] is non empty V25() set
{A9,(S `2_4)} is non empty set
{A9} is non empty trivial V47(1) set
{{A9,(S `2_4)},{A9}} is non empty set
D . [A9,(S `2_4)] is set
(D . (A9,(S `2_4))) "\/" (S `3_4) is Element of the carrier of A
FS . (f,FD) is Element of the carrier of A
FS . [f,FD] is set
f . (f,FD) is Element of the carrier of A
[f,FD] is non empty V25() set
{f,FD} is non empty set
{f} is non empty trivial V47(1) set
{{f,FD},{f}} is non empty set
f . [f,FD] is set
A9 is Element of L
D . (A9,(S `1_4)) is Element of the carrier of A
[A9,(S `1_4)] is non empty V25() set
{A9,(S `1_4)} is non empty set
{A9} is non empty trivial V47(1) set
{{A9,(S `1_4)},{A9}} is non empty set
D . [A9,(S `1_4)] is set
(D . (A9,(S `1_4))) "\/" (S `3_4) is Element of the carrier of A
FS . (f,FD) is Element of the carrier of A
FS . [f,FD] is set
f . (f,FD) is Element of the carrier of A
[f,FD] is non empty V25() set
{f,FD} is non empty set
{f} is non empty trivial V47(1) set
{{f,FD},{f}} is non empty set
f . [f,FD] is set
FS . (f,FD) is Element of the carrier of A
FS . [f,FD] is set
f . (f,FD) is Element of the carrier of A
[f,FD] is non empty V25() set
{f,FD} is non empty set
{f} is non empty trivial V47(1) set
{{f,FD},{f}} is non empty set
f . [f,FD] is set
FS . (f,FD) is Element of the carrier of A
FS . [f,FD] is set
f . (f,FD) is Element of the carrier of A
[f,FD] is non empty V25() set
{f,FD} is non empty set
{f} is non empty trivial V47(1) set
{{f,FD},{f}} is non empty set
f . [f,FD] is set
A9 is Element of L
D . (A9,(S `2_4)) is Element of the carrier of A
[A9,(S `2_4)] is non empty V25() set
{A9,(S `2_4)} is non empty set
{A9} is non empty trivial V47(1) set
{{A9,(S `2_4)},{A9}} is non empty set
D . [A9,(S `2_4)] is set
(D . (A9,(S `2_4))) "\/" (S `3_4) is Element of the carrier of A
FS . (f,FD) is Element of the carrier of A
FS . [f,FD] is set
f . (f,FD) is Element of the carrier of A
[f,FD] is non empty V25() set
{f,FD} is non empty set
{f} is non empty trivial V47(1) set
{{f,FD},{f}} is non empty set
f . [f,FD] is set
FS . (f,FD) is Element of the carrier of A
FS . [f,FD] is set
f . (f,FD) is Element of the carrier of A
[f,FD] is non empty V25() set
{f,FD} is non empty set
{f} is non empty trivial V47(1) set
{{f,FD},{f}} is non empty set
f . [f,FD] is set
FS . (f,FD) is Element of the carrier of A
FS . [f,FD] is set
L is non empty set
[:L,L:] is non empty set
(L) is non empty set
{L} is non empty trivial V47(1) set
{{L}} is non empty trivial V47(1) set
{{L},{{L}}} is non empty set
L \/ {{L},{{L}}} is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:L,L:], the carrier of A:]
S is Element of [:L,L, the carrier of A, the carrier of A:]
(L,A,D,S) is Relation-like [:(L),(L):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L),(L):], the carrier of A:]
[:(L),(L):] is non empty set
[:[:(L),(L):], the carrier of A:] is non empty set
bool [:[:(L),(L):], the carrier of A:] is non empty V271() set
Bottom A is Element of the carrier of A
"\/" ({},A) is Element of the carrier of A
FS is Element of (L)
(L,A,D,S) . (FS,FS) is Element of the carrier of A
[FS,FS] is non empty V25() set
{FS,FS} is non empty set
{FS} is non empty trivial V47(1) set
{{FS,FS},{FS}} is non empty set
(L,A,D,S) . [FS,FS] is set
FD is Element of L
D . (FD,FD) is Element of the carrier of A
[FD,FD] is non empty V25() set
{FD,FD} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,FD},{FD}} is non empty set
D . [FD,FD] is set
L is non empty set
[:L,L:] is non empty set
(L) is non empty set
{L} is non empty trivial V47(1) set
{{L}} is non empty trivial V47(1) set
{{L},{{L}}} is non empty set
L \/ {{L},{{L}}} is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:L,L:], the carrier of A:]
S is Element of [:L,L, the carrier of A, the carrier of A:]
(L,A,D,S) is Relation-like [:(L),(L):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L),(L):], the carrier of A:]
[:(L),(L):] is non empty set
[:[:(L),(L):], the carrier of A:] is non empty set
bool [:[:(L),(L):], the carrier of A:] is non empty V271() set
S `1_4 is Element of L
S `1 is set
(S `1) `1 is set
((S `1) `1) `1 is set
S `2_4 is Element of L
((S `1) `1) `2 is set
S `3_4 is Element of the carrier of A
(S `1) `2 is set
S `4_4 is Element of the carrier of A
f is Element of (L)
FD is Element of (L)
(L,A,D,S) . (f,FD) is Element of the carrier of A
[f,FD] is non empty V25() set
{f,FD} is non empty set
{f} is non empty trivial V47(1) set
{{f,FD},{f}} is non empty set
(L,A,D,S) . [f,FD] is set
(L,A,D,S) . (FD,f) is Element of the carrier of A
[FD,f] is non empty V25() set
{FD,f} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,f},{FD}} is non empty set
(L,A,D,S) . [FD,f] is set
A9 is Element of L
d9 is Element of L
D . (A9,d9) is Element of the carrier of A
[A9,d9] is non empty V25() set
{A9,d9} is non empty set
{A9} is non empty trivial V47(1) set
{{A9,d9},{A9}} is non empty set
D . [A9,d9] is set
D . (d9,A9) is Element of the carrier of A
[d9,A9] is non empty V25() set
{d9,A9} is non empty set
{d9} is non empty trivial V47(1) set
{{d9,A9},{d9}} is non empty set
D . [d9,A9] is set
A9 is Element of L
D . (A9,(S `1_4)) is Element of the carrier of A
[A9,(S `1_4)] is non empty V25() set
{A9,(S `1_4)} is non empty set
{A9} is non empty trivial V47(1) set
{{A9,(S `1_4)},{A9}} is non empty set
D . [A9,(S `1_4)] is set
(D . (A9,(S `1_4))) "\/" (S `3_4) is Element of the carrier of A
A9 is Element of L
D . (A9,(S `2_4)) is Element of the carrier of A
[A9,(S `2_4)] is non empty V25() set
{A9,(S `2_4)} is non empty set
{A9} is non empty trivial V47(1) set
{{A9,(S `2_4)},{A9}} is non empty set
D . [A9,(S `2_4)] is set
(D . (A9,(S `2_4))) "\/" (S `3_4) is Element of the carrier of A
A9 is Element of L
D . (A9,(S `1_4)) is Element of the carrier of A
[A9,(S `1_4)] is non empty V25() set
{A9,(S `1_4)} is non empty set
{A9} is non empty trivial V47(1) set
{{A9,(S `1_4)},{A9}} is non empty set
D . [A9,(S `1_4)] is set
(D . (A9,(S `1_4))) "\/" (S `3_4) is Element of the carrier of A
D . ((S `1_4),(S `2_4)) is Element of the carrier of A
[(S `1_4),(S `2_4)] is non empty V25() set
{(S `1_4),(S `2_4)} is non empty set
{(S `1_4)} is non empty trivial V47(1) set
{{(S `1_4),(S `2_4)},{(S `1_4)}} is non empty set
D . [(S `1_4),(S `2_4)] is set
(D . ((S `1_4),(S `2_4))) "\/" (S `3_4) is Element of the carrier of A
((D . ((S `1_4),(S `2_4))) "\/" (S `3_4)) "/\" (S `4_4) is Element of the carrier of A
A9 is Element of L
D . (A9,(S `2_4)) is Element of the carrier of A
[A9,(S `2_4)] is non empty V25() set
{A9,(S `2_4)} is non empty set
{A9} is non empty trivial V47(1) set
{{A9,(S `2_4)},{A9}} is non empty set
D . [A9,(S `2_4)] is set
(D . (A9,(S `2_4))) "\/" (S `3_4) is Element of the carrier of A
D . ((S `1_4),(S `2_4)) is Element of the carrier of A
[(S `1_4),(S `2_4)] is non empty V25() set
{(S `1_4),(S `2_4)} is non empty set
{(S `1_4)} is non empty trivial V47(1) set
{{(S `1_4),(S `2_4)},{(S `1_4)}} is non empty set
D . [(S `1_4),(S `2_4)] is set
(D . ((S `1_4),(S `2_4))) "\/" (S `3_4) is Element of the carrier of A
((D . ((S `1_4),(S `2_4))) "\/" (S `3_4)) "/\" (S `4_4) is Element of the carrier of A
L is non empty set
[:L,L:] is non empty set
(L) is non empty set
{L} is non empty trivial V47(1) set
{{L}} is non empty trivial V47(1) set
{{L},{{L}}} is non empty set
L \/ {{L},{{L}}} is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
[:L,L, the carrier of A, the carrier of A:] is non empty set
S is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:L,L:], the carrier of A:]
FS is Element of [:L,L, the carrier of A, the carrier of A:]
FS `1_4 is Element of L
FS `1 is set
(FS `1) `1 is set
((FS `1) `1) `1 is set
FS `2_4 is Element of L
((FS `1) `1) `2 is set
S . ((FS `1_4),(FS `2_4)) is Element of the carrier of A
[(FS `1_4),(FS `2_4)] is non empty V25() set
{(FS `1_4),(FS `2_4)} is non empty set
{(FS `1_4)} is non empty trivial V47(1) set
{{(FS `1_4),(FS `2_4)},{(FS `1_4)}} is non empty set
S . [(FS `1_4),(FS `2_4)] is set
FS `3_4 is Element of the carrier of A
(FS `1) `2 is set
FS `4_4 is Element of the carrier of A
(FS `3_4) "\/" (FS `4_4) is Element of the carrier of A
(L,A,S,FS) is Relation-like [:(L),(L):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L),(L):], the carrier of A:]
[:(L),(L):] is non empty set
[:[:(L),(L):], the carrier of A:] is non empty set
bool [:[:(L),(L):], the carrier of A:] is non empty V271() set
D is non empty set
d9 is Element of (L)
Aq9 is Element of (L)
dq9 is Element of (L)
(L,A,S,FS) . (d9,dq9) is Element of the carrier of A
[d9,dq9] is non empty V25() set
{d9,dq9} is non empty set
{d9} is non empty trivial V47(1) set
{{d9,dq9},{d9}} is non empty set
(L,A,S,FS) . [d9,dq9] is set
(L,A,S,FS) . (d9,Aq9) is Element of the carrier of A
[d9,Aq9] is non empty V25() set
{d9,Aq9} is non empty set
{{d9,Aq9},{d9}} is non empty set
(L,A,S,FS) . [d9,Aq9] is set
(L,A,S,FS) . (Aq9,dq9) is Element of the carrier of A
[Aq9,dq9] is non empty V25() set
{Aq9,dq9} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,dq9},{Aq9}} is non empty set
(L,A,S,FS) . [Aq9,dq9] is set
((L,A,S,FS) . (d9,Aq9)) "\/" ((L,A,S,FS) . (Aq9,dq9)) is Element of the carrier of A
q is Element of L
Q is Element of L
S . (q,Q) is Element of the carrier of A
[q,Q] is non empty V25() set
{q,Q} is non empty set
{q} is non empty trivial V47(1) set
{{q,Q},{q}} is non empty set
S . [q,Q] is set
S . (q,(FS `1_4)) is Element of the carrier of A
[q,(FS `1_4)] is non empty V25() set
{q,(FS `1_4)} is non empty set
{{q,(FS `1_4)},{q}} is non empty set
S . [q,(FS `1_4)] is set
S . (Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is non empty V25() set
{Q,(FS `1_4)} is non empty set
{Q} is non empty trivial V47(1) set
{{Q,(FS `1_4)},{Q}} is non empty set
S . [Q,(FS `1_4)] is set
(S . (q,Q)) "\/" (S . (Q,(FS `1_4))) is Element of the carrier of A
FD is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" FD is Element of the carrier of A
((S . (q,Q)) "\/" (S . (Q,(FS `1_4)))) "\/" FD is Element of the carrier of A
(S . (Q,(FS `1_4))) "\/" FD is Element of the carrier of A
q is Element of L
Q is Element of L
S . (q,Q) is Element of the carrier of A
[q,Q] is non empty V25() set
{q,Q} is non empty set
{q} is non empty trivial V47(1) set
{{q,Q},{q}} is non empty set
S . [q,Q] is set
S . (q,(FS `2_4)) is Element of the carrier of A
[q,(FS `2_4)] is non empty V25() set
{q,(FS `2_4)} is non empty set
{{q,(FS `2_4)},{q}} is non empty set
S . [q,(FS `2_4)] is set
S . (Q,(FS `2_4)) is Element of the carrier of A
[Q,(FS `2_4)] is non empty V25() set
{Q,(FS `2_4)} is non empty set
{Q} is non empty trivial V47(1) set
{{Q,(FS `2_4)},{Q}} is non empty set
S . [Q,(FS `2_4)] is set
(S . (q,Q)) "\/" (S . (Q,(FS `2_4))) is Element of the carrier of A
FD is Element of the carrier of A
(S . (q,(FS `2_4))) "\/" FD is Element of the carrier of A
((S . (q,Q)) "\/" (S . (Q,(FS `2_4)))) "\/" FD is Element of the carrier of A
(S . (Q,(FS `2_4))) "\/" FD is Element of the carrier of A
d9 is Element of (L)
Aq9 is Element of (L)
dq9 is Element of (L)
(L,A,S,FS) . (d9,dq9) is Element of the carrier of A
[d9,dq9] is non empty V25() set
{d9,dq9} is non empty set
{d9} is non empty trivial V47(1) set
{{d9,dq9},{d9}} is non empty set
(L,A,S,FS) . [d9,dq9] is set
(L,A,S,FS) . (d9,Aq9) is Element of the carrier of A
[d9,Aq9] is non empty V25() set
{d9,Aq9} is non empty set
{{d9,Aq9},{d9}} is non empty set
(L,A,S,FS) . [d9,Aq9] is set
(L,A,S,FS) . (Aq9,dq9) is Element of the carrier of A
[Aq9,dq9] is non empty V25() set
{Aq9,dq9} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,dq9},{Aq9}} is non empty set
(L,A,S,FS) . [Aq9,dq9] is set
((L,A,S,FS) . (d9,Aq9)) "\/" ((L,A,S,FS) . (Aq9,dq9)) is Element of the carrier of A
Bottom A is Element of the carrier of A
"\/" ({},A) is Element of the carrier of A
(Bottom A) "\/" ((L,A,S,FS) . (d9,Aq9)) is Element of the carrier of A
FD is Element of the carrier of A
FD "\/" (S . ((FS `1_4),(FS `2_4))) is Element of the carrier of A
(S . ((FS `1_4),(FS `2_4))) "\/" FD is Element of the carrier of A
A9 is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" A9 is Element of the carrier of A
FD "\/" (((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" A9) is Element of the carrier of A
FD "\/" A9 is Element of the carrier of A
(FD "\/" A9) "/\" (FD "\/" (S . ((FS `1_4),(FS `2_4)))) is Element of the carrier of A
q is Element of L
S . (q,(FS `2_4)) is Element of the carrier of A
[q,(FS `2_4)] is non empty V25() set
{q,(FS `2_4)} is non empty set
{q} is non empty trivial V47(1) set
{{q,(FS `2_4)},{q}} is non empty set
S . [q,(FS `2_4)] is set
S . (q,(FS `1_4)) is Element of the carrier of A
[q,(FS `1_4)] is non empty V25() set
{q,(FS `1_4)} is non empty set
{{q,(FS `1_4)},{q}} is non empty set
S . [q,(FS `1_4)] is set
(S . (q,(FS `1_4))) "\/" (S . ((FS `1_4),(FS `2_4))) is Element of the carrier of A
(S . (q,(FS `2_4))) "\/" FD is Element of the carrier of A
((S . (q,(FS `1_4))) "\/" (S . ((FS `1_4),(FS `2_4)))) "\/" FD is Element of the carrier of A
(FD "\/" A9) "\/" FD is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((S . ((FS `1_4),(FS `2_4))) "\/" FD) is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((FD "\/" A9) "\/" FD) is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" (((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((S . ((FS `1_4),(FS `2_4))) "\/" FD)) is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" (((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((FD "\/" A9) "\/" FD)) is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" FD is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" ((FD "\/" A9) "/\" (FD "\/" (S . ((FS `1_4),(FS `2_4))))) is Element of the carrier of A
FD "\/" FD is Element of the carrier of A
(FD "\/" FD) "\/" A9 is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((FD "\/" FD) "\/" A9) is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" (((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((FD "\/" FD) "\/" A9)) is Element of the carrier of A
FD is Element of the carrier of A
FD "\/" (S . ((FS `1_4),(FS `2_4))) is Element of the carrier of A
(S . ((FS `1_4),(FS `2_4))) "\/" FD is Element of the carrier of A
A9 is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" A9 is Element of the carrier of A
FD "\/" (((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" A9) is Element of the carrier of A
FD "\/" A9 is Element of the carrier of A
(FD "\/" A9) "/\" (FD "\/" (S . ((FS `1_4),(FS `2_4)))) is Element of the carrier of A
(FD "\/" A9) "\/" FD is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((S . ((FS `1_4),(FS `2_4))) "\/" FD) is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((FD "\/" A9) "\/" FD) is Element of the carrier of A
q is Element of L
S . (q,(FS `2_4)) is Element of the carrier of A
[q,(FS `2_4)] is non empty V25() set
{q,(FS `2_4)} is non empty set
{q} is non empty trivial V47(1) set
{{q,(FS `2_4)},{q}} is non empty set
S . [q,(FS `2_4)] is set
(S . (q,(FS `2_4))) "\/" (((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((S . ((FS `1_4),(FS `2_4))) "\/" FD)) is Element of the carrier of A
(S . (q,(FS `2_4))) "\/" (((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((FD "\/" A9) "\/" FD)) is Element of the carrier of A
S . ((FS `2_4),(FS `1_4)) is Element of the carrier of A
[(FS `2_4),(FS `1_4)] is non empty V25() set
{(FS `2_4),(FS `1_4)} is non empty set
{(FS `2_4)} is non empty trivial V47(1) set
{{(FS `2_4),(FS `1_4)},{(FS `2_4)}} is non empty set
S . [(FS `2_4),(FS `1_4)] is set
S . (q,(FS `1_4)) is Element of the carrier of A
[q,(FS `1_4)] is non empty V25() set
{q,(FS `1_4)} is non empty set
{{q,(FS `1_4)},{q}} is non empty set
S . [q,(FS `1_4)] is set
(S . (q,(FS `2_4))) "\/" (S . ((FS `1_4),(FS `2_4))) is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" FD is Element of the carrier of A
((S . (q,(FS `2_4))) "\/" (S . ((FS `1_4),(FS `2_4)))) "\/" FD is Element of the carrier of A
(S . (q,(FS `2_4))) "\/" FD is Element of the carrier of A
(S . (q,(FS `2_4))) "\/" ((FD "\/" A9) "/\" (FD "\/" (S . ((FS `1_4),(FS `2_4))))) is Element of the carrier of A
FD "\/" FD is Element of the carrier of A
(FD "\/" FD) "\/" A9 is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((FD "\/" FD) "\/" A9) is Element of the carrier of A
(S . (q,(FS `2_4))) "\/" (((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((FD "\/" FD) "\/" A9)) is Element of the carrier of A
Bottom A is Element of the carrier of A
"\/" ({},A) is Element of the carrier of A
(Bottom A) "\/" ((L,A,S,FS) . (d9,Aq9)) is Element of the carrier of A
d9 is Element of (L)
Aq9 is Element of (L)
dq9 is Element of (L)
(L,A,S,FS) . (d9,dq9) is Element of the carrier of A
[d9,dq9] is non empty V25() set
{d9,dq9} is non empty set
{d9} is non empty trivial V47(1) set
{{d9,dq9},{d9}} is non empty set
(L,A,S,FS) . [d9,dq9] is set
(L,A,S,FS) . (d9,Aq9) is Element of the carrier of A
[d9,Aq9] is non empty V25() set
{d9,Aq9} is non empty set
{{d9,Aq9},{d9}} is non empty set
(L,A,S,FS) . [d9,Aq9] is set
(L,A,S,FS) . (Aq9,dq9) is Element of the carrier of A
[Aq9,dq9] is non empty V25() set
{Aq9,dq9} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,dq9},{Aq9}} is non empty set
(L,A,S,FS) . [Aq9,dq9] is set
((L,A,S,FS) . (d9,Aq9)) "\/" ((L,A,S,FS) . (Aq9,dq9)) is Element of the carrier of A
Bottom A is Element of the carrier of A
"\/" ({},A) is Element of the carrier of A
q is Element of L
S . (q,(FS `1_4)) is Element of the carrier of A
[q,(FS `1_4)] is non empty V25() set
{q,(FS `1_4)} is non empty set
{q} is non empty trivial V47(1) set
{{q,(FS `1_4)},{q}} is non empty set
S . [q,(FS `1_4)] is set
S . ((FS `1_4),q) is Element of the carrier of A
[(FS `1_4),q] is non empty V25() set
{(FS `1_4),q} is non empty set
{{(FS `1_4),q},{(FS `1_4)}} is non empty set
S . [(FS `1_4),q] is set
S . (q,(FS `2_4)) is Element of the carrier of A
[q,(FS `2_4)] is non empty V25() set
{q,(FS `2_4)} is non empty set
{{q,(FS `2_4)},{q}} is non empty set
S . [q,(FS `2_4)] is set
(S . (q,(FS `1_4))) "\/" (S . (q,(FS `2_4))) is Element of the carrier of A
FD is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" FD is Element of the carrier of A
(S . (q,(FS `2_4))) "\/" FD is Element of the carrier of A
((S . (q,(FS `1_4))) "\/" FD) "\/" ((S . (q,(FS `2_4))) "\/" FD) is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" ((S . (q,(FS `2_4))) "\/" FD) is Element of the carrier of A
((S . (q,(FS `1_4))) "\/" ((S . (q,(FS `2_4))) "\/" FD)) "\/" FD is Element of the carrier of A
((S . (q,(FS `1_4))) "\/" (S . (q,(FS `2_4)))) "\/" FD is Element of the carrier of A
(((S . (q,(FS `1_4))) "\/" (S . (q,(FS `2_4)))) "\/" FD) "\/" FD is Element of the carrier of A
FD "\/" FD is Element of the carrier of A
((S . (q,(FS `1_4))) "\/" (S . (q,(FS `2_4)))) "\/" (FD "\/" FD) is Element of the carrier of A
(S . ((FS `1_4),(FS `2_4))) "\/" FD is Element of the carrier of A
A9 is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" A9 is Element of the carrier of A
q is Element of L
S . (q,(FS `1_4)) is Element of the carrier of A
[q,(FS `1_4)] is non empty V25() set
{q,(FS `1_4)} is non empty set
{q} is non empty trivial V47(1) set
{{q,(FS `1_4)},{q}} is non empty set
S . [q,(FS `1_4)] is set
S . ((FS `1_4),q) is Element of the carrier of A
[(FS `1_4),q] is non empty V25() set
{(FS `1_4),q} is non empty set
{{(FS `1_4),q},{(FS `1_4)}} is non empty set
S . [(FS `1_4),q] is set
S . (q,(FS `2_4)) is Element of the carrier of A
[q,(FS `2_4)] is non empty V25() set
{q,(FS `2_4)} is non empty set
{{q,(FS `2_4)},{q}} is non empty set
S . [q,(FS `2_4)] is set
(S . (q,(FS `1_4))) "\/" (S . (q,(FS `2_4))) is Element of the carrier of A
FD is Element of the carrier of A
(S . (q,(FS `2_4))) "\/" FD is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" FD is Element of the carrier of A
((S . (q,(FS `1_4))) "\/" FD) "\/" ((S . (q,(FS `2_4))) "\/" FD) is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" ((S . (q,(FS `2_4))) "\/" FD) is Element of the carrier of A
((S . (q,(FS `1_4))) "\/" ((S . (q,(FS `2_4))) "\/" FD)) "\/" FD is Element of the carrier of A
((S . (q,(FS `1_4))) "\/" (S . (q,(FS `2_4)))) "\/" FD is Element of the carrier of A
(((S . (q,(FS `1_4))) "\/" (S . (q,(FS `2_4)))) "\/" FD) "\/" FD is Element of the carrier of A
FD "\/" FD is Element of the carrier of A
((S . (q,(FS `1_4))) "\/" (S . (q,(FS `2_4)))) "\/" (FD "\/" FD) is Element of the carrier of A
(S . ((FS `1_4),(FS `2_4))) "\/" FD is Element of the carrier of A
A9 is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" A9 is Element of the carrier of A
Bottom A is Element of the carrier of A
"\/" ({},A) is Element of the carrier of A
d9 is Element of (L)
Aq9 is Element of (L)
dq9 is Element of (L)
(L,A,S,FS) . (d9,dq9) is Element of the carrier of A
[d9,dq9] is non empty V25() set
{d9,dq9} is non empty set
{d9} is non empty trivial V47(1) set
{{d9,dq9},{d9}} is non empty set
(L,A,S,FS) . [d9,dq9] is set
(L,A,S,FS) . (d9,Aq9) is Element of the carrier of A
[d9,Aq9] is non empty V25() set
{d9,Aq9} is non empty set
{{d9,Aq9},{d9}} is non empty set
(L,A,S,FS) . [d9,Aq9] is set
(L,A,S,FS) . (Aq9,dq9) is Element of the carrier of A
[Aq9,dq9] is non empty V25() set
{Aq9,dq9} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,dq9},{Aq9}} is non empty set
(L,A,S,FS) . [Aq9,dq9] is set
((L,A,S,FS) . (d9,Aq9)) "\/" ((L,A,S,FS) . (Aq9,dq9)) is Element of the carrier of A
Bottom A is Element of the carrier of A
"\/" ({},A) is Element of the carrier of A
Bottom A is Element of the carrier of A
"\/" ({},A) is Element of the carrier of A
(Bottom A) "\/" ((L,A,S,FS) . (d9,dq9)) is Element of the carrier of A
FD is Element of the carrier of A
(S . ((FS `1_4),(FS `2_4))) "\/" FD is Element of the carrier of A
A9 is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" A9 is Element of the carrier of A
(Bottom A) "\/" (((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" A9) is Element of the carrier of A
Bottom A is Element of the carrier of A
"\/" ({},A) is Element of the carrier of A
FD is Element of the carrier of A
(S . ((FS `1_4),(FS `2_4))) "\/" FD is Element of the carrier of A
A9 is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" A9 is Element of the carrier of A
(((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" A9) "\/" ((L,A,S,FS) . (Aq9,dq9)) is Element of the carrier of A
Bottom A is Element of the carrier of A
"\/" ({},A) is Element of the carrier of A
(Bottom A) "\/" (((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" A9) is Element of the carrier of A
FD is Element of the carrier of A
(S . ((FS `1_4),(FS `2_4))) "\/" FD is Element of the carrier of A
A9 is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" A9 is Element of the carrier of A
(((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" A9) "\/" ((L,A,S,FS) . (Aq9,dq9)) is Element of the carrier of A
Bottom A is Element of the carrier of A
"\/" ({},A) is Element of the carrier of A
(Bottom A) "\/" (((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" A9) is Element of the carrier of A
Bottom A is Element of the carrier of A
"\/" ({},A) is Element of the carrier of A
Bottom A is Element of the carrier of A
"\/" ({},A) is Element of the carrier of A
(Bottom A) "\/" ((L,A,S,FS) . (d9,dq9)) is Element of the carrier of A
FD is Element of the carrier of A
(S . ((FS `1_4),(FS `2_4))) "\/" FD is Element of the carrier of A
A9 is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" A9 is Element of the carrier of A
(Bottom A) "\/" (((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" A9) is Element of the carrier of A
Bottom A is Element of the carrier of A
"\/" ({},A) is Element of the carrier of A
d9 is Element of (L)
Aq9 is Element of (L)
dq9 is Element of (L)
(L,A,S,FS) . (d9,dq9) is Element of the carrier of A
[d9,dq9] is non empty V25() set
{d9,dq9} is non empty set
{d9} is non empty trivial V47(1) set
{{d9,dq9},{d9}} is non empty set
(L,A,S,FS) . [d9,dq9] is set
(L,A,S,FS) . (d9,Aq9) is Element of the carrier of A
[d9,Aq9] is non empty V25() set
{d9,Aq9} is non empty set
{{d9,Aq9},{d9}} is non empty set
(L,A,S,FS) . [d9,Aq9] is set
(L,A,S,FS) . (Aq9,dq9) is Element of the carrier of A
[Aq9,dq9] is non empty V25() set
{Aq9,dq9} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,dq9},{Aq9}} is non empty set
(L,A,S,FS) . [Aq9,dq9] is set
((L,A,S,FS) . (d9,Aq9)) "\/" ((L,A,S,FS) . (Aq9,dq9)) is Element of the carrier of A
Bottom A is Element of the carrier of A
"\/" ({},A) is Element of the carrier of A
(Bottom A) "\/" ((L,A,S,FS) . (Aq9,dq9)) is Element of the carrier of A
FD is Element of the carrier of A
FD "\/" (S . ((FS `1_4),(FS `2_4))) is Element of the carrier of A
(S . ((FS `1_4),(FS `2_4))) "\/" FD is Element of the carrier of A
A9 is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" A9 is Element of the carrier of A
FD "\/" (((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" A9) is Element of the carrier of A
FD "\/" A9 is Element of the carrier of A
(FD "\/" A9) "/\" (FD "\/" (S . ((FS `1_4),(FS `2_4)))) is Element of the carrier of A
q is Element of L
S . (q,(FS `2_4)) is Element of the carrier of A
[q,(FS `2_4)] is non empty V25() set
{q,(FS `2_4)} is non empty set
{q} is non empty trivial V47(1) set
{{q,(FS `2_4)},{q}} is non empty set
S . [q,(FS `2_4)] is set
S . (q,(FS `1_4)) is Element of the carrier of A
[q,(FS `1_4)] is non empty V25() set
{q,(FS `1_4)} is non empty set
{{q,(FS `1_4)},{q}} is non empty set
S . [q,(FS `1_4)] is set
(S . (q,(FS `1_4))) "\/" (S . ((FS `1_4),(FS `2_4))) is Element of the carrier of A
(S . (q,(FS `2_4))) "\/" FD is Element of the carrier of A
((S . (q,(FS `1_4))) "\/" (S . ((FS `1_4),(FS `2_4)))) "\/" FD is Element of the carrier of A
(FD "\/" A9) "\/" FD is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((S . ((FS `1_4),(FS `2_4))) "\/" FD) is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((FD "\/" A9) "\/" FD) is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" (((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((S . ((FS `1_4),(FS `2_4))) "\/" FD)) is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" (((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((FD "\/" A9) "\/" FD)) is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" FD is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" ((FD "\/" A9) "/\" (FD "\/" (S . ((FS `1_4),(FS `2_4))))) is Element of the carrier of A
FD "\/" FD is Element of the carrier of A
(FD "\/" FD) "\/" A9 is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((FD "\/" FD) "\/" A9) is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" (((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((FD "\/" FD) "\/" A9)) is Element of the carrier of A
FD is Element of the carrier of A
FD "\/" (S . ((FS `1_4),(FS `2_4))) is Element of the carrier of A
(S . ((FS `1_4),(FS `2_4))) "\/" FD is Element of the carrier of A
A9 is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" A9 is Element of the carrier of A
FD "\/" (((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" A9) is Element of the carrier of A
FD "\/" A9 is Element of the carrier of A
(FD "\/" A9) "/\" (FD "\/" (S . ((FS `1_4),(FS `2_4)))) is Element of the carrier of A
(FD "\/" A9) "\/" FD is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((S . ((FS `1_4),(FS `2_4))) "\/" FD) is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((FD "\/" A9) "\/" FD) is Element of the carrier of A
q is Element of L
S . (q,(FS `2_4)) is Element of the carrier of A
[q,(FS `2_4)] is non empty V25() set
{q,(FS `2_4)} is non empty set
{q} is non empty trivial V47(1) set
{{q,(FS `2_4)},{q}} is non empty set
S . [q,(FS `2_4)] is set
(S . (q,(FS `2_4))) "\/" (((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((S . ((FS `1_4),(FS `2_4))) "\/" FD)) is Element of the carrier of A
(S . (q,(FS `2_4))) "\/" (((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((FD "\/" A9) "\/" FD)) is Element of the carrier of A
S . ((FS `2_4),(FS `1_4)) is Element of the carrier of A
[(FS `2_4),(FS `1_4)] is non empty V25() set
{(FS `2_4),(FS `1_4)} is non empty set
{(FS `2_4)} is non empty trivial V47(1) set
{{(FS `2_4),(FS `1_4)},{(FS `2_4)}} is non empty set
S . [(FS `2_4),(FS `1_4)] is set
S . (q,(FS `1_4)) is Element of the carrier of A
[q,(FS `1_4)] is non empty V25() set
{q,(FS `1_4)} is non empty set
{{q,(FS `1_4)},{q}} is non empty set
S . [q,(FS `1_4)] is set
(S . (q,(FS `2_4))) "\/" (S . ((FS `1_4),(FS `2_4))) is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" FD is Element of the carrier of A
((S . (q,(FS `2_4))) "\/" (S . ((FS `1_4),(FS `2_4)))) "\/" FD is Element of the carrier of A
(S . (q,(FS `2_4))) "\/" FD is Element of the carrier of A
(S . (q,(FS `2_4))) "\/" ((FD "\/" A9) "/\" (FD "\/" (S . ((FS `1_4),(FS `2_4))))) is Element of the carrier of A
FD "\/" FD is Element of the carrier of A
(FD "\/" FD) "\/" A9 is Element of the carrier of A
((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((FD "\/" FD) "\/" A9) is Element of the carrier of A
(S . (q,(FS `2_4))) "\/" (((S . ((FS `1_4),(FS `2_4))) "\/" FD) "/\" ((FD "\/" FD) "\/" A9)) is Element of the carrier of A
Bottom A is Element of the carrier of A
"\/" ({},A) is Element of the carrier of A
(Bottom A) "\/" ((L,A,S,FS) . (Aq9,dq9)) is Element of the carrier of A
d9 is Element of (L)
Aq9 is Element of (L)
dq9 is Element of (L)
(L,A,S,FS) . (d9,dq9) is Element of the carrier of A
[d9,dq9] is non empty V25() set
{d9,dq9} is non empty set
{d9} is non empty trivial V47(1) set
{{d9,dq9},{d9}} is non empty set
(L,A,S,FS) . [d9,dq9] is set
(L,A,S,FS) . (d9,Aq9) is Element of the carrier of A
[d9,Aq9] is non empty V25() set
{d9,Aq9} is non empty set
{{d9,Aq9},{d9}} is non empty set
(L,A,S,FS) . [d9,Aq9] is set
(L,A,S,FS) . (Aq9,dq9) is Element of the carrier of A
[Aq9,dq9] is non empty V25() set
{Aq9,dq9} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,dq9},{Aq9}} is non empty set
(L,A,S,FS) . [Aq9,dq9] is set
((L,A,S,FS) . (d9,Aq9)) "\/" ((L,A,S,FS) . (Aq9,dq9)) is Element of the carrier of A
Q is Element of L
S . (Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is non empty V25() set
{Q,(FS `1_4)} is non empty set
{Q} is non empty trivial V47(1) set
{{Q,(FS `1_4)},{Q}} is non empty set
S . [Q,(FS `1_4)] is set
q is Element of L
S . (Q,q) is Element of the carrier of A
[Q,q] is non empty V25() set
{Q,q} is non empty set
{{Q,q},{Q}} is non empty set
S . [Q,q] is set
S . (q,(FS `1_4)) is Element of the carrier of A
[q,(FS `1_4)] is non empty V25() set
{q,(FS `1_4)} is non empty set
{q} is non empty trivial V47(1) set
{{q,(FS `1_4)},{q}} is non empty set
S . [q,(FS `1_4)] is set
(S . (Q,q)) "\/" (S . (q,(FS `1_4))) is Element of the carrier of A
S . (q,Q) is Element of the carrier of A
[q,Q] is non empty V25() set
{q,Q} is non empty set
{{q,Q},{q}} is non empty set
S . [q,Q] is set
(S . (q,Q)) "\/" (S . (q,(FS `1_4))) is Element of the carrier of A
FD is Element of the carrier of A
(S . (Q,(FS `1_4))) "\/" FD is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" (S . (q,Q)) is Element of the carrier of A
((S . (q,(FS `1_4))) "\/" (S . (q,Q))) "\/" FD is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" FD is Element of the carrier of A
((S . (q,(FS `1_4))) "\/" FD) "\/" (S . (q,Q)) is Element of the carrier of A
Q is Element of L
S . (Q,(FS `2_4)) is Element of the carrier of A
[Q,(FS `2_4)] is non empty V25() set
{Q,(FS `2_4)} is non empty set
{Q} is non empty trivial V47(1) set
{{Q,(FS `2_4)},{Q}} is non empty set
S . [Q,(FS `2_4)] is set
q is Element of L
S . (Q,q) is Element of the carrier of A
[Q,q] is non empty V25() set
{Q,q} is non empty set
{{Q,q},{Q}} is non empty set
S . [Q,q] is set
S . (q,(FS `2_4)) is Element of the carrier of A
[q,(FS `2_4)] is non empty V25() set
{q,(FS `2_4)} is non empty set
{q} is non empty trivial V47(1) set
{{q,(FS `2_4)},{q}} is non empty set
S . [q,(FS `2_4)] is set
(S . (Q,q)) "\/" (S . (q,(FS `2_4))) is Element of the carrier of A
S . (q,Q) is Element of the carrier of A
[q,Q] is non empty V25() set
{q,Q} is non empty set
{{q,Q},{q}} is non empty set
S . [q,Q] is set
(S . (q,Q)) "\/" (S . (q,(FS `2_4))) is Element of the carrier of A
FD is Element of the carrier of A
(S . (Q,(FS `2_4))) "\/" FD is Element of the carrier of A
(S . (q,(FS `2_4))) "\/" (S . (q,Q)) is Element of the carrier of A
((S . (q,(FS `2_4))) "\/" (S . (q,Q))) "\/" FD is Element of the carrier of A
(S . (q,(FS `2_4))) "\/" FD is Element of the carrier of A
((S . (q,(FS `2_4))) "\/" FD) "\/" (S . (q,Q)) is Element of the carrier of A
d9 is Element of (L)
Aq9 is Element of (L)
dq9 is Element of (L)
(L,A,S,FS) . (d9,dq9) is Element of the carrier of A
[d9,dq9] is non empty V25() set
{d9,dq9} is non empty set
{d9} is non empty trivial V47(1) set
{{d9,dq9},{d9}} is non empty set
(L,A,S,FS) . [d9,dq9] is set
(L,A,S,FS) . (d9,Aq9) is Element of the carrier of A
[d9,Aq9] is non empty V25() set
{d9,Aq9} is non empty set
{{d9,Aq9},{d9}} is non empty set
(L,A,S,FS) . [d9,Aq9] is set
(L,A,S,FS) . (Aq9,dq9) is Element of the carrier of A
[Aq9,dq9] is non empty V25() set
{Aq9,dq9} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,dq9},{Aq9}} is non empty set
(L,A,S,FS) . [Aq9,dq9] is set
((L,A,S,FS) . (d9,Aq9)) "\/" ((L,A,S,FS) . (Aq9,dq9)) is Element of the carrier of A
q is Element of L
Q is Element of L
S . (q,Q) is Element of the carrier of A
[q,Q] is non empty V25() set
{q,Q} is non empty set
{q} is non empty trivial V47(1) set
{{q,Q},{q}} is non empty set
S . [q,Q] is set
S . (q,(FS `1_4)) is Element of the carrier of A
[q,(FS `1_4)] is non empty V25() set
{q,(FS `1_4)} is non empty set
{{q,(FS `1_4)},{q}} is non empty set
S . [q,(FS `1_4)] is set
S . ((FS `1_4),Q) is Element of the carrier of A
[(FS `1_4),Q] is non empty V25() set
{(FS `1_4),Q} is non empty set
{{(FS `1_4),Q},{(FS `1_4)}} is non empty set
S . [(FS `1_4),Q] is set
(S . (q,(FS `1_4))) "\/" (S . ((FS `1_4),Q)) is Element of the carrier of A
S . (Q,(FS `1_4)) is Element of the carrier of A
[Q,(FS `1_4)] is non empty V25() set
{Q,(FS `1_4)} is non empty set
{Q} is non empty trivial V47(1) set
{{Q,(FS `1_4)},{Q}} is non empty set
S . [Q,(FS `1_4)] is set
(S . (q,(FS `1_4))) "\/" (S . (Q,(FS `1_4))) is Element of the carrier of A
FD is Element of the carrier of A
((S . (q,(FS `1_4))) "\/" (S . (Q,(FS `1_4)))) "\/" FD is Element of the carrier of A
(S . (Q,(FS `1_4))) "\/" FD is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" ((S . (Q,(FS `1_4))) "\/" FD) is Element of the carrier of A
FD "\/" FD is Element of the carrier of A
(S . (Q,(FS `1_4))) "\/" (FD "\/" FD) is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" ((S . (Q,(FS `1_4))) "\/" (FD "\/" FD)) is Element of the carrier of A
((S . (Q,(FS `1_4))) "\/" FD) "\/" FD is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" (((S . (Q,(FS `1_4))) "\/" FD) "\/" FD) is Element of the carrier of A
(S . (q,(FS `1_4))) "\/" FD is Element of the carrier of A
((S . (q,(FS `1_4))) "\/" FD) "\/" ((S . (Q,(FS `1_4))) "\/" FD) is Element of the carrier of A
q is Element of L
Q is Element of L
S . (q,Q) is Element of the carrier of A
[q,Q] is non empty V25() set
{q,Q} is non empty set
{q} is non empty trivial V47(1) set
{{q,Q},{q}} is non empty set
S . [q,Q] is set
S . (q,(FS `2_4)) is Element of the carrier of A
[q,(FS `2_4)] is non empty V25() set
{q,(FS `2_4)} is non empty set
{{q,(FS `2_4)},{q}} is non empty set
S . [q,(FS `2_4)] is set
S . ((FS `2_4),Q) is Element of the carrier of A
[(FS `2_4),Q] is non empty V25() set
{(FS `2_4),Q} is non empty set
{(FS `2_4)} is non empty trivial V47(1) set
{{(FS `2_4),Q},{(FS `2_4)}} is non empty set
S . [(FS `2_4),Q] is set
(S . (q,(FS `2_4))) "\/" (S . ((FS `2_4),Q)) is Element of the carrier of A
S . (Q,(FS `2_4)) is Element of the carrier of A
[Q,(FS `2_4)] is non empty V25() set
{Q,(FS `2_4)} is non empty set
{Q} is non empty trivial V47(1) set
{{Q,(FS `2_4)},{Q}} is non empty set
S . [Q,(FS `2_4)] is set
(S . (q,(FS `2_4))) "\/" (S . (Q,(FS `2_4))) is Element of the carrier of A
FD is Element of the carrier of A
((S . (q,(FS `2_4))) "\/" (S . (Q,(FS `2_4)))) "\/" FD is Element of the carrier of A
(S . (Q,(FS `2_4))) "\/" FD is Element of the carrier of A
(S . (q,(FS `2_4))) "\/" ((S . (Q,(FS `2_4))) "\/" FD) is Element of the carrier of A
FD "\/" FD is Element of the carrier of A
(S . (Q,(FS `2_4))) "\/" (FD "\/" FD) is Element of the carrier of A
(S . (q,(FS `2_4))) "\/" ((S . (Q,(FS `2_4))) "\/" (FD "\/" FD)) is Element of the carrier of A
((S . (Q,(FS `2_4))) "\/" FD) "\/" FD is Element of the carrier of A
(S . (q,(FS `2_4))) "\/" (((S . (Q,(FS `2_4))) "\/" FD) "\/" FD) is Element of the carrier of A
(S . (q,(FS `2_4))) "\/" FD is Element of the carrier of A
((S . (q,(FS `2_4))) "\/" FD) "\/" ((S . (Q,(FS `2_4))) "\/" FD) is Element of the carrier of A
d9 is Element of (L)
Aq9 is Element of (L)
dq9 is Element of (L)
(L,A,S,FS) . (d9,dq9) is Element of the carrier of A
[d9,dq9] is non empty V25() set
{d9,dq9} is non empty set
{d9} is non empty trivial V47(1) set
{{d9,dq9},{d9}} is non empty set
(L,A,S,FS) . [d9,dq9] is set
(L,A,S,FS) . (d9,Aq9) is Element of the carrier of A
[d9,Aq9] is non empty V25() set
{d9,Aq9} is non empty set
{{d9,Aq9},{d9}} is non empty set
(L,A,S,FS) . [d9,Aq9] is set
(L,A,S,FS) . (Aq9,dq9) is Element of the carrier of A
[Aq9,dq9] is non empty V25() set
{Aq9,dq9} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,dq9},{Aq9}} is non empty set
(L,A,S,FS) . [Aq9,dq9] is set
((L,A,S,FS) . (d9,Aq9)) "\/" ((L,A,S,FS) . (Aq9,dq9)) is Element of the carrier of A
Q is Element of L
u is Element of L
S . (Q,u) is Element of the carrier of A
[Q,u] is non empty V25() set
{Q,u} is non empty set
{Q} is non empty trivial V47(1) set
{{Q,u},{Q}} is non empty set
S . [Q,u] is set
q is Element of L
S . (q,u) is Element of the carrier of A
[q,u] is non empty V25() set
{q,u} is non empty set
{q} is non empty trivial V47(1) set
{{q,u},{q}} is non empty set
S . [q,u] is set
S . (q,Q) is Element of the carrier of A
[q,Q] is non empty V25() set
{q,Q} is non empty set
{{q,Q},{q}} is non empty set
S . [q,Q] is set
d9 is Element of (L)
dq9 is Element of (L)
(L,A,S,FS) . (d9,dq9) is Element of the carrier of A
[d9,dq9] is non empty V25() set
{d9,dq9} is non empty set
{d9} is non empty trivial V47(1) set
{{d9,dq9},{d9}} is non empty set
(L,A,S,FS) . [d9,dq9] is set
Aq9 is Element of (L)
(L,A,S,FS) . (d9,Aq9) is Element of the carrier of A
[d9,Aq9] is non empty V25() set
{d9,Aq9} is non empty set
{{d9,Aq9},{d9}} is non empty set
(L,A,S,FS) . [d9,Aq9] is set
(L,A,S,FS) . (Aq9,dq9) is Element of the carrier of A
[Aq9,dq9] is non empty V25() set
{Aq9,dq9} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,dq9},{Aq9}} is non empty set
(L,A,S,FS) . [Aq9,dq9] is set
((L,A,S,FS) . (d9,Aq9)) "\/" ((L,A,S,FS) . (Aq9,dq9)) is Element of the carrier of A
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:L,L:], the carrier of A:]
S is Element of [:L,L, the carrier of A, the carrier of A:]
(L,A,D,S) is Relation-like [:(L),(L):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L),(L):], the carrier of A:]
(L) is non empty set
{L} is non empty trivial V47(1) set
{{L}} is non empty trivial V47(1) set
{{L},{{L}}} is non empty set
L \/ {{L},{{L}}} is non empty set
[:(L),(L):] is non empty set
[:[:(L),(L):], the carrier of A:] is non empty set
bool [:[:(L),(L):], the carrier of A:] is non empty V271() set
dom D is Relation-like L -defined L -valued Element of bool [:L,L:]
bool [:L,L:] is non empty V271() set
FS is set
D . FS is set
(L,A,D,S) . FS is set
FD is set
f is set
[FD,f] is non empty V25() set
{FD,f} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,f},{FD}} is non empty set
D . [FD,f] is set
FS is Element of L
f is Element of L
D . (FS,f) is Element of the carrier of A
[FS,f] is non empty V25() set
{FS,f} is non empty set
{FS} is non empty trivial V47(1) set
{{FS,f},{FS}} is non empty set
D . [FS,f] is set
(L,A,D,S) . (FS,f) is set
(L,A,D,S) . [FS,f] is set
(L,A,D,S) . [FD,f] is set
dom (L,A,D,S) is Relation-like (L) -defined (L) -valued Element of bool [:(L),(L):]
bool [:(L),(L):] is non empty V271() set
A is epsilon-transitive epsilon-connected ordinal set
succ A is epsilon-transitive epsilon-connected ordinal non empty set
L is non empty set
L is non empty set
(L,{}) is set
D is set
A is epsilon-transitive epsilon-connected ordinal set
(L,A) is set
succ A is epsilon-transitive epsilon-connected ordinal non empty set
FS is set
FS is T-Sequence-like Relation-like Function-like set
last FS is set
proj1 FS is epsilon-transitive epsilon-connected ordinal set
S is epsilon-transitive epsilon-connected ordinal set
succ S is epsilon-transitive epsilon-connected ordinal non empty set
FS . {} is set
(L,S) is set
L is non empty set
A is epsilon-transitive epsilon-connected ordinal set
succ A is epsilon-transitive epsilon-connected ordinal non empty set
(L,(succ A)) is set
(L,A) is set
((L,A)) is non empty set
{(L,A)} is non empty trivial V47(1) set
{{(L,A)}} is non empty trivial V47(1) set
{{(L,A)},{{(L,A)}}} is non empty set
(L,A) \/ {{(L,A)},{{(L,A)}}} is non empty set
S is set
D is epsilon-transitive epsilon-connected ordinal set
(L,D) is set
succ D is epsilon-transitive epsilon-connected ordinal non empty set
FS is set
FD is T-Sequence-like Relation-like Function-like set
last FD is set
proj1 FD is epsilon-transitive epsilon-connected ordinal set
FS is epsilon-transitive epsilon-connected ordinal set
succ FS is epsilon-transitive epsilon-connected ordinal non empty set
FD . {} is set
(L,FS) is set
L is non empty set
A is epsilon-transitive epsilon-connected ordinal set
(L,A) is set
D is T-Sequence-like Relation-like Function-like set
proj1 D is epsilon-transitive epsilon-connected ordinal set
proj2 D is set
union (proj2 D) is set
FS is set
S is epsilon-transitive epsilon-connected ordinal set
(L,S) is set
succ S is epsilon-transitive epsilon-connected ordinal non empty set
FD is set
f is T-Sequence-like Relation-like Function-like set
last f is set
proj1 f is epsilon-transitive epsilon-connected ordinal set
FS is epsilon-transitive epsilon-connected ordinal set
succ FS is epsilon-transitive epsilon-connected ordinal non empty set
f . {} is set
(L,FS) is set
L is non empty set
A is epsilon-transitive epsilon-connected ordinal set
(L,A) is set
D is epsilon-transitive epsilon-connected ordinal set
(L,D) is set
succ D is epsilon-transitive epsilon-connected ordinal non empty set
(L,(succ D)) is set
((L,D)) is non empty set
{(L,D)} is non empty trivial V47(1) set
{{(L,D)}} is non empty trivial V47(1) set
{{(L,D)},{{(L,D)}}} is non empty set
(L,D) \/ {{(L,D)},{{(L,D)}}} is non empty set
D is epsilon-transitive epsilon-connected ordinal set
(L,D) is set
S is T-Sequence-like Relation-like Function-like set
proj1 S is epsilon-transitive epsilon-connected ordinal set
S . {} is set
(L,{}) is set
proj2 S is set
union (proj2 S) is set
(L,{}) is set
L is non empty set
A is epsilon-transitive epsilon-connected ordinal set
(L,A) is non empty set
D is epsilon-transitive epsilon-connected ordinal set
(L,D) is non empty set
succ D is epsilon-transitive epsilon-connected ordinal non empty set
(L,(succ D)) is non empty set
((L,D)) is non empty set
{(L,D)} is non empty trivial V47(1) set
{{(L,D)}} is non empty trivial V47(1) set
{{(L,D)},{{(L,D)}}} is non empty set
(L,D) \/ {{(L,D)},{{(L,D)}}} is non empty set
D is epsilon-transitive epsilon-connected ordinal set
(L,D) is non empty set
S is T-Sequence-like Relation-like Function-like set
proj1 S is epsilon-transitive epsilon-connected ordinal set
S . {} is set
(L,{}) is non empty set
proj2 S is set
union (proj2 S) is set
(L,{}) is non empty set
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:L,L:], the carrier of A:]
FS is epsilon-transitive epsilon-connected ordinal set
S is T-Sequence-like Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of D
proj1 S is epsilon-transitive epsilon-connected ordinal set
S . FS is set
(L,FS) is non empty set
[:(L,FS),(L,FS), the carrier of A, the carrier of A:] is non empty set
rng S is Element of bool [:L,L, the carrier of A, the carrier of A:]
bool [:L,L, the carrier of A, the carrier of A:] is non empty V271() set
{ [b<sub>1</sub>,b<sub>2</sub>,b<sub>3</sub>,b<sub>4</sub>] where b<sub>1</sub>, b<sub>2</sub> is Element of L, b<sub>3</sub>, b<sub>4</sub> is Element of the carrier of A : D . (b<sub>1</sub>,b<sub>2</sub>) <= b<sub>3</sub> "\/" b<sub>4</sub> } is set
FS is Element of L
FD is Element of L
f is Element of the carrier of A
FS is Element of the carrier of A
[FS,FD,f,FS] is V25() V26() V27() Element of [:L,L, the carrier of A, the carrier of A:]
[FS,FD,f] is V25() V26() set
[FS,FD] is non empty V25() set
{FS,FD} is non empty set
{FS} is non empty trivial V47(1) set
{{FS,FD},{FS}} is non empty set
[[FS,FD],f] is non empty V25() set
{[FS,FD],f} is non empty set
{[FS,FD]} is Function-like non empty trivial V47(1) set
{{[FS,FD],f},{[FS,FD]}} is non empty set
[[FS,FD,f],FS] is non empty V25() set
{[FS,FD,f],FS} is non empty set
{[FS,FD,f]} is non empty trivial V47(1) set
{{[FS,FD,f],FS},{[FS,FD,f]}} is non empty set
D . (FS,FD) is Element of the carrier of A
D . [FS,FD] is set
f "\/" FS is Element of the carrier of A
A9 is Element of (L,FS)
d9 is Element of (L,FS)
f is Element of the carrier of A
FD is Element of the carrier of A
[A9,d9,f,FD] is V25() V26() V27() Element of [:(L,FS),(L,FS), the carrier of A, the carrier of A:]
[A9,d9,f] is V25() V26() set
[A9,d9] is non empty V25() set
{A9,d9} is non empty set
{A9} is non empty trivial V47(1) set
{{A9,d9},{A9}} is non empty set
[[A9,d9],f] is non empty V25() set
{[A9,d9],f} is non empty set
{[A9,d9]} is Function-like non empty trivial V47(1) set
{{[A9,d9],f},{[A9,d9]}} is non empty set
[[A9,d9,f],FD] is non empty V25() set
{[A9,d9,f],FD} is non empty set
{[A9,d9,f]} is non empty trivial V47(1) set
{{[A9,d9,f],FD},{[A9,d9,f]}} is non empty set
Aq9 is Element of [:(L,FS),(L,FS), the carrier of A, the carrier of A:]
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:L,L:], the carrier of A:]
FS is epsilon-transitive epsilon-connected ordinal set
succ FS is epsilon-transitive epsilon-connected ordinal non empty set
S is T-Sequence-like Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of D
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:L,L:], the carrier of A:]
S is T-Sequence-like Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of D
(L,A,D,S,{}) is set
FS is set
FS is epsilon-transitive epsilon-connected ordinal set
(L,A,D,S,FS) is set
succ FS is epsilon-transitive epsilon-connected ordinal non empty set
f is set
FS is T-Sequence-like Relation-like Function-like set
last FS is set
proj1 FS is epsilon-transitive epsilon-connected ordinal set
FD is epsilon-transitive epsilon-connected ordinal set
succ FD is epsilon-transitive epsilon-connected ordinal non empty set
FS . {} is set
(L,A,D,S,FD) is set
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:L,L:], the carrier of A:]
S is T-Sequence-like Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of D
FS is epsilon-transitive epsilon-connected ordinal set
succ FS is epsilon-transitive epsilon-connected ordinal non empty set
(L,A,D,S,(succ FS)) is set
(L,FS) is non empty set
(L,A,D,S,FS) is set
BiFun ((L,A,D,S,FS),(L,FS),A) is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
[:(L,FS),(L,FS):] is non empty set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty V271() set
(L,A,D,S,FS) is Element of [:(L,FS),(L,FS), the carrier of A, the carrier of A:]
[:(L,FS),(L,FS), the carrier of A, the carrier of A:] is non empty set
((L,FS),A,(BiFun ((L,A,D,S,FS),(L,FS),A)),(L,A,D,S,FS)) is Relation-like [:((L,FS)),((L,FS)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:((L,FS)),((L,FS)):], the carrier of A:]
((L,FS)) is non empty set
{(L,FS)} is non empty trivial V47(1) set
{{(L,FS)}} is non empty trivial V47(1) set
{{(L,FS)},{{(L,FS)}}} is non empty set
(L,FS) \/ {{(L,FS)},{{(L,FS)}}} is non empty set
[:((L,FS)),((L,FS)):] is non empty set
[:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty set
bool [:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty V271() set
FD is set
FS is epsilon-transitive epsilon-connected ordinal set
(L,A,D,S,FS) is set
succ FS is epsilon-transitive epsilon-connected ordinal non empty set
FS is set
f is T-Sequence-like Relation-like Function-like set
last f is set
proj1 f is epsilon-transitive epsilon-connected ordinal set
f is epsilon-transitive epsilon-connected ordinal set
succ f is epsilon-transitive epsilon-connected ordinal non empty set
f . {} is set
(L,A,D,S,f) is set
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:L,L:], the carrier of A:]
S is T-Sequence-like Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of D
FS is T-Sequence-like Relation-like Function-like set
proj1 FS is epsilon-transitive epsilon-connected ordinal set
proj2 FS is set
union (proj2 FS) is set
FS is epsilon-transitive epsilon-connected ordinal set
(L,A,D,S,FS) is set
f is set
FD is epsilon-transitive epsilon-connected ordinal set
(L,A,D,S,FD) is set
succ FD is epsilon-transitive epsilon-connected ordinal non empty set
f is set
FD is T-Sequence-like Relation-like Function-like set
last FD is set
proj1 FD is epsilon-transitive epsilon-connected ordinal set
FS is epsilon-transitive epsilon-connected ordinal set
succ FS is epsilon-transitive epsilon-connected ordinal non empty set
FD . {} is set
(L,A,D,S,FS) is set
L is non empty set
D is epsilon-transitive epsilon-connected ordinal set
S is epsilon-transitive epsilon-connected ordinal set
(L,D) is non empty set
(L,S) is non empty set
FS is epsilon-transitive epsilon-connected ordinal set
(L,FS) is non empty set
succ FS is epsilon-transitive epsilon-connected ordinal non empty set
(L,(succ FS)) is non empty set
((L,FS)) is non empty set
{(L,FS)} is non empty trivial V47(1) set
{{(L,FS)}} is non empty trivial V47(1) set
{{(L,FS)},{{(L,FS)}}} is non empty set
(L,FS) \/ {{(L,FS)},{{(L,FS)}}} is non empty set
FS is epsilon-transitive epsilon-connected ordinal set
(L,FS) is non empty set
FS is T-Sequence-like Relation-like Function-like set
proj1 FS is epsilon-transitive epsilon-connected ordinal set
proj2 FS is set
union (proj2 FS) is set
FS . D is set
(L,{}) is non empty set
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:L,L:], the carrier of A:]
S is T-Sequence-like Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of D
FS is epsilon-transitive epsilon-connected ordinal set
(L,A,D,S,FS) is set
(L,FS) is non empty set
[:(L,FS),(L,FS):] is non empty set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty V271() set
FS is epsilon-transitive epsilon-connected ordinal set
(L,A,D,S,FS) is set
(L,FS) is non empty set
[:(L,FS),(L,FS):] is non empty set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty V271() set
succ FS is epsilon-transitive epsilon-connected ordinal non empty set
(L,A,D,S,(succ FS)) is set
(L,(succ FS)) is non empty set
[:(L,(succ FS)),(L,(succ FS)):] is non empty set
[:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:] is non empty set
bool [:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:] is non empty V271() set
BiFun ((L,A,D,S,FS),(L,FS),A) is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
(L,A,D,S,FS) is Element of [:(L,FS),(L,FS), the carrier of A, the carrier of A:]
[:(L,FS),(L,FS), the carrier of A, the carrier of A:] is non empty set
((L,FS),A,(BiFun ((L,A,D,S,FS),(L,FS),A)),(L,A,D,S,FS)) is Relation-like [:((L,FS)),((L,FS)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:((L,FS)),((L,FS)):], the carrier of A:]
((L,FS)) is non empty set
{(L,FS)} is non empty trivial V47(1) set
{{(L,FS)}} is non empty trivial V47(1) set
{{(L,FS)},{{(L,FS)}}} is non empty set
(L,FS) \/ {{(L,FS)},{{(L,FS)}}} is non empty set
[:((L,FS)),((L,FS)):] is non empty set
[:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty set
bool [:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty V271() set
FD is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
((L,FS),A,FD,(L,A,D,S,FS)) is Relation-like [:((L,FS)),((L,FS)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:((L,FS)),((L,FS)):], the carrier of A:]
FS is epsilon-transitive epsilon-connected ordinal set
(L,A,D,S,FS) is set
(L,FS) is non empty set
[:(L,FS),(L,FS):] is non empty set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty V271() set
FD is epsilon-transitive epsilon-connected ordinal non empty set
{ [:(L,b<sub>1</sub>),(L,b<sub>1</sub>):] where b<sub>1</sub> is epsilon-transitive epsilon-connected ordinal Element of FD : verum } is set
FS is T-Sequence-like Relation-like Function-like set
proj1 FS is epsilon-transitive epsilon-connected ordinal set
f is epsilon-transitive epsilon-connected ordinal set
FS . f is set
FD is epsilon-transitive epsilon-connected ordinal set
FS . FD is set
A9 is T-Sequence-like Relation-like Function-like set
proj1 A9 is epsilon-transitive epsilon-connected ordinal set
(L,A,D,S,FD) is set
proj2 A9 is set
union (proj2 A9) is set
(L,A,D,S,f) is set
A9 . f is set
FD is epsilon-transitive epsilon-connected ordinal set
FS . FD is set
succ FD is epsilon-transitive epsilon-connected ordinal non empty set
FS . (succ FD) is set
(L,FD) is non empty set
[:(L,FD),(L,FD):] is non empty set
[:[:(L,FD),(L,FD):], the carrier of A:] is non empty set
bool [:[:(L,FD),(L,FD):], the carrier of A:] is non empty V271() set
(L,A,D,S,FD) is set
(L,A,D,S,(succ FD)) is set
BiFun ((L,A,D,S,FD),(L,FD),A) is Relation-like [:(L,FD),(L,FD):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FD),(L,FD):], the carrier of A:]
(L,A,D,S,FD) is Element of [:(L,FD),(L,FD), the carrier of A, the carrier of A:]
[:(L,FD),(L,FD), the carrier of A, the carrier of A:] is non empty set
((L,FD),A,(BiFun ((L,A,D,S,FD),(L,FD),A)),(L,A,D,S,FD)) is Relation-like [:((L,FD)),((L,FD)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:((L,FD)),((L,FD)):], the carrier of A:]
((L,FD)) is non empty set
{(L,FD)} is non empty trivial V47(1) set
{{(L,FD)}} is non empty trivial V47(1) set
{{(L,FD)},{{(L,FD)}}} is non empty set
(L,FD) \/ {{(L,FD)},{{(L,FD)}}} is non empty set
[:((L,FD)),((L,FD)):] is non empty set
[:[:((L,FD)),((L,FD)):], the carrier of A:] is non empty set
bool [:[:((L,FD)),((L,FD)):], the carrier of A:] is non empty V271() set
A9 is Relation-like [:(L,FD),(L,FD):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FD),(L,FD):], the carrier of A:]
((L,FD),A,A9,(L,A,D,S,FD)) is Relation-like [:((L,FD)),((L,FD)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:((L,FD)),((L,FD)):], the carrier of A:]
FS . {} is set
proj2 FS is set
f is set
FD is set
A9 is set
FS . A9 is set
d9 is set
FS . d9 is set
Aq9 is epsilon-transitive epsilon-connected ordinal set
dq9 is epsilon-transitive epsilon-connected ordinal set
union (proj2 FS) is set
PFuncs ([:(L,FS),(L,FS):], the carrier of A) is functional non empty set
d9 is set
Aq9 is set
FS . Aq9 is set
dq9 is epsilon-transitive epsilon-connected ordinal set
FS . dq9 is set
(L,A,D,S,dq9) is set
(L,dq9) is non empty set
[:(L,dq9),(L,dq9):] is non empty set
[:[:(L,dq9),(L,dq9):], the carrier of A:] is non empty set
bool [:[:(L,dq9),(L,dq9):], the carrier of A:] is non empty V271() set
q is Relation-like [:(L,dq9),(L,dq9):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,dq9),(L,dq9):], the carrier of A:]
dom q is Relation-like (L,dq9) -defined (L,dq9) -valued Element of bool [:(L,dq9),(L,dq9):]
bool [:(L,dq9),(L,dq9):] is non empty V271() set
rng q is Element of bool the carrier of A
bool the carrier of A is non empty V271() set
d9 is set
FS . d9 is set
Aq9 is epsilon-transitive epsilon-connected ordinal set
FS . Aq9 is set
(L,A,D,S,Aq9) is set
doms FS is Relation-like Function-like set
proj2 (doms FS) is set
Aq9 is set
proj1 (doms FS) is set
dq9 is set
(doms FS) . dq9 is set
d9 is Relation-like Function-like Function-yielding V32() set
proj1 d9 is set
q is epsilon-transitive epsilon-connected ordinal Element of FD
FS . q is set
(L,A,D,S,q) is set
(L,q) is non empty set
[:(L,q),(L,q):] is non empty set
[:[:(L,q),(L,q):], the carrier of A:] is non empty set
bool [:[:(L,q),(L,q):], the carrier of A:] is non empty V271() set
Q is Relation-like [:(L,q),(L,q):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,q),(L,q):], the carrier of A:]
dom Q is Relation-like (L,q) -defined (L,q) -valued Element of bool [:(L,q),(L,q):]
bool [:(L,q),(L,q):] is non empty V271() set
Aq9 is set
dq9 is epsilon-transitive epsilon-connected ordinal Element of FD
(L,dq9) is non empty set
[:(L,dq9),(L,dq9):] is non empty set
FS . dq9 is set
(L,A,D,S,dq9) is set
[:[:(L,dq9),(L,dq9):], the carrier of A:] is non empty set
bool [:[:(L,dq9),(L,dq9):], the carrier of A:] is non empty V271() set
d9 is Relation-like Function-like Function-yielding V32() set
proj1 d9 is set
doms d9 is Relation-like Function-like set
proj1 (doms d9) is set
q is Relation-like [:(L,dq9),(L,dq9):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,dq9),(L,dq9):], the carrier of A:]
dom q is Relation-like (L,dq9) -defined (L,dq9) -valued Element of bool [:(L,dq9),(L,dq9):]
bool [:(L,dq9),(L,dq9):] is non empty V271() set
(doms FS) . dq9 is set
dq9 is Relation-like Function-like set
proj1 dq9 is set
proj2 dq9 is set
dq9 is T-Sequence-like Relation-like Function-like set
proj1 dq9 is epsilon-transitive epsilon-connected ordinal set
proj2 dq9 is set
q is non empty set
{ [:b<sub>1</sub>,b<sub>1</sub>:] where b<sub>1</sub> is Element of q : b<sub>1</sub> in q } is set
u is set
v is epsilon-transitive epsilon-connected ordinal Element of FD
(L,v) is non empty set
[:(L,v),(L,v):] is non empty set
dq9 . v is set
a is Element of q
[:a,a:] is set
u is set
v is Element of q
[:v,v:] is set
a is set
dq9 . a is set
b is epsilon-transitive epsilon-connected ordinal set
(L,b) is non empty set
Q is set
u is set
v is set
dq9 . v is set
a is set
dq9 . a is set
e is epsilon-transitive epsilon-connected ordinal set
dq9 . e is set
(L,e) is non empty set
b is epsilon-transitive epsilon-connected ordinal set
dq9 . b is set
(L,b) is non empty set
Aq9 is Relation-like Function-like set
proj1 Aq9 is set
d9 is Relation-like Function-like Function-yielding V32() set
doms d9 is Relation-like Function-like set
proj2 (doms d9) is set
union (proj2 (doms d9)) is set
union (proj2 dq9) is set
[:(union (proj2 dq9)),(L,FS):] is set
union q is set
[:(union q),(union q):] is set
Q is Relation-like Function-like set
proj1 Q is set
proj2 Q is set
(L,{}) is non empty set
(L,A,D,S,{}) is set
[:(L,{}),(L,{}):] is non empty set
[:[:(L,{}),(L,{}):], the carrier of A:] is non empty set
bool [:[:(L,{}),(L,{}):], the carrier of A:] is non empty V271() set
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:L,L:], the carrier of A:]
S is T-Sequence-like Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of D
FS is epsilon-transitive epsilon-connected ordinal set
(L,A,D,S,FS) is set
(L,FS) is non empty set
[:(L,FS),(L,FS):] is non empty set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty V271() set
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:L,L:], the carrier of A:]
S is T-Sequence-like Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of D
FS is epsilon-transitive epsilon-connected ordinal set
(L,A,D,S,FS) is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
(L,FS) is non empty set
[:(L,FS),(L,FS):] is non empty set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty V271() set
FS is epsilon-transitive epsilon-connected ordinal set
(L,A,D,S,FS) is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
(L,FS) is non empty set
[:(L,FS),(L,FS):] is non empty set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty V271() set
succ FS is epsilon-transitive epsilon-connected ordinal non empty set
(L,A,D,S,(succ FS)) is Relation-like [:(L,(succ FS)),(L,(succ FS)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:]
(L,(succ FS)) is non empty set
[:(L,(succ FS)),(L,(succ FS)):] is non empty set
[:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:] is non empty set
bool [:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:] is non empty V271() set
BiFun ((L,A,D,S,FS),(L,FS),A) is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
(L,A,D,S,FS) is Element of [:(L,FS),(L,FS), the carrier of A, the carrier of A:]
[:(L,FS),(L,FS), the carrier of A, the carrier of A:] is non empty set
((L,FS),A,(BiFun ((L,A,D,S,FS),(L,FS),A)),(L,A,D,S,FS)) is Relation-like [:((L,FS)),((L,FS)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:((L,FS)),((L,FS)):], the carrier of A:]
((L,FS)) is non empty set
{(L,FS)} is non empty trivial V47(1) set
{{(L,FS)}} is non empty trivial V47(1) set
{{(L,FS)},{{(L,FS)}}} is non empty set
(L,FS) \/ {{(L,FS)},{{(L,FS)}}} is non empty set
[:((L,FS)),((L,FS)):] is non empty set
[:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty set
bool [:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty V271() set
((L,FS),A,(L,A,D,S,FS),(L,A,D,S,FS)) is Relation-like [:((L,FS)),((L,FS)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:((L,FS)),((L,FS)):], the carrier of A:]
FS is epsilon-transitive epsilon-connected ordinal set
(L,A,D,S,FS) is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
(L,FS) is non empty set
[:(L,FS),(L,FS):] is non empty set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty V271() set
FD is T-Sequence-like Relation-like Function-like set
proj1 FD is epsilon-transitive epsilon-connected ordinal set
FD . {} is set
(L,A,D,S,{}) is Relation-like [:(L,{}),(L,{}):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,{}),(L,{}):], the carrier of A:]
(L,{}) is non empty set
[:(L,{}),(L,{}):] is non empty set
[:[:(L,{}),(L,{}):], the carrier of A:] is non empty set
bool [:[:(L,{}),(L,{}):], the carrier of A:] is non empty V271() set
proj2 FD is set
union (proj2 FD) is set
(L,A,D,S,{}) is Relation-like [:(L,{}),(L,{}):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,{}),(L,{}):], the carrier of A:]
(L,{}) is non empty set
[:(L,{}),(L,{}):] is non empty set
[:[:(L,{}),(L,{}):], the carrier of A:] is non empty set
bool [:[:(L,{}),(L,{}):], the carrier of A:] is non empty V271() set
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:L,L:], the carrier of A:]
S is epsilon-transitive epsilon-connected ordinal set
FS is epsilon-transitive epsilon-connected ordinal set
(L,S) is non empty set
[:(L,S),(L,S):] is non empty set
FS is T-Sequence-like Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of D
(L,A,D,FS,S) is Relation-like [:(L,S),(L,S):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,S),(L,S):], the carrier of A:]
[:[:(L,S),(L,S):], the carrier of A:] is non empty set
bool [:[:(L,S),(L,S):], the carrier of A:] is non empty V271() set
(L,A,D,FS,FS) is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
(L,FS) is non empty set
[:(L,FS),(L,FS):] is non empty set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty V271() set
FD is epsilon-transitive epsilon-connected ordinal set
(L,A,D,FS,FD) is Relation-like [:(L,FD),(L,FD):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FD),(L,FD):], the carrier of A:]
(L,FD) is non empty set
[:(L,FD),(L,FD):] is non empty set
[:[:(L,FD),(L,FD):], the carrier of A:] is non empty set
bool [:[:(L,FD),(L,FD):], the carrier of A:] is non empty V271() set
f is T-Sequence-like Relation-like Function-like set
proj1 f is epsilon-transitive epsilon-connected ordinal set
proj2 f is set
union (proj2 f) is set
f . S is set
FD is epsilon-transitive epsilon-connected ordinal set
(L,A,D,FS,FD) is Relation-like [:(L,FD),(L,FD):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FD),(L,FD):], the carrier of A:]
(L,FD) is non empty set
[:(L,FD),(L,FD):] is non empty set
[:[:(L,FD),(L,FD):], the carrier of A:] is non empty set
bool [:[:(L,FD),(L,FD):], the carrier of A:] is non empty V271() set
succ FD is epsilon-transitive epsilon-connected ordinal non empty set
(L,A,D,FS,(succ FD)) is Relation-like [:(L,(succ FD)),(L,(succ FD)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,(succ FD)),(L,(succ FD)):], the carrier of A:]
(L,(succ FD)) is non empty set
[:(L,(succ FD)),(L,(succ FD)):] is non empty set
[:[:(L,(succ FD)),(L,(succ FD)):], the carrier of A:] is non empty set
bool [:[:(L,(succ FD)),(L,(succ FD)):], the carrier of A:] is non empty V271() set
BiFun ((L,A,D,FS,FD),(L,FD),A) is Relation-like [:(L,FD),(L,FD):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FD),(L,FD):], the carrier of A:]
(L,A,D,FS,FD) is Element of [:(L,FD),(L,FD), the carrier of A, the carrier of A:]
[:(L,FD),(L,FD), the carrier of A, the carrier of A:] is non empty set
((L,FD),A,(BiFun ((L,A,D,FS,FD),(L,FD),A)),(L,A,D,FS,FD)) is Relation-like [:((L,FD)),((L,FD)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:((L,FD)),((L,FD)):], the carrier of A:]
((L,FD)) is non empty set
{(L,FD)} is non empty trivial V47(1) set
{{(L,FD)}} is non empty trivial V47(1) set
{{(L,FD)},{{(L,FD)}}} is non empty set
(L,FD) \/ {{(L,FD)},{{(L,FD)}}} is non empty set
[:((L,FD)),((L,FD)):] is non empty set
[:[:((L,FD)),((L,FD)):], the carrier of A:] is non empty set
bool [:[:((L,FD)),((L,FD)):], the carrier of A:] is non empty V271() set
((L,FD),A,(L,A,D,FS,FD),(L,A,D,FS,FD)) is Relation-like [:((L,FD)),((L,FD)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:((L,FD)),((L,FD)):], the carrier of A:]
(L,A,D,FS,{}) is Relation-like [:(L,{}),(L,{}):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,{}),(L,{}):], the carrier of A:]
(L,{}) is non empty set
[:(L,{}),(L,{}):] is non empty set
[:[:(L,{}),(L,{}):], the carrier of A:] is non empty set
bool [:[:(L,{}),(L,{}):], the carrier of A:] is non empty V271() set
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:L,L:], the carrier of A:]
S is T-Sequence-like Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of D
FS is epsilon-transitive epsilon-connected ordinal set
(L,FS) is non empty set
(L,A,D,S,FS) is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
[:(L,FS),(L,FS):] is non empty set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty V271() set
FS is epsilon-transitive epsilon-connected ordinal set
(L,FS) is non empty set
(L,A,D,S,FS) is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
[:(L,FS),(L,FS):] is non empty set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty V271() set
succ FS is epsilon-transitive epsilon-connected ordinal non empty set
(L,(succ FS)) is non empty set
(L,A,D,S,(succ FS)) is Relation-like [:(L,(succ FS)),(L,(succ FS)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:]
[:(L,(succ FS)),(L,(succ FS)):] is non empty set
[:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:] is non empty set
bool [:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:] is non empty V271() set
((L,FS)) is non empty set
{(L,FS)} is non empty trivial V47(1) set
{{(L,FS)}} is non empty trivial V47(1) set
{{(L,FS)},{{(L,FS)}}} is non empty set
(L,FS) \/ {{(L,FS)},{{(L,FS)}}} is non empty set
(L,A,D,S,FS) is Element of [:(L,FS),(L,FS), the carrier of A, the carrier of A:]
[:(L,FS),(L,FS), the carrier of A, the carrier of A:] is non empty set
((L,FS),A,(L,A,D,S,FS),(L,A,D,S,FS)) is Relation-like [:((L,FS)),((L,FS)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:((L,FS)),((L,FS)):], the carrier of A:]
[:((L,FS)),((L,FS)):] is non empty set
[:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty set
bool [:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty V271() set
FD is Element of (L,(succ FS))
(L,A,D,S,(succ FS)) . (FD,FD) is Element of the carrier of A
[FD,FD] is non empty V25() set
{FD,FD} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,FD},{FD}} is non empty set
(L,A,D,S,(succ FS)) . [FD,FD] is set
Bottom A is Element of the carrier of A
"\/" ({},A) is Element of the carrier of A
BiFun ((L,A,D,S,FS),(L,FS),A) is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
((L,FS),A,(BiFun ((L,A,D,S,FS),(L,FS),A)),(L,A,D,S,FS)) is Relation-like [:((L,FS)),((L,FS)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:((L,FS)),((L,FS)):], the carrier of A:]
f is Element of ((L,FS))
((L,FS),A,(L,A,D,S,FS),(L,A,D,S,FS)) . (f,f) is Element of the carrier of A
[f,f] is non empty V25() set
{f,f} is non empty set
{f} is non empty trivial V47(1) set
{{f,f},{f}} is non empty set
((L,FS),A,(L,A,D,S,FS),(L,A,D,S,FS)) . [f,f] is set
FS is epsilon-transitive epsilon-connected ordinal set
(L,FS) is non empty set
(L,A,D,S,FS) is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
[:(L,FS),(L,FS):] is non empty set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty V271() set
f is T-Sequence-like Relation-like Function-like set
proj1 f is epsilon-transitive epsilon-connected ordinal set
proj2 f is set
union (proj2 f) is set
f is T-Sequence-like Relation-like Function-like set
proj1 f is epsilon-transitive epsilon-connected ordinal set
proj2 f is set
union (proj2 f) is set
FS is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
FD is Element of (L,FS)
FS . (FD,FD) is Element of the carrier of A
[FD,FD] is non empty V25() set
{FD,FD} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,FD},{FD}} is non empty set
FS . [FD,FD] is set
Bottom A is Element of the carrier of A
"\/" ({},A) is Element of the carrier of A
A9 is set
d9 is set
f . d9 is set
Aq9 is epsilon-transitive epsilon-connected ordinal set
f . Aq9 is set
(L,A,D,S,Aq9) is Relation-like [:(L,Aq9),(L,Aq9):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,Aq9),(L,Aq9):], the carrier of A:]
(L,Aq9) is non empty set
[:(L,Aq9),(L,Aq9):] is non empty set
[:[:(L,Aq9),(L,Aq9):], the carrier of A:] is non empty set
bool [:[:(L,Aq9),(L,Aq9):], the carrier of A:] is non empty V271() set
dq9 is Relation-like [:(L,Aq9),(L,Aq9):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,Aq9),(L,Aq9):], the carrier of A:]
dom dq9 is Relation-like (L,Aq9) -defined (L,Aq9) -valued Element of bool [:(L,Aq9),(L,Aq9):]
bool [:(L,Aq9),(L,Aq9):] is non empty V271() set
Q is Element of (L,Aq9)
dq9 . (Q,Q) is Element of the carrier of A
[Q,Q] is non empty V25() set
{Q,Q} is non empty set
{Q} is non empty trivial V47(1) set
{{Q,Q},{Q}} is non empty set
dq9 . [Q,Q] is set
(L,A,D,S,Aq9) . (Q,Q) is Element of the carrier of A
(L,A,D,S,Aq9) . [Q,Q] is set
[FD,FD] is non empty V25() Element of [:(L,FS),(L,FS):]
q is Element of (L,Aq9)
dq9 . (q,q) is Element of the carrier of A
[q,q] is non empty V25() set
{q,q} is non empty set
{q} is non empty trivial V47(1) set
{{q,q},{q}} is non empty set
dq9 . [q,q] is set
(L,{}) is non empty set
(L,A,D,S,{}) is Relation-like [:(L,{}),(L,{}):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,{}),(L,{}):], the carrier of A:]
[:(L,{}),(L,{}):] is non empty set
[:[:(L,{}),(L,{}):], the carrier of A:] is non empty set
bool [:[:(L,{}),(L,{}):], the carrier of A:] is non empty V271() set
FS is Element of (L,{})
(L,A,D,S,{}) . (FS,FS) is Element of the carrier of A
[FS,FS] is non empty V25() set
{FS,FS} is non empty set
{FS} is non empty trivial V47(1) set
{{FS,FS},{FS}} is non empty set
(L,A,D,S,{}) . [FS,FS] is set
Bottom A is Element of the carrier of A
"\/" ({},A) is Element of the carrier of A
FD is Element of L
D . (FD,FD) is Element of the carrier of A
[FD,FD] is non empty V25() set
{FD,FD} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,FD},{FD}} is non empty set
D . [FD,FD] is set
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:L,L:], the carrier of A:]
S is T-Sequence-like Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of D
FS is epsilon-transitive epsilon-connected ordinal set
(L,FS) is non empty set
(L,A,D,S,FS) is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
[:(L,FS),(L,FS):] is non empty set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty V271() set
FS is epsilon-transitive epsilon-connected ordinal set
(L,FS) is non empty set
(L,A,D,S,FS) is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
[:(L,FS),(L,FS):] is non empty set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty V271() set
succ FS is epsilon-transitive epsilon-connected ordinal non empty set
(L,(succ FS)) is non empty set
(L,A,D,S,(succ FS)) is Relation-like [:(L,(succ FS)),(L,(succ FS)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:]
[:(L,(succ FS)),(L,(succ FS)):] is non empty set
[:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:] is non empty set
bool [:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:] is non empty V271() set
((L,FS)) is non empty set
{(L,FS)} is non empty trivial V47(1) set
{{(L,FS)}} is non empty trivial V47(1) set
{{(L,FS)},{{(L,FS)}}} is non empty set
(L,FS) \/ {{(L,FS)},{{(L,FS)}}} is non empty set
(L,A,D,S,FS) is Element of [:(L,FS),(L,FS), the carrier of A, the carrier of A:]
[:(L,FS),(L,FS), the carrier of A, the carrier of A:] is non empty set
((L,FS),A,(L,A,D,S,FS),(L,A,D,S,FS)) is Relation-like [:((L,FS)),((L,FS)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:((L,FS)),((L,FS)):], the carrier of A:]
[:((L,FS)),((L,FS)):] is non empty set
[:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty set
bool [:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty V271() set
FD is Element of (L,(succ FS))
f is Element of (L,(succ FS))
(L,A,D,S,(succ FS)) . (FD,f) is Element of the carrier of A
[FD,f] is non empty V25() set
{FD,f} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,f},{FD}} is non empty set
(L,A,D,S,(succ FS)) . [FD,f] is set
(L,A,D,S,(succ FS)) . (f,FD) is Element of the carrier of A
[f,FD] is non empty V25() set
{f,FD} is non empty set
{f} is non empty trivial V47(1) set
{{f,FD},{f}} is non empty set
(L,A,D,S,(succ FS)) . [f,FD] is set
BiFun ((L,A,D,S,FS),(L,FS),A) is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
((L,FS),A,(BiFun ((L,A,D,S,FS),(L,FS),A)),(L,A,D,S,FS)) is Relation-like [:((L,FS)),((L,FS)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:((L,FS)),((L,FS)):], the carrier of A:]
f is Element of ((L,FS))
FS is Element of ((L,FS))
((L,FS),A,(L,A,D,S,FS),(L,A,D,S,FS)) . (f,FS) is Element of the carrier of A
[f,FS] is non empty V25() set
{f,FS} is non empty set
{f} is non empty trivial V47(1) set
{{f,FS},{f}} is non empty set
((L,FS),A,(L,A,D,S,FS),(L,A,D,S,FS)) . [f,FS] is set
FS is epsilon-transitive epsilon-connected ordinal set
(L,FS) is non empty set
(L,A,D,S,FS) is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
[:(L,FS),(L,FS):] is non empty set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty V271() set
f is T-Sequence-like Relation-like Function-like set
proj1 f is epsilon-transitive epsilon-connected ordinal set
proj2 f is set
union (proj2 f) is set
f is T-Sequence-like Relation-like Function-like set
proj1 f is epsilon-transitive epsilon-connected ordinal set
proj2 f is set
union (proj2 f) is set
FS is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
FD is Element of (L,FS)
A9 is Element of (L,FS)
FS . (FD,A9) is Element of the carrier of A
[FD,A9] is non empty V25() set
{FD,A9} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,A9},{FD}} is non empty set
FS . [FD,A9] is set
FS . (A9,FD) is Element of the carrier of A
[A9,FD] is non empty V25() set
{A9,FD} is non empty set
{A9} is non empty trivial V47(1) set
{{A9,FD},{A9}} is non empty set
FS . [A9,FD] is set
d9 is set
Aq9 is set
f . Aq9 is set
dq9 is set
q is set
f . q is set
Q is epsilon-transitive epsilon-connected ordinal set
(L,Q) is non empty set
f . Q is set
(L,A,D,S,Q) is Relation-like [:(L,Q),(L,Q):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,Q),(L,Q):], the carrier of A:]
[:(L,Q),(L,Q):] is non empty set
[:[:(L,Q),(L,Q):], the carrier of A:] is non empty set
bool [:[:(L,Q),(L,Q):], the carrier of A:] is non empty V271() set
v is Relation-like [:(L,Q),(L,Q):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,Q),(L,Q):], the carrier of A:]
a is Element of (L,Q)
b is Element of (L,Q)
v . (a,b) is Element of the carrier of A
[a,b] is non empty V25() set
{a,b} is non empty set
{a} is non empty trivial V47(1) set
{{a,b},{a}} is non empty set
v . [a,b] is set
v . (b,a) is Element of the carrier of A
[b,a] is non empty V25() set
{b,a} is non empty set
{b} is non empty trivial V47(1) set
{{b,a},{b}} is non empty set
v . [b,a] is set
(L,A,D,S,Q) . (a,b) is Element of the carrier of A
(L,A,D,S,Q) . [a,b] is set
(L,A,D,S,Q) . (b,a) is Element of the carrier of A
(L,A,D,S,Q) . [b,a] is set
dom v is Relation-like (L,Q) -defined (L,Q) -valued Element of bool [:(L,Q),(L,Q):]
bool [:(L,Q),(L,Q):] is non empty V271() set
u is epsilon-transitive epsilon-connected ordinal set
(L,u) is non empty set
f . u is set
(L,A,D,S,u) is Relation-like [:(L,u),(L,u):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,u),(L,u):], the carrier of A:]
[:(L,u),(L,u):] is non empty set
[:[:(L,u),(L,u):], the carrier of A:] is non empty set
bool [:[:(L,u),(L,u):], the carrier of A:] is non empty V271() set
a is Relation-like [:(L,u),(L,u):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,u),(L,u):], the carrier of A:]
b is Element of (L,u)
e is Element of (L,u)
a . (b,e) is Element of the carrier of A
[b,e] is non empty V25() set
{b,e} is non empty set
{b} is non empty trivial V47(1) set
{{b,e},{b}} is non empty set
a . [b,e] is set
a . (e,b) is Element of the carrier of A
[e,b] is non empty V25() set
{e,b} is non empty set
{e} is non empty trivial V47(1) set
{{e,b},{e}} is non empty set
a . [e,b] is set
(L,A,D,S,u) . (b,e) is Element of the carrier of A
(L,A,D,S,u) . [b,e] is set
(L,A,D,S,u) . (e,b) is Element of the carrier of A
(L,A,D,S,u) . [e,b] is set
dom a is Relation-like (L,u) -defined (L,u) -valued Element of bool [:(L,u),(L,u):]
bool [:(L,u),(L,u):] is non empty V271() set
[A9,FD] is non empty V25() Element of [:(L,FS),(L,FS):]
[FD,A9] is non empty V25() Element of [:(L,FS),(L,FS):]
b is Element of (L,u)
e is Element of (L,u)
a . (b,e) is Element of the carrier of A
[b,e] is non empty V25() set
{b,e} is non empty set
{b} is non empty trivial V47(1) set
{{b,e},{b}} is non empty set
a . [b,e] is set
a . (e,b) is Element of the carrier of A
[e,b] is non empty V25() set
{e,b} is non empty set
{e} is non empty trivial V47(1) set
{{e,b},{e}} is non empty set
a . [e,b] is set
[A9,FD] is non empty V25() Element of [:(L,FS),(L,FS):]
[FD,A9] is non empty V25() Element of [:(L,FS),(L,FS):]
b is Element of (L,Q)
e is Element of (L,Q)
v . (b,e) is Element of the carrier of A
[b,e] is non empty V25() set
{b,e} is non empty set
{b} is non empty trivial V47(1) set
{{b,e},{b}} is non empty set
v . [b,e] is set
v . (e,b) is Element of the carrier of A
[e,b] is non empty V25() set
{e,b} is non empty set
{e} is non empty trivial V47(1) set
{{e,b},{e}} is non empty set
v . [e,b] is set
(L,{}) is non empty set
(L,A,D,S,{}) is Relation-like [:(L,{}),(L,{}):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,{}),(L,{}):], the carrier of A:]
[:(L,{}),(L,{}):] is non empty set
[:[:(L,{}),(L,{}):], the carrier of A:] is non empty set
bool [:[:(L,{}),(L,{}):], the carrier of A:] is non empty V271() set
FS is Element of (L,{})
FD is Element of (L,{})
(L,A,D,S,{}) . (FS,FD) is Element of the carrier of A
[FS,FD] is non empty V25() set
{FS,FD} is non empty set
{FS} is non empty trivial V47(1) set
{{FS,FD},{FS}} is non empty set
(L,A,D,S,{}) . [FS,FD] is set
(L,A,D,S,{}) . (FD,FS) is Element of the carrier of A
[FD,FS] is non empty V25() set
{FD,FS} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,FS},{FD}} is non empty set
(L,A,D,S,{}) . [FD,FS] is set
f is Element of L
FS is Element of L
D . (f,FS) is Element of the carrier of A
[f,FS] is non empty V25() set
{f,FS} is non empty set
{f} is non empty trivial V47(1) set
{{f,FS},{f}} is non empty set
D . [f,FS] is set
D . (FS,f) is Element of the carrier of A
[FS,f] is non empty V25() set
{FS,f} is non empty set
{FS} is non empty trivial V47(1) set
{{FS,f},{FS}} is non empty set
D . [FS,f] is set
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:L,L:], the carrier of A:]
DistEsti D is epsilon-transitive epsilon-connected ordinal V45() set
S is epsilon-transitive epsilon-connected ordinal set
(L,S) is non empty set
FS is T-Sequence-like Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of D
(L,A,D,FS,S) is Relation-like [:(L,S),(L,S):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,S),(L,S):], the carrier of A:]
[:(L,S),(L,S):] is non empty set
[:[:(L,S),(L,S):], the carrier of A:] is non empty set
bool [:[:(L,S),(L,S):], the carrier of A:] is non empty V271() set
FS is epsilon-transitive epsilon-connected ordinal set
(L,FS) is non empty set
(L,A,D,FS,FS) is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
[:(L,FS),(L,FS):] is non empty set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty V271() set
succ FS is epsilon-transitive epsilon-connected ordinal non empty set
(L,(succ FS)) is non empty set
(L,A,D,FS,(succ FS)) is Relation-like [:(L,(succ FS)),(L,(succ FS)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:]
[:(L,(succ FS)),(L,(succ FS)):] is non empty set
[:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:] is non empty set
bool [:[:(L,(succ FS)),(L,(succ FS)):], the carrier of A:] is non empty V271() set
proj1 FS is epsilon-transitive epsilon-connected ordinal set
FS . FS is set
rng FS is Element of bool [:L,L, the carrier of A, the carrier of A:]
bool [:L,L, the carrier of A, the carrier of A:] is non empty V271() set
{ [b<sub>1</sub>,b<sub>2</sub>,b<sub>3</sub>,b<sub>4</sub>] where b<sub>1</sub>, b<sub>2</sub> is Element of L, b<sub>3</sub>, b<sub>4</sub> is Element of the carrier of A : D . (b<sub>1</sub>,b<sub>2</sub>) <= b<sub>3</sub> "\/" b<sub>4</sub> } is set
FD is Element of (L,(succ FS))
FS is Element of (L,(succ FS))
(L,A,D,FS,(succ FS)) . (FD,FS) is Element of the carrier of A
[FD,FS] is non empty V25() set
{FD,FS} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,FS},{FD}} is non empty set
(L,A,D,FS,(succ FS)) . [FD,FS] is set
f is Element of (L,(succ FS))
(L,A,D,FS,(succ FS)) . (FD,f) is Element of the carrier of A
[FD,f] is non empty V25() set
{FD,f} is non empty set
{{FD,f},{FD}} is non empty set
(L,A,D,FS,(succ FS)) . [FD,f] is set
(L,A,D,FS,(succ FS)) . (f,FS) is Element of the carrier of A
[f,FS] is non empty V25() set
{f,FS} is non empty set
{f} is non empty trivial V47(1) set
{{f,FS},{f}} is non empty set
(L,A,D,FS,(succ FS)) . [f,FS] is set
((L,A,D,FS,(succ FS)) . (FD,f)) "\/" ((L,A,D,FS,(succ FS)) . (f,FS)) is Element of the carrier of A
((L,FS)) is non empty set
{(L,FS)} is non empty trivial V47(1) set
{{(L,FS)}} is non empty trivial V47(1) set
{{(L,FS)},{{(L,FS)}}} is non empty set
(L,FS) \/ {{(L,FS)},{{(L,FS)}}} is non empty set
(L,A,D,FS,FS) is Element of [:(L,FS),(L,FS), the carrier of A, the carrier of A:]
[:(L,FS),(L,FS), the carrier of A, the carrier of A:] is non empty set
((L,FS),A,(L,A,D,FS,FS),(L,A,D,FS,FS)) is Relation-like [:((L,FS)),((L,FS)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:((L,FS)),((L,FS)):], the carrier of A:]
[:((L,FS)),((L,FS)):] is non empty set
[:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty set
bool [:[:((L,FS)),((L,FS)):], the carrier of A:] is non empty V271() set
(L,A,D,FS,FS) `1_4 is Element of (L,FS)
(L,A,D,FS,FS) `1 is set
((L,A,D,FS,FS) `1) `1 is set
(((L,A,D,FS,FS) `1) `1) `1 is set
(L,A,D,FS,FS) `2_4 is Element of (L,FS)
(((L,A,D,FS,FS) `1) `1) `2 is set
(L,A,D,FS,FS) `3_4 is Element of the carrier of A
((L,A,D,FS,FS) `1) `2 is set
(L,A,D,FS,FS) `4_4 is Element of the carrier of A
dom D is Relation-like L -defined L -valued Element of bool [:L,L:]
bool [:L,L:] is non empty V271() set
u is Element of L
v is Element of L
a is Element of the carrier of A
b is Element of the carrier of A
[u,v,a,b] is V25() V26() V27() Element of [:L,L, the carrier of A, the carrier of A:]
[u,v,a] is V25() V26() set
[u,v] is non empty V25() set
{u,v} is non empty set
{u} is non empty trivial V47(1) set
{{u,v},{u}} is non empty set
[[u,v],a] is non empty V25() set
{[u,v],a} is non empty set
{[u,v]} is Function-like non empty trivial V47(1) set
{{[u,v],a},{[u,v]}} is non empty set
[[u,v,a],b] is non empty V25() set
{[u,v,a],b} is non empty set
{[u,v,a]} is non empty trivial V47(1) set
{{[u,v,a],b},{[u,v,a]}} is non empty set
D . (u,v) is Element of the carrier of A
D . [u,v] is set
a "\/" b is Element of the carrier of A
q is Element of the carrier of A
Q is Element of the carrier of A
[u,v] is non empty V25() Element of [:L,L:]
D . [u,v] is Element of the carrier of A
(L,A,D,FS,FS) . (((L,A,D,FS,FS) `1_4),((L,A,D,FS,FS) `2_4)) is Element of the carrier of A
[((L,A,D,FS,FS) `1_4),((L,A,D,FS,FS) `2_4)] is non empty V25() set
{((L,A,D,FS,FS) `1_4),((L,A,D,FS,FS) `2_4)} is non empty set
{((L,A,D,FS,FS) `1_4)} is non empty trivial V47(1) set
{{((L,A,D,FS,FS) `1_4),((L,A,D,FS,FS) `2_4)},{((L,A,D,FS,FS) `1_4)}} is non empty set
(L,A,D,FS,FS) . [((L,A,D,FS,FS) `1_4),((L,A,D,FS,FS) `2_4)] is set
f is Element of ((L,FS))
A9 is Element of ((L,FS))
((L,FS),A,(L,A,D,FS,FS),(L,A,D,FS,FS)) . (f,A9) is Element of the carrier of A
[f,A9] is non empty V25() set
{f,A9} is non empty set
{f} is non empty trivial V47(1) set
{{f,A9},{f}} is non empty set
((L,FS),A,(L,A,D,FS,FS),(L,A,D,FS,FS)) . [f,A9] is set
FD is Element of ((L,FS))
((L,FS),A,(L,A,D,FS,FS),(L,A,D,FS,FS)) . (f,FD) is Element of the carrier of A
[f,FD] is non empty V25() set
{f,FD} is non empty set
{{f,FD},{f}} is non empty set
((L,FS),A,(L,A,D,FS,FS),(L,A,D,FS,FS)) . [f,FD] is set
((L,FS),A,(L,A,D,FS,FS),(L,A,D,FS,FS)) . (FD,A9) is Element of the carrier of A
[FD,A9] is non empty V25() set
{FD,A9} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,A9},{FD}} is non empty set
((L,FS),A,(L,A,D,FS,FS),(L,A,D,FS,FS)) . [FD,A9] is set
(((L,FS),A,(L,A,D,FS,FS),(L,A,D,FS,FS)) . (f,FD)) "\/" (((L,FS),A,(L,A,D,FS,FS),(L,A,D,FS,FS)) . (FD,A9)) is Element of the carrier of A
BiFun ((L,A,D,FS,FS),(L,FS),A) is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
((L,FS),A,(BiFun ((L,A,D,FS,FS),(L,FS),A)),(L,A,D,FS,FS)) is Relation-like [:((L,FS)),((L,FS)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:((L,FS)),((L,FS)):], the carrier of A:]
FS is epsilon-transitive epsilon-connected ordinal set
(L,FS) is non empty set
(L,A,D,FS,FS) is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
[:(L,FS),(L,FS):] is non empty set
[:[:(L,FS),(L,FS):], the carrier of A:] is non empty set
bool [:[:(L,FS),(L,FS):], the carrier of A:] is non empty V271() set
f is T-Sequence-like Relation-like Function-like set
proj1 f is epsilon-transitive epsilon-connected ordinal set
proj2 f is set
union (proj2 f) is set
f is T-Sequence-like Relation-like Function-like set
proj1 f is epsilon-transitive epsilon-connected ordinal set
proj2 f is set
union (proj2 f) is set
FS is Relation-like [:(L,FS),(L,FS):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,FS),(L,FS):], the carrier of A:]
FD is Element of (L,FS)
d9 is Element of (L,FS)
FS . (FD,d9) is Element of the carrier of A
[FD,d9] is non empty V25() set
{FD,d9} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,d9},{FD}} is non empty set
FS . [FD,d9] is set
A9 is Element of (L,FS)
FS . (FD,A9) is Element of the carrier of A
[FD,A9] is non empty V25() set
{FD,A9} is non empty set
{{FD,A9},{FD}} is non empty set
FS . [FD,A9] is set
FS . (A9,d9) is Element of the carrier of A
[A9,d9] is non empty V25() set
{A9,d9} is non empty set
{A9} is non empty trivial V47(1) set
{{A9,d9},{A9}} is non empty set
FS . [A9,d9] is set
(FS . (FD,A9)) "\/" (FS . (A9,d9)) is Element of the carrier of A
Aq9 is set
dq9 is set
f . dq9 is set
q is set
Q is set
f . Q is set
u is set
v is set
f . v is set
a is epsilon-transitive epsilon-connected ordinal set
(L,a) is non empty set
e is epsilon-transitive epsilon-connected ordinal set
f . e is set
(L,A,D,FS,e) is Relation-like [:(L,e),(L,e):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,e),(L,e):], the carrier of A:]
(L,e) is non empty set
[:(L,e),(L,e):] is non empty set
[:[:(L,e),(L,e):], the carrier of A:] is non empty set
bool [:[:(L,e),(L,e):], the carrier of A:] is non empty V271() set
W is Relation-like [:(L,e),(L,e):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,e),(L,e):], the carrier of A:]
V is Element of (L,e)
c₂₆ is Element of (L,e)
W . (V,c₂₆) is Element of the carrier of A
[V,c₂₆] is non empty V25() set
{V,c₂₆} is non empty set
{V} is non empty trivial V47(1) set
{{V,c₂₆},{V}} is non empty set
W . [V,c₂₆] is set
h is Element of (L,e)
W . (V,h) is Element of the carrier of A
[V,h] is non empty V25() set
{V,h} is non empty set
{{V,h},{V}} is non empty set
W . [V,h] is set
W . (h,c₂₆) is Element of the carrier of A
[h,c₂₆] is non empty V25() set
{h,c₂₆} is non empty set
{h} is non empty trivial V47(1) set
{{h,c₂₆},{h}} is non empty set
W . [h,c₂₆] is set
(W . (V,h)) "\/" (W . (h,c₂₆)) is Element of the carrier of A
dom W is Relation-like (L,e) -defined (L,e) -valued Element of bool [:(L,e),(L,e):]
bool [:(L,e),(L,e):] is non empty V271() set
b is epsilon-transitive epsilon-connected ordinal set
f . b is set
(L,A,D,FS,b) is Relation-like [:(L,b),(L,b):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,b),(L,b):], the carrier of A:]
(L,b) is non empty set
[:(L,b),(L,b):] is non empty set
[:[:(L,b),(L,b):], the carrier of A:] is non empty set
bool [:[:(L,b),(L,b):], the carrier of A:] is non empty V271() set
V is Relation-like [:(L,b),(L,b):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,b),(L,b):], the carrier of A:]
h is Element of (L,b)
i is Element of (L,b)
V . (h,i) is Element of the carrier of A
[h,i] is non empty V25() set
{h,i} is non empty set
{h} is non empty trivial V47(1) set
{{h,i},{h}} is non empty set
V . [h,i] is set
c₂₆ is Element of (L,b)
V . (h,c₂₆) is Element of the carrier of A
[h,c₂₆] is non empty V25() set
{h,c₂₆} is non empty set
{{h,c₂₆},{h}} is non empty set
V . [h,c₂₆] is set
V . (c₂₆,i) is Element of the carrier of A
[c₂₆,i] is non empty V25() set
{c₂₆,i} is non empty set
{c₂₆} is non empty trivial V47(1) set
{{c₂₆,i},{c₂₆}} is non empty set
V . [c₂₆,i] is set
(V . (h,c₂₆)) "\/" (V . (c₂₆,i)) is Element of the carrier of A
dom V is Relation-like (L,b) -defined (L,b) -valued Element of bool [:(L,b),(L,b):]
bool [:(L,b),(L,b):] is non empty V271() set
f . a is set
(L,A,D,FS,a) is Relation-like [:(L,a),(L,a):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,a),(L,a):], the carrier of A:]
[:(L,a),(L,a):] is non empty set
[:[:(L,a),(L,a):], the carrier of A:] is non empty set
bool [:[:(L,a),(L,a):], the carrier of A:] is non empty V271() set
h is Relation-like [:(L,a),(L,a):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,a),(L,a):], the carrier of A:]
c₂₆ is Element of (L,a)
z19 is Element of (L,a)
h . (c₂₆,z19) is Element of the carrier of A
[c₂₆,z19] is non empty V25() set
{c₂₆,z19} is non empty set
{c₂₆} is non empty trivial V47(1) set
{{c₂₆,z19},{c₂₆}} is non empty set
h . [c₂₆,z19] is set
i is Element of (L,a)
h . (c₂₆,i) is Element of the carrier of A
[c₂₆,i] is non empty V25() set
{c₂₆,i} is non empty set
{{c₂₆,i},{c₂₆}} is non empty set
h . [c₂₆,i] is set
h . (i,z19) is Element of the carrier of A
[i,z19] is non empty V25() set
{i,z19} is non empty set
{i} is non empty trivial V47(1) set
{{i,z19},{i}} is non empty set
h . [i,z19] is set
(h . (c₂₆,i)) "\/" (h . (i,z19)) is Element of the carrier of A
dom h is Relation-like (L,a) -defined (L,a) -valued Element of bool [:(L,a),(L,a):]
bool [:(L,a),(L,a):] is non empty V271() set
[A9,d9] is non empty V25() Element of [:(L,FS),(L,FS):]
z19 is Element of (L,e)
c₂₆ is Element of (L,e)
W . (z19,c₂₆) is Element of the carrier of A
[z19,c₂₆] is non empty V25() set
{z19,c₂₆} is non empty set
{z19} is non empty trivial V47(1) set
{{z19,c₂₆},{z19}} is non empty set
W . [z19,c₂₆] is set
[FD,d9] is non empty V25() Element of [:(L,FS),(L,FS):]
i is Element of (L,e)
W . (i,c₂₆) is Element of the carrier of A
[i,c₂₆] is non empty V25() set
{i,c₂₆} is non empty set
{i} is non empty trivial V47(1) set
{{i,c₂₆},{i}} is non empty set
W . [i,c₂₆] is set
[FD,A9] is non empty V25() Element of [:(L,FS),(L,FS):]
W . (i,z19) is Element of the carrier of A
[i,z19] is non empty V25() set
{i,z19} is non empty set
{{i,z19},{i}} is non empty set
W . [i,z19] is set
[A9,d9] is non empty V25() Element of [:(L,FS),(L,FS):]
c₂₆ is Element of (L,b)
i is Element of (L,b)
V . (c₂₆,i) is Element of the carrier of A
[c₂₆,i] is non empty V25() set
{c₂₆,i} is non empty set
{c₂₆} is non empty trivial V47(1) set
{{c₂₆,i},{c₂₆}} is non empty set
V . [c₂₆,i] is set
[FD,A9] is non empty V25() Element of [:(L,FS),(L,FS):]
z19 is Element of (L,b)
V . (z19,c₂₆) is Element of the carrier of A
[z19,c₂₆] is non empty V25() set
{z19,c₂₆} is non empty set
{z19} is non empty trivial V47(1) set
{{z19,c₂₆},{z19}} is non empty set
V . [z19,c₂₆] is set
[FD,d9] is non empty V25() Element of [:(L,FS),(L,FS):]
V . (z19,i) is Element of the carrier of A
[z19,i] is non empty V25() set
{z19,i} is non empty set
{{z19,i},{z19}} is non empty set
V . [z19,i] is set
[FD,A9] is non empty V25() Element of [:(L,FS),(L,FS):]
i is Element of (L,b)
c₂₆ is Element of (L,b)
V . (i,c₂₆) is Element of the carrier of A
[i,c₂₆] is non empty V25() set
{i,c₂₆} is non empty set
{i} is non empty trivial V47(1) set
{{i,c₂₆},{i}} is non empty set
V . [i,c₂₆] is set
[A9,d9] is non empty V25() Element of [:(L,FS),(L,FS):]
z19 is Element of (L,b)
V . (c₂₆,z19) is Element of the carrier of A
[c₂₆,z19] is non empty V25() set
{c₂₆,z19} is non empty set
{c₂₆} is non empty trivial V47(1) set
{{c₂₆,z19},{c₂₆}} is non empty set
V . [c₂₆,z19] is set
[FD,d9] is non empty V25() Element of [:(L,FS),(L,FS):]
V . (i,z19) is Element of the carrier of A
[i,z19] is non empty V25() set
{i,z19} is non empty set
{{i,z19},{i}} is non empty set
V . [i,z19] is set
[FD,A9] is non empty V25() Element of [:(L,FS),(L,FS):]
c₂₆ is Element of (L,a)
z19 is Element of (L,a)
h . (c₂₆,z19) is Element of the carrier of A
[c₂₆,z19] is non empty V25() set
{c₂₆,z19} is non empty set
{c₂₆} is non empty trivial V47(1) set
{{c₂₆,z19},{c₂₆}} is non empty set
h . [c₂₆,z19] is set
[FD,d9] is non empty V25() Element of [:(L,FS),(L,FS):]
i is Element of (L,a)
h . (c₂₆,i) is Element of the carrier of A
[c₂₆,i] is non empty V25() set
{c₂₆,i} is non empty set
{{c₂₆,i},{c₂₆}} is non empty set
h . [c₂₆,i] is set
[A9,d9] is non empty V25() Element of [:(L,FS),(L,FS):]
h . (z19,i) is Element of the carrier of A
[z19,i] is non empty V25() set
{z19,i} is non empty set
{z19} is non empty trivial V47(1) set
{{z19,i},{z19}} is non empty set
h . [z19,i] is set
(L,{}) is non empty set
(L,A,D,FS,{}) is Relation-like [:(L,{}),(L,{}):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,{}),(L,{}):], the carrier of A:]
[:(L,{}),(L,{}):] is non empty set
[:[:(L,{}),(L,{}):], the carrier of A:] is non empty set
bool [:[:(L,{}),(L,{}):], the carrier of A:] is non empty V271() set
FS is Element of (L,{})
f is Element of (L,{})
(L,A,D,FS,{}) . (FS,f) is Element of the carrier of A
[FS,f] is non empty V25() set
{FS,f} is non empty set
{FS} is non empty trivial V47(1) set
{{FS,f},{FS}} is non empty set
(L,A,D,FS,{}) . [FS,f] is set
FD is Element of (L,{})
(L,A,D,FS,{}) . (FS,FD) is Element of the carrier of A
[FS,FD] is non empty V25() set
{FS,FD} is non empty set
{{FS,FD},{FS}} is non empty set
(L,A,D,FS,{}) . [FS,FD] is set
(L,A,D,FS,{}) . (FD,f) is Element of the carrier of A
[FD,f] is non empty V25() set
{FD,f} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,f},{FD}} is non empty set
(L,A,D,FS,{}) . [FD,f] is set
((L,A,D,FS,{}) . (FS,FD)) "\/" ((L,A,D,FS,{}) . (FD,f)) is Element of the carrier of A
FS is Element of L
FD is Element of L
D . (FS,FD) is Element of the carrier of A
[FS,FD] is non empty V25() set
{FS,FD} is non empty set
{FS} is non empty trivial V47(1) set
{{FS,FD},{FS}} is non empty set
D . [FS,FD] is set
f is Element of L
D . (FS,f) is Element of the carrier of A
[FS,f] is non empty V25() set
{FS,f} is non empty set
{{FS,f},{FS}} is non empty set
D . [FS,f] is set
D . (f,FD) is Element of the carrier of A
[f,FD] is non empty V25() set
{f,FD} is non empty set
{f} is non empty trivial V47(1) set
{{f,FD},{f}} is non empty set
D . [f,FD] is set
(D . (FS,f)) "\/" (D . (f,FD)) is Element of the carrier of A
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima modular RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:L,L:], the carrier of A:]
S is epsilon-transitive epsilon-connected ordinal set
DistEsti D is epsilon-transitive epsilon-connected ordinal V45() set
FS is T-Sequence-like Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of D
(L,A,D,FS,S) is Relation-like [:(L,S),(L,S):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,S),(L,S):], the carrier of A:]
(L,S) is non empty set
[:(L,S),(L,S):] is non empty set
[:[:(L,S),(L,S):], the carrier of A:] is non empty set
bool [:[:(L,S),(L,S):], the carrier of A:] is non empty V271() set
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:L,L:], the carrier of A:]
DistEsti D is epsilon-transitive epsilon-connected ordinal V45() set
(L,(DistEsti D)) is non empty set
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:L,L:], the carrier of A:]
(L,A,D) is set
DistEsti D is epsilon-transitive epsilon-connected ordinal V45() set
(L,(DistEsti D)) is non empty set
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:L,L:], the carrier of A:]
S is T-Sequence-like Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of D
DistEsti D is epsilon-transitive epsilon-connected ordinal V45() set
(L,A,D,S,(DistEsti D)) is Relation-like [:(L,(DistEsti D)),(L,(DistEsti D)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,(DistEsti D)),(L,(DistEsti D)):], the carrier of A:]
(L,(DistEsti D)) is non empty set
[:(L,(DistEsti D)),(L,(DistEsti D)):] is non empty set
[:[:(L,(DistEsti D)),(L,(DistEsti D)):], the carrier of A:] is non empty set
bool [:[:(L,(DistEsti D)),(L,(DistEsti D)):], the carrier of A:] is non empty V271() set
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima modular RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
[:L,L, the carrier of A, the carrier of A:] is non empty set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:L,L:], the carrier of A:]
S is T-Sequence-like Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of D
(L,A,D,S) is set
DistEsti D is epsilon-transitive epsilon-connected ordinal V45() set
(L,A,D,S,(DistEsti D)) is Relation-like [:(L,(DistEsti D)),(L,(DistEsti D)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,(DistEsti D)),(L,(DistEsti D)):], the carrier of A:]
(L,(DistEsti D)) is non empty set
[:(L,(DistEsti D)),(L,(DistEsti D)):] is non empty set
[:[:(L,(DistEsti D)),(L,(DistEsti D)):], the carrier of A:] is non empty set
bool [:[:(L,(DistEsti D)),(L,(DistEsti D)):], the carrier of A:] is non empty V271() set
(L,A,D) is non empty set
[:(L,A,D),(L,A,D):] is non empty set
[:[:(L,A,D),(L,A,D):], the carrier of A:] is non empty set
bool [:[:(L,A,D),(L,A,D):], the carrier of A:] is non empty V271() set
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
S is non empty set
[:S,S:] is non empty set
[:[:S,S:], the carrier of A:] is non empty set
bool [:[:S,S:], the carrier of A:] is non empty V271() set
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:L,L:], the carrier of A:]
S is non empty set
[:S,S:] is non empty set
[:[:S,S:], the carrier of A:] is non empty set
bool [:[:S,S:], the carrier of A:] is non empty V271() set
FS is Relation-like [:S,S:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:S,S:], the carrier of A:]
[:L,L, the carrier of A, the carrier of A:] is non empty set
(L,A,D) is non empty set
DistEsti D is epsilon-transitive epsilon-connected ordinal V45() set
(L,(DistEsti D)) is non empty set
FS is T-Sequence-like Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of D
(L,A,D,FS) is set
(L,A,D,FS,(DistEsti D)) is Relation-like [:(L,(DistEsti D)),(L,(DistEsti D)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,(DistEsti D)),(L,(DistEsti D)):], the carrier of A:]
[:(L,(DistEsti D)),(L,(DistEsti D)):] is non empty set
[:[:(L,(DistEsti D)),(L,(DistEsti D)):], the carrier of A:] is non empty set
bool [:[:(L,(DistEsti D)),(L,(DistEsti D)):], the carrier of A:] is non empty V271() set
FD is Element of L
f is Element of L
D . (FD,f) is Element of the carrier of A
[FD,f] is non empty V25() set
{FD,f} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,f},{FD}} is non empty set
D . [FD,f] is set
FS is Element of the carrier of A
f is Element of the carrier of A
FS "\/" f is Element of the carrier of A
(D . (FD,f)) "\/" FS is Element of the carrier of A
((D . (FD,f)) "\/" FS) "/\" f is Element of the carrier of A
rng FS is Element of bool [:L,L, the carrier of A, the carrier of A:]
bool [:L,L, the carrier of A, the carrier of A:] is non empty V271() set
{ [b₁,b₂,b₃,b₄] where b₁, b₂ is Element of L, b₃, b₄ is Element of the carrier of A : D . (b₁,b₂) <= b₃ "\/" b₄ } is set
[FD,f,FS,f] is V25() V26() V27() Element of [:L,L, the carrier of A, the carrier of A:]
[FD,f,FS] is V25() V26() set
[[FD,f],FS] is non empty V25() set
{[FD,f],FS} is non empty set
{[FD,f]} is Function-like non empty trivial V47(1) set
{{[FD,f],FS},{[FD,f]}} is non empty set
[[FD,f,FS],f] is non empty V25() set
{[FD,f,FS],f} is non empty set
{[FD,f,FS]} is non empty trivial V47(1) set
{{[FD,f,FS],f},{[FD,f,FS]}} is non empty set
proj1 FS is epsilon-transitive epsilon-connected ordinal set
FD is set
FS . FD is set
A9 is epsilon-transitive epsilon-connected ordinal set
FS . A9 is set
(L,A,D,FS,A9) is Element of [:(L,A9),(L,A9), the carrier of A, the carrier of A:]
(L,A9) is non empty set
[:(L,A9),(L,A9), the carrier of A, the carrier of A:] is non empty set
(L,A,D,FS,A9) `1_4 is Element of (L,A9)
(L,A,D,FS,A9) `1 is set
((L,A,D,FS,A9) `1) `1 is set
(((L,A,D,FS,A9) `1) `1) `1 is set
(L,A,D,FS,A9) `4_4 is Element of the carrier of A
(L,A,D,FS,A9) `2_4 is Element of (L,A9)
(((L,A,D,FS,A9) `1) `1) `2 is set
d9 is non empty set
{d9} is non empty trivial V47(1) set
{{d9}} is non empty trivial V47(1) set
{{d9},{{d9}}} is non empty set
d9 \/ {{d9},{{d9}}} is non empty set
succ A9 is epsilon-transitive epsilon-connected ordinal non empty set
(L,(succ A9)) is non empty set
[:(L,(succ A9)),(L,(succ A9)):] is non empty set
(L,A,D,FS,(succ A9)) is Relation-like [:(L,(succ A9)),(L,(succ A9)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,(succ A9)),(L,(succ A9)):], the carrier of A:]
[:[:(L,(succ A9)),(L,(succ A9)):], the carrier of A:] is non empty set
bool [:[:(L,(succ A9)),(L,(succ A9)):], the carrier of A:] is non empty V271() set
[:d9,d9:] is non empty set
[:[:d9,d9:], the carrier of A:] is non empty set
bool [:[:d9,d9:], the carrier of A:] is non empty V271() set
(L,A,D,FS,A9) is Relation-like [:(L,A9),(L,A9):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,A9),(L,A9):], the carrier of A:]
[:(L,A9),(L,A9):] is non empty set
[:[:(L,A9),(L,A9):], the carrier of A:] is non empty set
bool [:[:(L,A9),(L,A9):], the carrier of A:] is non empty V271() set
[:d9,d9, the carrier of A, the carrier of A:] is non empty set
(d9) is non empty set
q is Element of S
FS . (FD,q) is set
[FD,q] is non empty V25() set
{FD,q} is non empty set
{{FD,q},{FD}} is non empty set
FS . [FD,q] is set
Q is Element of S
FS . (q,Q) is Element of the carrier of A
[q,Q] is non empty V25() set
{q,Q} is non empty set
{q} is non empty trivial V47(1) set
{{q,Q},{q}} is non empty set
FS . [q,Q] is set
FS . (Q,f) is set
[Q,f] is non empty V25() set
{Q,f} is non empty set
{Q} is non empty trivial V47(1) set
{{Q,f},{Q}} is non empty set
FS . [Q,f] is set
Aq9 is Relation-like [:d9,d9:] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:d9,d9:], the carrier of A:]
u is Element of d9
v is Element of d9
BiFun ((L,A,D,FS,A9),(L,A9),A) is Relation-like [:(L,A9),(L,A9):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,A9),(L,A9):], the carrier of A:]
((L,A9),A,(BiFun ((L,A,D,FS,A9),(L,A9),A)),(L,A,D,FS,A9)) is Relation-like [:((L,A9)),((L,A9)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:((L,A9)),((L,A9)):], the carrier of A:]
((L,A9)) is non empty set
{(L,A9)} is non empty trivial V47(1) set
{{(L,A9)}} is non empty trivial V47(1) set
{{(L,A9)},{{(L,A9)}}} is non empty set
(L,A9) \/ {{(L,A9)},{{(L,A9)}}} is non empty set
[:((L,A9)),((L,A9)):] is non empty set
[:[:((L,A9)),((L,A9)):], the carrier of A:] is non empty set
bool [:[:((L,A9)),((L,A9)):], the carrier of A:] is non empty V271() set
dq9 is Element of [:d9,d9, the carrier of A, the carrier of A:]
(d9,A,Aq9,dq9) is Relation-like [:(d9),(d9):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(d9),(d9):], the carrier of A:]
[:(d9),(d9):] is non empty set
[:[:(d9),(d9):], the carrier of A:] is non empty set
bool [:[:(d9),(d9):], the carrier of A:] is non empty V271() set
dom D is Relation-like L -defined L -valued Element of bool [:L,L:]
bool [:L,L:] is non empty V271() set
[u,v] is non empty V25() Element of [:d9,d9:]
{u,v} is non empty set
{u} is non empty trivial V47(1) set
{{u,v},{u}} is non empty set
Aq9 . (u,v) is Element of the carrier of A
[u,v] is non empty V25() set
Aq9 . [u,v] is set
(L,A,D,FS,A9) `3_4 is Element of the carrier of A
((L,A,D,FS,A9) `1) `2 is set
dom (d9,A,Aq9,dq9) is Relation-like (d9) -defined (d9) -valued Element of bool [:(d9),(d9):]
bool [:(d9),(d9):] is non empty V271() set
a is Element of (d9)
[a,{d9}] is non empty V25() set
{a,{d9}} is non empty set
{a} is non empty trivial V47(1) set
{{a,{d9}},{a}} is non empty set
(d9,A,Aq9,dq9) . (a,{d9}) is set
(d9,A,Aq9,dq9) . [a,{d9}] is set
Aq9 . (u,u) is Element of the carrier of A
[u,u] is non empty V25() set
{u,u} is non empty set
{{u,u},{u}} is non empty set
Aq9 . [u,u] is set
(Aq9 . (u,u)) "\/" FS is Element of the carrier of A
Bottom A is Element of the carrier of A
"\/" ({},A) is Element of the carrier of A
(Bottom A) "\/" FS is Element of the carrier of A
[{d9},{{d9}}] is non empty V25() set
{{{d9},{{d9}}},{{d9}}} is non empty set
(d9,A,Aq9,dq9) . ({d9},{{d9}}) is set
(d9,A,Aq9,dq9) . [{d9},{{d9}}] is set
b is Element of (d9)
[{{d9}},b] is non empty V25() set
{{{d9}},b} is non empty set
{{{d9}}} is non empty trivial V47(1) set
{{{{d9}},b},{{{d9}}}} is non empty set
(d9,A,Aq9,dq9) . ({{d9}},b) is set
(d9,A,Aq9,dq9) . [{{d9}},b] is set
Aq9 . (v,v) is Element of the carrier of A
[v,v] is non empty V25() set
{v,v} is non empty set
{v} is non empty trivial V47(1) set
{{v,v},{v}} is non empty set
Aq9 . [v,v] is set
(Aq9 . (v,v)) "\/" FS is Element of the carrier of A
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima modular RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:L,L:], the carrier of A:]
[L,D] is non empty V25() set
{L,D} is non empty set
{L} is non empty trivial V47(1) set
{{L,D},{L}} is non empty set
S is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
FS is set
FS is non empty set
[:FS,FS:] is non empty set
[:[:FS,FS:], the carrier of A:] is non empty set
bool [:[:FS,FS:], the carrier of A:] is non empty V271() set
f is non empty set
[:f,f:] is non empty set
[:[:f,f:], the carrier of A:] is non empty set
bool [:[:f,f:], the carrier of A:] is non empty V271() set
FD is Relation-like [:FS,FS:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:FS,FS:], the carrier of A:]
FS is Relation-like [:f,f:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:f,f:], the carrier of A:]
[FS,FD] is non empty V25() set
{FS,FD} is non empty set
{FS} is non empty trivial V47(1) set
{{FS,FD},{FS}} is non empty set
FS is non empty set
[:FS,FS:] is non empty set
[:[:FS,FS:], the carrier of A:] is non empty set
bool [:[:FS,FS:], the carrier of A:] is non empty V271() set
f is non empty set
[:f,f:] is non empty set
[:[:f,f:], the carrier of A:] is non empty set
bool [:[:f,f:], the carrier of A:] is non empty V271() set
FD is Relation-like [:FS,FS:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:FS,FS:], the carrier of A:]
FS is Relation-like [:f,f:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:f,f:], the carrier of A:]
[FS,FD] is non empty V25() set
{FS,FD} is non empty set
{FS} is non empty trivial V47(1) set
{{FS,FD},{FS}} is non empty set
[f,FS] is non empty V25() set
{f,FS} is non empty set
{f} is non empty trivial V47(1) set
{{f,FS},{f}} is non empty set
f is non empty set
[:f,f:] is non empty set
[:[:f,f:], the carrier of A:] is non empty set
bool [:[:f,f:], the carrier of A:] is non empty V271() set
A9 is non empty set
[:A9,A9:] is non empty set
[:[:A9,A9:], the carrier of A:] is non empty set
bool [:[:A9,A9:], the carrier of A:] is non empty V271() set
FD is Relation-like [:f,f:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:f,f:], the carrier of A:]
d9 is Relation-like [:A9,A9:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:A9,A9:], the carrier of A:]
[f,FD] is non empty V25() set
{f,FD} is non empty set
{f} is non empty trivial V47(1) set
{{f,FD},{f}} is non empty set
FS is non empty set
[:FS,FS:] is non empty set
[:[:FS,FS:], the carrier of A:] is non empty set
bool [:[:FS,FS:], the carrier of A:] is non empty V271() set
f is non empty set
[:f,f:] is non empty set
[:[:f,f:], the carrier of A:] is non empty set
bool [:[:f,f:], the carrier of A:] is non empty V271() set
FD is Relation-like [:FS,FS:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:FS,FS:], the carrier of A:]
FS is Relation-like [:f,f:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:f,f:], the carrier of A:]
[FS,FD] is non empty V25() set
{FS,FD} is non empty set
{FS} is non empty trivial V47(1) set
{{FS,FD},{FS}} is non empty set
FS is non empty set
[:FS,FS:] is non empty set
[:[:FS,FS:], the carrier of A:] is non empty set
bool [:[:FS,FS:], the carrier of A:] is non empty V271() set
f is non empty set
[:f,f:] is non empty set
[:[:f,f:], the carrier of A:] is non empty set
bool [:[:f,f:], the carrier of A:] is non empty V271() set
FD is Relation-like [:FS,FS:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:FS,FS:], the carrier of A:]
FS is Relation-like [:f,f:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:f,f:], the carrier of A:]
[FS,FD] is non empty V25() set
{FS,FD} is non empty set
{FS} is non empty trivial V47(1) set
{{FS,FD},{FS}} is non empty set
S is Relation-like Function-like set
proj1 S is set
S . 0 is set
FS is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
S . FS is set
FS + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
S . (FS + 1) is set
(FS + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
S . ((FS + 1) + 1) is set
FS is non empty set
[:FS,FS:] is non empty set
[:[:FS,FS:], the carrier of A:] is non empty set
bool [:[:FS,FS:], the carrier of A:] is non empty V271() set
f is non empty set
[:f,f:] is non empty set
[:[:f,f:], the carrier of A:] is non empty set
bool [:[:f,f:], the carrier of A:] is non empty V271() set
FD is Relation-like [:FS,FS:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:FS,FS:], the carrier of A:]
FS is Relation-like [:f,f:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:f,f:], the carrier of A:]
[FS,FD] is non empty V25() set
{FS,FD} is non empty set
{FS} is non empty trivial V47(1) set
{{FS,FD},{FS}} is non empty set
[f,FS] is non empty V25() set
{f,FS} is non empty set
{f} is non empty trivial V47(1) set
{{f,FS},{f}} is non empty set
[:f,f, the carrier of A, the carrier of A:] is non empty set
the T-Sequence-like Relation-like [:f,f, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of FS is T-Sequence-like Relation-like [:f,f, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of FS
(f,A,FS) is non empty set
DistEsti FS is epsilon-transitive epsilon-connected ordinal V45() set
(f,(DistEsti FS)) is non empty set
(f,A,FS, the T-Sequence-like Relation-like [:f,f, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of FS) is Relation-like [:(f,A,FS),(f,A,FS):] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:(f,A,FS),(f,A,FS):], the carrier of A:]
[:(f,A,FS),(f,A,FS):] is non empty set
[:[:(f,A,FS),(f,A,FS):], the carrier of A:] is non empty set
bool [:[:(f,A,FS),(f,A,FS):], the carrier of A:] is non empty V271() set
(f,A,FS, the T-Sequence-like Relation-like [:f,f, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of FS,(DistEsti FS)) is Relation-like [:(f,(DistEsti FS)),(f,(DistEsti FS)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(f,(DistEsti FS)),(f,(DistEsti FS)):], the carrier of A:]
[:(f,(DistEsti FS)),(f,(DistEsti FS)):] is non empty set
[:[:(f,(DistEsti FS)),(f,(DistEsti FS)):], the carrier of A:] is non empty set
bool [:[:(f,(DistEsti FS)),(f,(DistEsti FS)):], the carrier of A:] is non empty V271() set
f is non empty set
[:f,f:] is non empty set
[:[:f,f:], the carrier of A:] is non empty set
bool [:[:f,f:], the carrier of A:] is non empty V271() set
A9 is non empty set
[:A9,A9:] is non empty set
[:[:A9,A9:], the carrier of A:] is non empty set
bool [:[:A9,A9:], the carrier of A:] is non empty V271() set
FD is Relation-like [:f,f:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:f,f:], the carrier of A:]
d9 is Relation-like [:A9,A9:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:A9,A9:], the carrier of A:]
[f,FD] is non empty V25() set
{f,FD} is non empty set
{f} is non empty trivial V47(1) set
{{f,FD},{f}} is non empty set
(L,A,D) is non empty set
DistEsti D is epsilon-transitive epsilon-connected ordinal V45() set
(L,(DistEsti D)) is non empty set
[:L,L, the carrier of A, the carrier of A:] is non empty set
the T-Sequence-like Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of D is T-Sequence-like Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of D
[:(L,A,D),(L,A,D):] is non empty set
[:[:(L,A,D),(L,A,D):], the carrier of A:] is non empty set
bool [:[:(L,A,D),(L,A,D):], the carrier of A:] is non empty V271() set
(L,A,D, the T-Sequence-like Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of D) is Relation-like [:(L,A,D),(L,A,D):] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:(L,A,D),(L,A,D):], the carrier of A:]
(L,A,D, the T-Sequence-like Relation-like [:L,L, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of D,(DistEsti D)) is Relation-like [:(L,(DistEsti D)),(L,(DistEsti D)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(L,(DistEsti D)),(L,(DistEsti D)):], the carrier of A:]
[:(L,(DistEsti D)),(L,(DistEsti D)):] is non empty set
[:[:(L,(DistEsti D)),(L,(DistEsti D)):], the carrier of A:] is non empty set
bool [:[:(L,(DistEsti D)),(L,(DistEsti D)):], the carrier of A:] is non empty V271() set
FD is Relation-like [:(L,A,D),(L,A,D):] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:(L,A,D),(L,A,D):], the carrier of A:]
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
S . (0 + 1) is set
FS is non empty set
[:FS,FS:] is non empty set
[:[:FS,FS:], the carrier of A:] is non empty set
bool [:[:FS,FS:], the carrier of A:] is non empty V271() set
FD is non empty set
[:FD,FD:] is non empty set
[:[:FD,FD:], the carrier of A:] is non empty set
bool [:[:FD,FD:], the carrier of A:] is non empty V271() set
FS is Relation-like [:FS,FS:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:FS,FS:], the carrier of A:]
f is Relation-like [:FD,FD:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:FD,FD:], the carrier of A:]
[FS,FS] is non empty V25() set
{FS,FS} is non empty set
{FS} is non empty trivial V47(1) set
{{FS,FS},{FS}} is non empty set
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima modular RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:L,L:], the carrier of A:]
S is Relation-like Function-like (L,A,D)
FS is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
S . FS is set
(S . FS) `1 is set
FS is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
S . FS is set
(S . FS) `1 is set
FS + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
S . (FS + 1) is set
(S . (FS + 1)) `1 is set
FD is non empty set
[:FD,FD:] is non empty set
[:[:FD,FD:], the carrier of A:] is non empty set
bool [:[:FD,FD:], the carrier of A:] is non empty V271() set
FS is non empty set
[:FS,FS:] is non empty set
[:[:FS,FS:], the carrier of A:] is non empty set
bool [:[:FS,FS:], the carrier of A:] is non empty V271() set
f is Relation-like [:FD,FD:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:FD,FD:], the carrier of A:]
f is Relation-like [:FS,FS:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:FS,FS:], the carrier of A:]
[FD,f] is non empty V25() set
{FD,f} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,f},{FD}} is non empty set
[FS,f] is non empty V25() set
{FS,f} is non empty set
{FS} is non empty trivial V47(1) set
{{FS,f},{FS}} is non empty set
[FD,f] `1 is set
DistEsti f is epsilon-transitive epsilon-connected ordinal V45() set
(FD,(DistEsti f)) is non empty set
[:FD,FD, the carrier of A, the carrier of A:] is non empty set
(FD,A,f) is non empty set
[:(FD,A,f),(FD,A,f):] is non empty set
[FS,f] `1 is set
FD is T-Sequence-like Relation-like [:FD,FD, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of f
(FD,A,f,FD) is Relation-like [:(FD,A,f),(FD,A,f):] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:(FD,A,f),(FD,A,f):], the carrier of A:]
[:[:(FD,A,f),(FD,A,f):], the carrier of A:] is non empty set
bool [:[:(FD,A,f),(FD,A,f):], the carrier of A:] is non empty V271() set
(FD,A,f,FD,(DistEsti f)) is Relation-like [:(FD,(DistEsti f)),(FD,(DistEsti f)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(FD,(DistEsti f)),(FD,(DistEsti f)):], the carrier of A:]
[:(FD,(DistEsti f)),(FD,(DistEsti f)):] is non empty set
[:[:(FD,(DistEsti f)),(FD,(DistEsti f)):], the carrier of A:] is non empty set
bool [:[:(FD,(DistEsti f)),(FD,(DistEsti f)):], the carrier of A:] is non empty V271() set
S . 0 is set
(S . 0) `1 is set
L is non empty set
[:L,L:] is non empty set
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima modular RelStr
the carrier of A is non empty set
[:[:L,L:], the carrier of A:] is non empty set
bool [:[:L,L:], the carrier of A:] is non empty V271() set
D is Relation-like [:L,L:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:L,L:], the carrier of A:]
S is Relation-like Function-like (L,A,D)
FS is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
S . FS is set
(S . FS) `2 is set
FS is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
S . FS is set
(S . FS) `2 is set
FS + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
S . (FS + 1) is set
(S . (FS + 1)) `2 is set
FD is non empty set
[:FD,FD:] is non empty set
[:[:FD,FD:], the carrier of A:] is non empty set
bool [:[:FD,FD:], the carrier of A:] is non empty V271() set
FS is non empty set
[:FS,FS:] is non empty set
[:[:FS,FS:], the carrier of A:] is non empty set
bool [:[:FS,FS:], the carrier of A:] is non empty V271() set
f is Relation-like [:FD,FD:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:FD,FD:], the carrier of A:]
f is Relation-like [:FS,FS:] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:FS,FS:], the carrier of A:]
[FD,f] is non empty V25() set
{FD,f} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,f},{FD}} is non empty set
[FS,f] is non empty V25() set
{FS,f} is non empty set
{FS} is non empty trivial V47(1) set
{{FS,f},{FS}} is non empty set
[:FD,FD, the carrier of A, the carrier of A:] is non empty set
(FD,A,f) is non empty set
DistEsti f is epsilon-transitive epsilon-connected ordinal V45() set
(FD,(DistEsti f)) is non empty set
[:(FD,A,f),(FD,A,f):] is non empty set
FD is T-Sequence-like Relation-like [:FD,FD, the carrier of A, the carrier of A:] -valued Function-like QuadrSeq of f
(FD,A,f,FD) is Relation-like [:(FD,A,f),(FD,A,f):] -defined the carrier of A -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:(FD,A,f),(FD,A,f):], the carrier of A:]
[:[:(FD,A,f),(FD,A,f):], the carrier of A:] is non empty set
bool [:[:(FD,A,f),(FD,A,f):], the carrier of A:] is non empty V271() set
(FD,A,f,FD,(DistEsti f)) is Relation-like [:(FD,(DistEsti f)),(FD,(DistEsti f)):] -defined the carrier of A -valued Function-like quasi_total Element of bool [:[:(FD,(DistEsti f)),(FD,(DistEsti f)):], the carrier of A:]
[:(FD,(DistEsti f)),(FD,(DistEsti f)):] is non empty set
[:[:(FD,(DistEsti f)),(FD,(DistEsti f)):], the carrier of A:] is non empty set
bool [:[:(FD,(DistEsti f)),(FD,(DistEsti f)):], the carrier of A:] is non empty V271() set
[FD,f] `2 is set
[FS,f] `2 is set
S . 0 is set
(S . 0) `2 is set
L is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima modular RelStr
the carrier of L is non empty set
BasicDF L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is non empty set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is non empty set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is non empty V271() set
A is Relation-like Function-like ( the carrier of L,L, BasicDF L)
{ ((A . b<sub>1</sub>) `1) where b₁ is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT : verum } is set
union { ((A . b₁) `1) where b<sub>1</sub> is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT : verum } is set
{ ((A . b<sub>1</sub>) `2) where b₁ is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT : verum } is set
union { ((A . b₁) `2) where b<sub>1</sub> is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT : verum } is set
D is non empty set
[:D,D:] is non empty set
[:[:D,D:], the carrier of L:] is non empty set
bool [:[:D,D:], the carrier of L:] is non empty V271() set
FD is set
f is set
FS is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . FS is set
(A . FS) `2 is set
f is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . f is set
(A . f) `2 is set
S is non empty set
[:S,S:] is non empty set
PFuncs ([:S,S:], the carrier of L) is functional non empty set
FD is set
f is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . f is set
(A . f) `2 is set
f + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . (f + 1) is set
FS is non empty set
[:FS,FS:] is non empty set
[:[:FS,FS:], the carrier of L:] is non empty set
bool [:[:FS,FS:], the carrier of L:] is non empty V271() set
FD is non empty set
[:FD,FD:] is non empty set
[:[:FD,FD:], the carrier of L:] is non empty set
bool [:[:FD,FD:], the carrier of L:] is non empty V271() set
f is Relation-like [:FS,FS:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:FS,FS:], the carrier of L:]
A9 is Relation-like [:FD,FD:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:FD,FD:], the carrier of L:]
[FS,f] is non empty V25() set
{FS,f} is non empty set
{FS} is non empty trivial V47(1) set
{{FS,f},{FS}} is non empty set
[FD,A9] is non empty V25() set
{FD,A9} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,A9},{FD}} is non empty set
[FS,f] `1 is set
[FS,f] `2 is set
dom f is Relation-like FS -defined FS -valued Element of bool [:FS,FS:]
bool [:FS,FS:] is non empty V271() set
rng f is Element of bool the carrier of L
bool the carrier of L is non empty V271() set
A . 0 is set
(A . 0) `1 is set
FD is non empty set
{ [:b<sub>1</sub>,b<sub>1</sub>:] where b<sub>1</sub> is Element of FD : b<sub>1</sub> in FD } is set
{ [:((A . b<sub>1</sub>) `1),((A . b₁) `1):] where b<sub>1</sub> is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT : verum } is set
f is set
FD is Element of FD
[:FD,FD:] is set
A9 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . A9 is set
(A . A9) `1 is set
f is set
FD is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . FD is set
(A . FD) `1 is set
[:((A . FD) `1),((A . FD) `1):] is set
FD is Relation-like Function-like set
proj1 FD is set
proj2 FD is set
FD is set
A . FD is set
(A . FD) `2 is set
FD is Relation-like Function-like set
proj1 FD is set
proj2 FD is set
A9 is set
d9 is set
FD . d9 is set
Aq9 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . Aq9 is set
(A . Aq9) `2 is set
A9 is set
d9 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . d9 is set
(A . d9) `2 is set
FD . d9 is set
A9 is set
FD . A9 is set
d9 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . d9 is set
d9 + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . (d9 + 1) is set
Aq9 is non empty set
[:Aq9,Aq9:] is non empty set
[:[:Aq9,Aq9:], the carrier of L:] is non empty set
bool [:[:Aq9,Aq9:], the carrier of L:] is non empty V271() set
q is non empty set
[:q,q:] is non empty set
[:[:q,q:], the carrier of L:] is non empty set
bool [:[:q,q:], the carrier of L:] is non empty V271() set
dq9 is Relation-like [:Aq9,Aq9:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:Aq9,Aq9:], the carrier of L:]
Q is Relation-like [:q,q:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:q,q:], the carrier of L:]
[Aq9,dq9] is non empty V25() set
{Aq9,dq9} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,dq9},{Aq9}} is non empty set
[q,Q] is non empty V25() set
{q,Q} is non empty set
{q} is non empty trivial V47(1) set
{{q,Q},{q}} is non empty set
[Aq9,dq9] `2 is set
A9 is Relation-like Function-like Function-yielding V32() set
doms A9 is Relation-like Function-like set
proj2 (doms A9) is set
d9 is set
proj1 (doms A9) is set
Aq9 is set
(doms A9) . Aq9 is set
proj1 A9 is set
dq9 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . dq9 is set
dq9 + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . (dq9 + 1) is set
q is non empty set
[:q,q:] is non empty set
[:[:q,q:], the carrier of L:] is non empty set
bool [:[:q,q:], the carrier of L:] is non empty V271() set
u is non empty set
[:u,u:] is non empty set
[:[:u,u:], the carrier of L:] is non empty set
bool [:[:u,u:], the carrier of L:] is non empty V271() set
Q is Relation-like [:q,q:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:q,q:], the carrier of L:]
v is Relation-like [:u,u:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:u,u:], the carrier of L:]
[q,Q] is non empty V25() set
{q,Q} is non empty set
{q} is non empty trivial V47(1) set
{{q,Q},{q}} is non empty set
[u,v] is non empty V25() set
{u,v} is non empty set
{u} is non empty trivial V47(1) set
{{u,v},{u}} is non empty set
[q,Q] `2 is set
[q,Q] `1 is set
A9 . dq9 is Relation-like Function-like set
proj1 (A9 . dq9) is set
dom Q is Relation-like q -defined q -valued Element of bool [:q,q:]
bool [:q,q:] is non empty V271() set
(A . dq9) `1 is set
[:((A . dq9) `1),((A . dq9) `1):] is set
d9 is set
Aq9 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . Aq9 is set
(A . Aq9) `1 is set
[:((A . Aq9) `1),((A . Aq9) `1):] is set
Aq9 + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . (Aq9 + 1) is set
dq9 is non empty set
[:dq9,dq9:] is non empty set
[:[:dq9,dq9:], the carrier of L:] is non empty set
bool [:[:dq9,dq9:], the carrier of L:] is non empty V271() set
Q is non empty set
[:Q,Q:] is non empty set
[:[:Q,Q:], the carrier of L:] is non empty set
bool [:[:Q,Q:], the carrier of L:] is non empty V271() set
q is Relation-like [:dq9,dq9:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:dq9,dq9:], the carrier of L:]
u is Relation-like [:Q,Q:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:Q,Q:], the carrier of L:]
[dq9,q] is non empty V25() set
{dq9,q} is non empty set
{dq9} is non empty trivial V47(1) set
{{dq9,q},{dq9}} is non empty set
[Q,u] is non empty V25() set
{Q,u} is non empty set
{Q} is non empty trivial V47(1) set
{{Q,u},{Q}} is non empty set
[dq9,q] `2 is set
proj1 (doms A9) is set
[dq9,q] `1 is set
dom q is Relation-like dq9 -defined dq9 -valued Element of bool [:dq9,dq9:]
bool [:dq9,dq9:] is non empty V271() set
A9 . Aq9 is Relation-like Function-like set
proj1 (A9 . Aq9) is set
(doms A9) . Aq9 is set
d9 is set
Aq9 is set
dq9 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . dq9 is set
(A . dq9) `1 is set
q is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . q is set
(A . q) `1 is set
union (proj2 (doms A9)) is set
f is Relation-like Function-like set
proj1 f is set
[:[:S,S:], the carrier of L:] is non empty set
bool [:[:S,S:], the carrier of L:] is non empty V271() set
Aq9 is Relation-like Function-like set
proj1 Aq9 is set
proj2 Aq9 is set
d9 is Relation-like [:S,S:] -defined the carrier of L -valued Function-like quasi_total Element of bool [:[:S,S:], the carrier of L:]
Aq9 is Element of S
dq9 is Element of S
d9 . (Aq9,dq9) is Element of the carrier of L
[Aq9,dq9] is non empty V25() set
{Aq9,dq9} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,dq9},{Aq9}} is non empty set
d9 . [Aq9,dq9] is set
d9 . (dq9,Aq9) is Element of the carrier of L
[dq9,Aq9] is non empty V25() set
{dq9,Aq9} is non empty set
{dq9} is non empty trivial V47(1) set
{{dq9,Aq9},{dq9}} is non empty set
d9 . [dq9,Aq9] is set
q is set
Q is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . Q is set
(A . Q) `1 is set
Q + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . (Q + 1) is set
u is non empty set
[:u,u:] is non empty set
[:[:u,u:], the carrier of L:] is non empty set
bool [:[:u,u:], the carrier of L:] is non empty V271() set
a is non empty set
[:a,a:] is non empty set
[:[:a,a:], the carrier of L:] is non empty set
bool [:[:a,a:], the carrier of L:] is non empty V271() set
v is Relation-like [:u,u:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:u,u:], the carrier of L:]
b is Relation-like [:a,a:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:a,a:], the carrier of L:]
[u,v] is non empty V25() set
{u,v} is non empty set
{u} is non empty trivial V47(1) set
{{u,v},{u}} is non empty set
[a,b] is non empty V25() set
{a,b} is non empty set
{a} is non empty trivial V47(1) set
{{a,b},{a}} is non empty set
[u,v] `1 is set
[u,v] `2 is set
e is set
W is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . W is set
(A . W) `1 is set
W + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . (W + 1) is set
V is non empty set
[:V,V:] is non empty set
[:[:V,V:], the carrier of L:] is non empty set
bool [:[:V,V:], the carrier of L:] is non empty V271() set
c<sub>26</sub> is non empty set
[:c<sub>26</sub>,c<sub>26</sub>:] is non empty set
[:[:c<sub>26</sub>,c<sub>26</sub>:], the carrier of L:] is non empty set
bool [:[:c<sub>26</sub>,c<sub>26</sub>:], the carrier of L:] is non empty V271() set
h is Relation-like [:V,V:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:V,V:], the carrier of L:]
i is Relation-like [:c<sub>26</sub>,c<sub>26</sub>:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:c<sub>26</sub>,c<sub>26</sub>:], the carrier of L:]
[V,h] is non empty V25() set
{V,h} is non empty set
{V} is non empty trivial V47(1) set
{{V,h},{V}} is non empty set
[c<sub>26</sub>,i] is non empty V25() set
{c<sub>26</sub>,i} is non empty set
{c<sub>26</sub>} is non empty trivial V47(1) set
{{c<sub>26</sub>,i},{c<sub>26</sub>}} is non empty set
[V,h] `1 is set
[V,h] `2 is set
dom h is Relation-like V -defined V -valued Element of bool [:V,V:]
bool [:V,V:] is non empty V271() set
z19 is Element of V
z29 is Element of V
[z19,z29] is non empty V25() Element of [:V,V:]
{z19,z29} is non empty set
{z19} is non empty trivial V47(1) set
{{z19,z29},{z19}} is non empty set
h . [z19,z29] is Element of the carrier of L
h . (z19,z29) is Element of the carrier of L
[z19,z29] is non empty V25() set
h . [z19,z29] is set
h . (z29,z19) is Element of the carrier of L
[z29,z19] is non empty V25() set
{z29,z19} is non empty set
{z29} is non empty trivial V47(1) set
{{z29,z19},{z29}} is non empty set
h . [z29,z19] is set
[z29,z19] is non empty V25() Element of [:V,V:]
d9 . [z29,z19] is set
dom v is Relation-like u -defined u -valued Element of bool [:u,u:]
bool [:u,u:] is non empty V271() set
z19 is Element of u
z29 is Element of u
[z19,z29] is non empty V25() Element of [:u,u:]
{z19,z29} is non empty set
{z19} is non empty trivial V47(1) set
{{z19,z29},{z19}} is non empty set
v . [z19,z29] is Element of the carrier of L
v . (z19,z29) is Element of the carrier of L
[z19,z29] is non empty V25() set
v . [z19,z29] is set
v . (z29,z19) is Element of the carrier of L
[z29,z19] is non empty V25() set
{z29,z19} is non empty set
{z29} is non empty trivial V47(1) set
{{z29,z19},{z29}} is non empty set
v . [z29,z19] is set
[z29,z19] is non empty V25() Element of [:u,u:]
d9 . [z29,z19] is set
Aq9 is Element of S
q is Element of S
d9 . (Aq9,q) is Element of the carrier of L
[Aq9,q] is non empty V25() set
{Aq9,q} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,q},{Aq9}} is non empty set
d9 . [Aq9,q] is set
dq9 is Element of S
d9 . (Aq9,dq9) is Element of the carrier of L
[Aq9,dq9] is non empty V25() set
{Aq9,dq9} is non empty set
{{Aq9,dq9},{Aq9}} is non empty set
d9 . [Aq9,dq9] is set
d9 . (dq9,q) is Element of the carrier of L
[dq9,q] is non empty V25() set
{dq9,q} is non empty set
{dq9} is non empty trivial V47(1) set
{{dq9,q},{dq9}} is non empty set
d9 . [dq9,q] is set
(d9 . (Aq9,dq9)) "\/" (d9 . (dq9,q)) is Element of the carrier of L
Q is set
u is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . u is set
(A . u) `1 is set
u + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . (u + 1) is set
v is non empty set
[:v,v:] is non empty set
[:[:v,v:], the carrier of L:] is non empty set
bool [:[:v,v:], the carrier of L:] is non empty V271() set
b is non empty set
[:b,b:] is non empty set
[:[:b,b:], the carrier of L:] is non empty set
bool [:[:b,b:], the carrier of L:] is non empty V271() set
a is Relation-like [:v,v:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:v,v:], the carrier of L:]
e is Relation-like [:b,b:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:b,b:], the carrier of L:]
[v,a] is non empty V25() set
{v,a} is non empty set
{v} is non empty trivial V47(1) set
{{v,a},{v}} is non empty set
[b,e] is non empty V25() set
{b,e} is non empty set
{b} is non empty trivial V47(1) set
{{b,e},{b}} is non empty set
[v,a] `1 is set
[v,a] `2 is set
dom a is Relation-like v -defined v -valued Element of bool [:v,v:]
bool [:v,v:] is non empty V271() set
W is set
V is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . V is set
(A . V) `1 is set
V + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . (V + 1) is set
h is non empty set
[:h,h:] is non empty set
[:[:h,h:], the carrier of L:] is non empty set
bool [:[:h,h:], the carrier of L:] is non empty V271() set
i is non empty set
[:i,i:] is non empty set
[:[:i,i:], the carrier of L:] is non empty set
bool [:[:i,i:], the carrier of L:] is non empty V271() set
c<sub>26</sub> is Relation-like [:h,h:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:h,h:], the carrier of L:]
z19 is Relation-like [:i,i:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:i,i:], the carrier of L:]
[h,c<sub>26</sub>] is non empty V25() set
{h,c<sub>26</sub>} is non empty set
{h} is non empty trivial V47(1) set
{{h,c<sub>26</sub>},{h}} is non empty set
[i,z19] is non empty V25() set
{i,z19} is non empty set
{i} is non empty trivial V47(1) set
{{i,z19},{i}} is non empty set
[h,c<sub>26</sub>] `1 is set
[h,c₂₆] `2 is set
dom c<sub>26</sub> is Relation-like h -defined h -valued Element of bool [:h,h:]
bool [:h,h:] is non empty V271() set
z29 is set
c<sub>30</sub> is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . c<sub>30</sub> is set
(A . c<sub>30</sub>) `1 is set
c₃₀ + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . (c₃₀ + 1) is set
A3 is non empty set
[:A3,A3:] is non empty set
[:[:A3,A3:], the carrier of L:] is non empty set
bool [:[:A3,A3:], the carrier of L:] is non empty V271() set
Aq3 is non empty set
[:Aq3,Aq3:] is non empty set
[:[:Aq3,Aq3:], the carrier of L:] is non empty set
bool [:[:Aq3,Aq3:], the carrier of L:] is non empty V271() set
d3 is Relation-like [:A3,A3:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:A3,A3:], the carrier of L:]
dq3 is Relation-like [:Aq3,Aq3:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:Aq3,Aq3:], the carrier of L:]
[A3,d3] is non empty V25() set
{A3,d3} is non empty set
{A3} is non empty trivial V47(1) set
{{A3,d3},{A3}} is non empty set
[Aq3,dq3] is non empty V25() set
{Aq3,dq3} is non empty set
{Aq3} is non empty trivial V47(1) set
{{Aq3,dq3},{Aq3}} is non empty set
[A3,d3] `1 is set
[A3,d3] `2 is set
dom d3 is Relation-like A3 -defined A3 -valued Element of bool [:A3,A3:]
bool [:A3,A3:] is non empty V271() set
y9 is Element of A3
z9 is Element of A3
[y9,z9] is non empty V25() Element of [:A3,A3:]
{y9,z9} is non empty set
{y9} is non empty trivial V47(1) set
{{y9,z9},{y9}} is non empty set
d3 . [y9,z9] is Element of the carrier of L
d3 . (y9,z9) is Element of the carrier of L
[y9,z9] is non empty V25() set
d3 . [y9,z9] is set
x9 is Element of A3
[x9,z9] is non empty V25() Element of [:A3,A3:]
{x9,z9} is non empty set
{x9} is non empty trivial V47(1) set
{{x9,z9},{x9}} is non empty set
d3 . [x9,z9] is Element of the carrier of L
d3 . (x9,z9) is Element of the carrier of L
[x9,z9] is non empty V25() set
d3 . [x9,z9] is set
[x9,y9] is non empty V25() Element of [:A3,A3:]
{x9,y9} is non empty set
{{x9,y9},{x9}} is non empty set
d3 . [x9,y9] is Element of the carrier of L
d3 . (x9,y9) is Element of the carrier of L
[x9,y9] is non empty V25() set
d3 . [x9,y9] is set
y9 is Element of h
z9 is Element of h
[y9,z9] is non empty V25() Element of [:h,h:]
{y9,z9} is non empty set
{y9} is non empty trivial V47(1) set
{{y9,z9},{y9}} is non empty set
c₂₆ . [y9,z9] is Element of the carrier of L
c₂₆ . (y9,z9) is Element of the carrier of L
[y9,z9] is non empty V25() set
c₂₆ . [y9,z9] is set
x9 is Element of h
[x9,z9] is non empty V25() Element of [:h,h:]
{x9,z9} is non empty set
{x9} is non empty trivial V47(1) set
{{x9,z9},{x9}} is non empty set
c₂₆ . [x9,z9] is Element of the carrier of L
c₂₆ . (x9,z9) is Element of the carrier of L
[x9,z9] is non empty V25() set
c₂₆ . [x9,z9] is set
[x9,y9] is non empty V25() Element of [:h,h:]
{x9,y9} is non empty set
{{x9,y9},{x9}} is non empty set
c₂₆ . [x9,y9] is Element of the carrier of L
c₂₆ . (x9,y9) is Element of the carrier of L
[x9,y9] is non empty V25() set
c₂₆ . [x9,y9] is set
y9 is Element of A3
z9 is Element of A3
[y9,z9] is non empty V25() Element of [:A3,A3:]
{y9,z9} is non empty set
{y9} is non empty trivial V47(1) set
{{y9,z9},{y9}} is non empty set
d3 . [y9,z9] is Element of the carrier of L
d3 . (y9,z9) is Element of the carrier of L
[y9,z9] is non empty V25() set
d3 . [y9,z9] is set
x9 is Element of A3
[x9,z9] is non empty V25() Element of [:A3,A3:]
{x9,z9} is non empty set
{x9} is non empty trivial V47(1) set
{{x9,z9},{x9}} is non empty set
d3 . [x9,z9] is Element of the carrier of L
d3 . (x9,z9) is Element of the carrier of L
[x9,z9] is non empty V25() set
d3 . [x9,z9] is set
[x9,y9] is non empty V25() Element of [:A3,A3:]
{x9,y9} is non empty set
{{x9,y9},{x9}} is non empty set
d3 . [x9,y9] is Element of the carrier of L
d3 . (x9,y9) is Element of the carrier of L
[x9,y9] is non empty V25() set
d3 . [x9,y9] is set
y9 is Element of v
z9 is Element of v
[y9,z9] is non empty V25() Element of [:v,v:]
{y9,z9} is non empty set
{y9} is non empty trivial V47(1) set
{{y9,z9},{y9}} is non empty set
a . [y9,z9] is Element of the carrier of L
a . (y9,z9) is Element of the carrier of L
[y9,z9] is non empty V25() set
a . [y9,z9] is set
x9 is Element of v
[x9,z9] is non empty V25() Element of [:v,v:]
{x9,z9} is non empty set
{x9} is non empty trivial V47(1) set
{{x9,z9},{x9}} is non empty set
a . [x9,z9] is Element of the carrier of L
a . (x9,z9) is Element of the carrier of L
[x9,z9] is non empty V25() set
a . [x9,z9] is set
[x9,y9] is non empty V25() Element of [:v,v:]
{x9,y9} is non empty set
{{x9,y9},{x9}} is non empty set
a . [x9,y9] is Element of the carrier of L
a . (x9,y9) is Element of the carrier of L
[x9,y9] is non empty V25() set
a . [x9,y9] is set
Aq9 is Element of S
d9 . (Aq9,Aq9) is Element of the carrier of L
[Aq9,Aq9] is non empty V25() set
{Aq9,Aq9} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,Aq9},{Aq9}} is non empty set
d9 . [Aq9,Aq9] is set
Bottom L is Element of the carrier of L
"\/" ({},L) is Element of the carrier of L
dq9 is set
q is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . q is set
(A . q) `1 is set
q + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . (q + 1) is set
Q is non empty set
[:Q,Q:] is non empty set
[:[:Q,Q:], the carrier of L:] is non empty set
bool [:[:Q,Q:], the carrier of L:] is non empty V271() set
v is non empty set
[:v,v:] is non empty set
[:[:v,v:], the carrier of L:] is non empty set
bool [:[:v,v:], the carrier of L:] is non empty V271() set
u is Relation-like [:Q,Q:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:Q,Q:], the carrier of L:]
a is Relation-like [:v,v:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:v,v:], the carrier of L:]
[Q,u] is non empty V25() set
{Q,u} is non empty set
{Q} is non empty trivial V47(1) set
{{Q,u},{Q}} is non empty set
[v,a] is non empty V25() set
{v,a} is non empty set
{v} is non empty trivial V47(1) set
{{v,a},{v}} is non empty set
[Q,u] `2 is set
[Q,u] `1 is set
dom u is Relation-like Q -defined Q -valued Element of bool [:Q,Q:]
bool [:Q,Q:] is non empty V271() set
b is Element of Q
[b,b] is non empty V25() Element of [:Q,Q:]
{b,b} is non empty set
{b} is non empty trivial V47(1) set
{{b,b},{b}} is non empty set
u . [b,b] is Element of the carrier of L
u . (b,b) is Element of the carrier of L
[b,b] is non empty V25() set
u . [b,b] is set
L is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima modular RelStr
the carrier of L is non empty set
BasicDF L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is non empty set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is non empty set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is non empty V271() set
A is Relation-like Function-like ( the carrier of L,L, BasicDF L)
{ ((A . b<sub>1</sub>) `1) where b₁ is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT : verum } is set
union { ((A . b₁) `1) where b<sub>1</sub> is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT : verum } is set
{ ((A . b<sub>1</sub>) `2) where b₁ is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT : verum } is set
union { ((A . b₁) `2) where b<sub>1</sub> is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT : verum } is set
D is non empty set
[:D,D:] is non empty set
[:[:D,D:], the carrier of L:] is non empty set
bool [:[:D,D:], the carrier of L:] is non empty V271() set
S is Relation-like [:D,D:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:D,D:], the carrier of L:]
FS is Element of D
FS is Element of D
S . (FS,FS) is Element of the carrier of L
[FS,FS] is non empty V25() set
{FS,FS} is non empty set
{FS} is non empty trivial V47(1) set
{{FS,FS},{FS}} is non empty set
S . [FS,FS] is set
FD is Element of the carrier of L
f is Element of the carrier of L
FD "\/" f is Element of the carrier of L
(S . (FS,FS)) "\/" FD is Element of the carrier of L
((S . (FS,FS)) "\/" FD) "/\" f is Element of the carrier of L
A . 0 is set
(A . 0) `1 is set
FS is non empty set
f is set
FD is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . FD is set
(A . FD) `1 is set
FD + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . (FD + 1) is set
A9 is non empty set
[:A9,A9:] is non empty set
[:[:A9,A9:], the carrier of L:] is non empty set
bool [:[:A9,A9:], the carrier of L:] is non empty V271() set
Aq9 is non empty set
[:Aq9,Aq9:] is non empty set
[:[:Aq9,Aq9:], the carrier of L:] is non empty set
bool [:[:Aq9,Aq9:], the carrier of L:] is non empty V271() set
d9 is Relation-like [:A9,A9:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:A9,A9:], the carrier of L:]
dq9 is Relation-like [:Aq9,Aq9:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:Aq9,Aq9:], the carrier of L:]
[A9,d9] is non empty V25() set
{A9,d9} is non empty set
{A9} is non empty trivial V47(1) set
{{A9,d9},{A9}} is non empty set
[Aq9,dq9] is non empty V25() set
{Aq9,dq9} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,dq9},{Aq9}} is non empty set
[A9,d9] `1 is set
[A9,d9] `2 is set
[Aq9,dq9] `1 is set
[Aq9,dq9] `2 is set
q is set
Q is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . Q is set
(A . Q) `1 is set
Q + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
A . (Q + 1) is set
u is non empty set
[:u,u:] is non empty set
[:[:u,u:], the carrier of L:] is non empty set
bool [:[:u,u:], the carrier of L:] is non empty V271() set
a is non empty set
[:a,a:] is non empty set
[:[:a,a:], the carrier of L:] is non empty set
bool [:[:a,a:], the carrier of L:] is non empty V271() set
v is Relation-like [:u,u:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:u,u:], the carrier of L:]
b is Relation-like [:a,a:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:a,a:], the carrier of L:]
[u,v] is non empty V25() set
{u,v} is non empty set
{u} is non empty trivial V47(1) set
{{u,v},{u}} is non empty set
[a,b] is non empty V25() set
{a,b} is non empty set
{a} is non empty trivial V47(1) set
{{a,b},{a}} is non empty set
[u,v] `1 is set
[u,v] `2 is set
[a,b] `1 is set
[a,b] `2 is set
e is Element of u
W is Element of u
dom v is Relation-like u -defined u -valued Element of bool [:u,u:]
bool [:u,u:] is non empty V271() set
[e,W] is non empty V25() Element of [:u,u:]
{e,W} is non empty set
{e} is non empty trivial V47(1) set
{{e,W},{e}} is non empty set
v . [e,W] is Element of the carrier of L
v . (e,W) is Element of the carrier of L
[e,W] is non empty V25() set
v . [e,W] is set
(v . (e,W)) "\/" FD is Element of the carrier of L
((v . (e,W)) "\/" FD) "/\" f is Element of the carrier of L
c₂₆ is Element of a
b . (FS,c₂₆) is set
[FS,c₂₆] is non empty V25() set
{FS,c₂₆} is non empty set
{{FS,c₂₆},{FS}} is non empty set
b . [FS,c₂₆] is set
i is Element of a
b . (c₂₆,i) is Element of the carrier of L
[c₂₆,i] is non empty V25() set
{c₂₆,i} is non empty set
{c₂₆} is non empty trivial V47(1) set
{{c₂₆,i},{c₂₆}} is non empty set
b . [c₂₆,i] is set
b . (i,FS) is set
[i,FS] is non empty V25() set
{i,FS} is non empty set
{i} is non empty trivial V47(1) set
{{i,FS},{i}} is non empty set
b . [i,FS] is set
z19 is Element of D
S . (FS,z19) is Element of the carrier of L
[FS,z19] is non empty V25() set
{FS,z19} is non empty set
{{FS,z19},{FS}} is non empty set
S . [FS,z19] is set
z29 is Element of D
S . (z19,z29) is Element of the carrier of L
[z19,z29] is non empty V25() set
{z19,z29} is non empty set
{z19} is non empty trivial V47(1) set
{{z19,z29},{z19}} is non empty set
S . [z19,z29] is set
S . (z29,FS) is Element of the carrier of L
[z29,FS] is non empty V25() set
{z29,FS} is non empty set
{z29} is non empty trivial V47(1) set
{{z29,FS},{z29}} is non empty set
S . [z29,FS] is set
dom b is Relation-like a -defined a -valued Element of bool [:a,a:]
bool [:a,a:] is non empty V271() set
V is Element of a
[V,c₂₆] is non empty V25() Element of [:a,a:]
{V,c₂₆} is non empty set
{V} is non empty trivial V47(1) set
{{V,c₂₆},{V}} is non empty set
b . [V,c₂₆] is Element of the carrier of L
[c₂₆,i] is non empty V25() Element of [:a,a:]
b . [c₂₆,i] is Element of the carrier of L
h is Element of a
[i,h] is non empty V25() Element of [:a,a:]
{i,h} is non empty set
{{i,h},{i}} is non empty set
b . [i,h] is Element of the carrier of L
e is Element of A9
W is Element of A9
dom d9 is Relation-like A9 -defined A9 -valued Element of bool [:A9,A9:]
bool [:A9,A9:] is non empty V271() set
[e,W] is non empty V25() Element of [:A9,A9:]
{e,W} is non empty set
{e} is non empty trivial V47(1) set
{{e,W},{e}} is non empty set
d9 . [e,W] is Element of the carrier of L
d9 . (e,W) is Element of the carrier of L
[e,W] is non empty V25() set
d9 . [e,W] is set
(d9 . (e,W)) "\/" FD is Element of the carrier of L
((d9 . (e,W)) "\/" FD) "/\" f is Element of the carrier of L
c₂₆ is Element of Aq9
dq9 . (FS,c₂₆) is set
[FS,c₂₆] is non empty V25() set
{FS,c₂₆} is non empty set
{{FS,c₂₆},{FS}} is non empty set
dq9 . [FS,c₂₆] is set
i is Element of Aq9
dq9 . (c₂₆,i) is Element of the carrier of L
[c₂₆,i] is non empty V25() set
{c₂₆,i} is non empty set
{c₂₆} is non empty trivial V47(1) set
{{c₂₆,i},{c₂₆}} is non empty set
dq9 . [c₂₆,i] is set
dq9 . (i,FS) is set
[i,FS] is non empty V25() set
{i,FS} is non empty set
{i} is non empty trivial V47(1) set
{{i,FS},{i}} is non empty set
dq9 . [i,FS] is set
z19 is Element of D
S . (FS,z19) is Element of the carrier of L
[FS,z19] is non empty V25() set
{FS,z19} is non empty set
{{FS,z19},{FS}} is non empty set
S . [FS,z19] is set
z29 is Element of D
S . (z19,z29) is Element of the carrier of L
[z19,z29] is non empty V25() set
{z19,z29} is non empty set
{z19} is non empty trivial V47(1) set
{{z19,z29},{z19}} is non empty set
S . [z19,z29] is set
S . (z29,FS) is Element of the carrier of L
[z29,FS] is non empty V25() set
{z29,FS} is non empty set
{z29} is non empty trivial V47(1) set
{{z29,FS},{z29}} is non empty set
S . [z29,FS] is set
dom dq9 is Relation-like Aq9 -defined Aq9 -valued Element of bool [:Aq9,Aq9:]
bool [:Aq9,Aq9:] is non empty V271() set
V is Element of Aq9
[V,c₂₆] is non empty V25() Element of [:Aq9,Aq9:]
{V,c₂₆} is non empty set
{V} is non empty trivial V47(1) set
{{V,c₂₆},{V}} is non empty set
dq9 . [V,c₂₆] is Element of the carrier of L
[c₂₆,i] is non empty V25() Element of [:Aq9,Aq9:]
dq9 . [c₂₆,i] is Element of the carrier of L
h is Element of Aq9
[i,h] is non empty V25() Element of [:Aq9,Aq9:]
{i,h} is non empty set
{{i,h},{i}} is non empty set
dq9 . [i,h] is Element of the carrier of L
Seg 4 is non empty V40() V47(4) Element of bool NAT
L is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
L is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
3 + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
2 + 2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
L is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima modular RelStr
the carrier of L is non empty set
BasicDF L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is non empty set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is non empty set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is non empty V271() set
A is Relation-like Function-like ( the carrier of L,L, BasicDF L)
{ ((A . b₁) `1) where b<sub>1</sub> is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT : verum } is set
union { ((A . b<sub>1</sub>) `1) where b₁ is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT : verum } is set
{ ((A . b₁) `2) where b<sub>1</sub> is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT : verum } is set
union { ((A . b<sub>1</sub>) `2) where b₁ is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT : verum } is set
D is non empty set
[:D,D:] is non empty set
[:[:D,D:], the carrier of L:] is non empty set
bool [:[:D,D:], the carrier of L:] is non empty V271() set
EqRelLATT D is non empty reflexive transitive antisymmetric lower-bounded upper-bounded V227() with_suprema with_infima V297() RelStr
the carrier of (EqRelLATT D) is non empty set
[: the carrier of L, the carrier of (EqRelLATT D):] is non empty set
bool [: the carrier of L, the carrier of (EqRelLATT D):] is non empty V271() set
bool [:D,D:] is non empty V271() set
S is Relation-like [:D,D:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:D,D:], the carrier of L:]
alpha S is Relation-like the carrier of L -defined the carrier of (EqRelLATT D) -valued Function-like quasi_total Element of bool [: the carrier of L, the carrier of (EqRelLATT D):]
FS is Relation-like the carrier of L -defined the carrier of (EqRelLATT D) -valued Function-like quasi_total monotone meet-preserving join-preserving Element of bool [: the carrier of L, the carrier of (EqRelLATT D):]
Image FS is non empty strict reflexive transitive antisymmetric full meet-inheriting join-inheriting with_suprema with_infima SubRelStr of EqRelLATT D
rng FS is Element of bool the carrier of (EqRelLATT D)
bool the carrier of (EqRelLATT D) is non empty V271() set
subrelstr (rng FS) is strict reflexive transitive antisymmetric full SubRelStr of EqRelLATT D
the carrier of (Image FS) is non empty set
FS is Relation-like D -defined D -valued total V72() V74() V79() Element of bool [:D,D:]
FD is Relation-like D -defined D -valued total V72() V74() V79() Element of bool [:D,D:]
FS "\/" FD is Relation-like D -defined D -valued total V72() V74() V79() Element of bool [:D,D:]
f is set
FS is set
[f,FS] is non empty V25() set
{f,FS} is non empty set
{f} is non empty trivial V47(1) set
{{f,FS},{f}} is non empty set
dom FS is Element of bool the carrier of L
bool the carrier of L is non empty V271() set
f is set
FS . f is set
FD is set
FS . FD is set
A9 is Element of the carrier of L
d9 is Element of the carrier of L
Aq9 is Element of the carrier of L
dq9 is Element of the carrier of L
Aq9 "\/" dq9 is Element of the carrier of L
FS . (Aq9 "\/" dq9) is Element of the carrier of (EqRelLATT D)
q is Relation-like D -defined D -valued total V72() V74() V79() Element of bool [:D,D:]
FS . dq9 is Element of the carrier of (EqRelLATT D)
Q is Relation-like D -defined D -valued total V72() V74() V79() Element of bool [:D,D:]
FS . Aq9 is Element of the carrier of (EqRelLATT D)
u is Relation-like D -defined D -valued total V72() V74() V79() Element of bool [:D,D:]
field (FS "\/" FD) is set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT : ( 1 <= b₁ & b₁ <= 4 ) } is set
(FS . Aq9) "\/" (FS . dq9) is Element of the carrier of (EqRelLATT D)
v is Element of D
a is Element of D
S . (v,a) is Element of the carrier of L
[v,a] is non empty V25() set
{v,a} is non empty set
{v} is non empty trivial V47(1) set
{{v,a},{v}} is non empty set
S . [v,a] is set
(S . (v,a)) "\/" Aq9 is Element of the carrier of L
((S . (v,a)) "\/" Aq9) "/\" dq9 is Element of the carrier of L
b is Element of D
S . (v,b) is Element of the carrier of L
[v,b] is non empty V25() set
{v,b} is non empty set
{{v,b},{v}} is non empty set
S . [v,b] is set
e is Element of D
S . (b,e) is Element of the carrier of L
[b,e] is non empty V25() set
{b,e} is non empty set
{b} is non empty trivial V47(1) set
{{b,e},{b}} is non empty set
S . [b,e] is set
S . (e,a) is Element of the carrier of L
[e,a] is non empty V25() set
{e,a} is non empty set
{e} is non empty trivial V47(1) set
{{e,a},{e}} is non empty set
S . [e,a] is set
W is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() set
W is Relation-like NAT -defined Function-like V40() FinSequence-like FinSubsequence-like set
dom W is Element of bool NAT
W is Relation-like NAT -defined Function-like V40() FinSequence-like FinSubsequence-like set
dom W is Element of bool NAT
len W is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
proj2 W is set
V is set
h is set
W . h is set
V is Relation-like NAT -defined D -valued Function-like V40() FinSequence-like FinSubsequence-like FinSequence of D
len V is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
h is Relation-like NAT -defined D -valued Function-like non empty V40() FinSequence-like FinSubsequence-like FinSequence of D
h . 1 is set
len h is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() ext-real V38() V40() V45() Element of NAT
c₂₆ is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
h . c₂₆ is set
c₂₆ + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
h . (c₂₆ + 1) is set
[(h . c₂₆),(h . (c₂₆ + 1))] is non empty V25() set
{(h . c₂₆),(h . (c₂₆ + 1))} is non empty set
{(h . c₂₆)} is non empty trivial V47(1) set
{{(h . c₂₆),(h . (c₂₆ + 1))},{(h . c₂₆)}} is non empty set
[v,b] is non empty V25() Element of [:D,D:]
[(h . 1),b] is non empty V25() set
{(h . 1),b} is non empty set
{(h . 1)} is non empty trivial V47(1) set
{{(h . 1),b},{(h . 1)}} is non empty set
(Aq9 "\/" dq9) "\/" Aq9 is Element of the carrier of L
Aq9 "\/" Aq9 is Element of the carrier of L
dq9 "\/" (Aq9 "\/" Aq9) is Element of the carrier of L
dq9 "\/" Aq9 is Element of the carrier of L
dq9 "/\" (dq9 "\/" Aq9) is Element of the carrier of L
[b,e] is non empty V25() Element of [:D,D:]
h . 2 is set
[(h . 2),e] is non empty V25() set
{(h . 2),e} is non empty set
{(h . 2)} is non empty trivial V47(1) set
{{(h . 2),e},{(h . 2)}} is non empty set
i is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
2 * i is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() even Element of NAT
[e,a] is non empty V25() Element of [:D,D:]
h . 3 is set
[(h . 3),a] is non empty V25() set
{(h . 3),a} is non empty set
{(h . 3)} is non empty trivial V47(1) set
{{(h . 3),a},{(h . 3)}} is non empty set
i is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
2 * i is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() even Element of NAT
(2 * i) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() ext-real V38() V40() V45() non even Element of NAT
h . (len h) is set
h . 4 is set
L is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima modular RelStr
the carrier of L is non empty set
BasicDF L is Relation-like [: the carrier of L, the carrier of L:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[: the carrier of L, the carrier of L:], the carrier of L:]
[: the carrier of L, the carrier of L:] is non empty set
[:[: the carrier of L, the carrier of L:], the carrier of L:] is non empty set
bool [:[: the carrier of L, the carrier of L:], the carrier of L:] is non empty V271() set
the Relation-like Function-like ( the carrier of L,L, BasicDF L) is Relation-like Function-like ( the carrier of L,L, BasicDF L)
{ (( the Relation-like Function-like ( the carrier of L,L, BasicDF L) . b₁) `1) where b<sub>1</sub> is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT : verum } is set
union { (( the Relation-like Function-like ( the carrier of L,L, BasicDF L) . b<sub>1</sub>) `1) where b₁ is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT : verum } is set
the Relation-like Function-like ( the carrier of L,L, BasicDF L) . 0 is set
( the Relation-like Function-like ( the carrier of L,L, BasicDF L) . 0) `1 is set
[ the carrier of L,(BasicDF L)] is non empty V25() set
{ the carrier of L,(BasicDF L)} is non empty set
{ the carrier of L} is non empty trivial V47(1) set
{{ the carrier of L,(BasicDF L)},{ the carrier of L}} is non empty set
[ the carrier of L,(BasicDF L)] `1 is set
FS is non empty set
[:FS,FS:] is non empty set
[:[:FS,FS:], the carrier of L:] is non empty set
bool [:[:FS,FS:], the carrier of L:] is non empty V271() set
{ (( the Relation-like Function-like ( the carrier of L,L, BasicDF L) . b₁) `2) where b<sub>1</sub> is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT : verum } is set
union { (( the Relation-like Function-like ( the carrier of L,L, BasicDF L) . b<sub>1</sub>) `2) where b₁ is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT : verum } is set
EqRelLATT FS is non empty reflexive transitive antisymmetric lower-bounded upper-bounded V227() with_suprema with_infima V297() RelStr
FD is Relation-like [:FS,FS:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:FS,FS:], the carrier of L:]
alpha FD is Relation-like the carrier of L -defined the carrier of (EqRelLATT FS) -valued Function-like quasi_total Element of bool [: the carrier of L, the carrier of (EqRelLATT FS):]
the carrier of (EqRelLATT FS) is non empty set
[: the carrier of L, the carrier of (EqRelLATT FS):] is non empty set
bool [: the carrier of L, the carrier of (EqRelLATT FS):] is non empty V271() set
FS is Element of the carrier of L
f is Element of the carrier of L
{FS,f} is non empty Element of bool the carrier of L
bool the carrier of L is non empty V271() set
(alpha FD) .: {FS,f} is Element of bool the carrier of (EqRelLATT FS)
bool the carrier of (EqRelLATT FS) is non empty V271() set
bool [:FS,FS:] is non empty V271() set
(alpha FD) . f is Element of the carrier of (EqRelLATT FS)
FD is Relation-like FS -defined FS -valued total V72() V74() V79() Element of bool [:FS,FS:]
(alpha FD) . FS is Element of the carrier of (EqRelLATT FS)
A9 is Relation-like FS -defined FS -valued total V72() V74() V79() Element of bool [:FS,FS:]
FS "\/" f is Element of the carrier of L
(alpha FD) . (FS "\/" f) is Element of the carrier of (EqRelLATT FS)
d9 is Relation-like FS -defined FS -valued total V72() V74() V79() Element of bool [:FS,FS:]
field FD is set
f "\/" FS is Element of the carrier of L
Aq9 is set
dq9 is set
[Aq9,dq9] is non empty V25() set
{Aq9,dq9} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,dq9},{Aq9}} is non empty set
q is Element of FS
Q is Element of FS
FD . (q,Q) is Element of the carrier of L
[q,Q] is non empty V25() set
{q,Q} is non empty set
{q} is non empty trivial V47(1) set
{{q,Q},{q}} is non empty set
FD . [q,Q] is set
field d9 is set
A9 "\/" FD is Relation-like FS -defined FS -valued total V72() V74() V79() Element of bool [:FS,FS:]
Aq9 is set
dq9 is set
[Aq9,dq9] is non empty V25() set
{Aq9,dq9} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,dq9},{Aq9}} is non empty set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT : ( 1 <= b₁ & b₁ <= 4 ) } is set
q is Element of FS
Q is Element of FS
FD . (q,Q) is Element of the carrier of L
[q,Q] is non empty V25() set
{q,Q} is non empty set
{q} is non empty trivial V47(1) set
{{q,Q},{q}} is non empty set
FD . [q,Q] is set
(FD . (q,Q)) "\/" FS is Element of the carrier of L
((FD . (q,Q)) "\/" FS) "/\" f is Element of the carrier of L
u is Element of FS
FD . (q,u) is Element of the carrier of L
[q,u] is non empty V25() set
{q,u} is non empty set
{{q,u},{q}} is non empty set
FD . [q,u] is set
v is Element of FS
FD . (u,v) is Element of the carrier of L
[u,v] is non empty V25() set
{u,v} is non empty set
{u} is non empty trivial V47(1) set
{{u,v},{u}} is non empty set
FD . [u,v] is set
FD . (v,Q) is Element of the carrier of L
[v,Q] is non empty V25() set
{v,Q} is non empty set
{v} is non empty trivial V47(1) set
{{v,Q},{v}} is non empty set
FD . [v,Q] is set
a is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() set
a is Relation-like NAT -defined Function-like V40() FinSequence-like FinSubsequence-like set
dom a is Element of bool NAT
a is Relation-like NAT -defined Function-like V40() FinSequence-like FinSubsequence-like set
dom a is Element of bool NAT
len a is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
a . 1 is set
A9 \/ FD is Relation-like FS -defined FS -valued Element of bool [:FS,FS:]
b is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
a . b is set
b + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
a . (b + 1) is set
[(a . b),(a . (b + 1))] is non empty V25() set
{(a . b),(a . (b + 1))} is non empty set
{(a . b)} is non empty trivial V47(1) set
{{(a . b),(a . (b + 1))},{(a . b)}} is non empty set
[q,u] is non empty V25() Element of [:FS,FS:]
[(a . 1),u] is non empty V25() set
{(a . 1),u} is non empty set
{(a . 1)} is non empty trivial V47(1) set
{{(a . 1),u},{(a . 1)}} is non empty set
a . 2 is set
[(a . 1),(a . 2)] is non empty V25() set
{(a . 1),(a . 2)} is non empty set
{{(a . 1),(a . 2)},{(a . 1)}} is non empty set
(FS "\/" f) "\/" FS is Element of the carrier of L
FS "\/" FS is Element of the carrier of L
f "\/" (FS "\/" FS) is Element of the carrier of L
f "/\" (f "\/" FS) is Element of the carrier of L
[u,v] is non empty V25() Element of [:FS,FS:]
a . 2 is set
[(a . 2),v] is non empty V25() set
{(a . 2),v} is non empty set
{(a . 2)} is non empty trivial V47(1) set
{{(a . 2),v},{(a . 2)}} is non empty set
a . 3 is set
[(a . 2),(a . 3)] is non empty V25() set
{(a . 2),(a . 3)} is non empty set
{{(a . 2),(a . 3)},{(a . 2)}} is non empty set
[v,Q] is non empty V25() Element of [:FS,FS:]
a . 3 is set
[(a . 3),Q] is non empty V25() set
{(a . 3),Q} is non empty set
{(a . 3)} is non empty trivial V47(1) set
{{(a . 3),Q},{(a . 3)}} is non empty set
a . 4 is set
[(a . 3),(a . 4)] is non empty V25() set
{(a . 3),(a . 4)} is non empty set
{{(a . 3),(a . 4)},{(a . 3)}} is non empty set
a . 4 is set
a . (len a) is set
field A9 is set
Aq9 is set
dq9 is set
[Aq9,dq9] is non empty V25() set
{Aq9,dq9} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,dq9},{Aq9}} is non empty set
q is Element of FS
Q is Element of FS
FD . (q,Q) is Element of the carrier of L
[q,Q] is non empty V25() set
{q,Q} is non empty set
{q} is non empty trivial V47(1) set
{{q,Q},{q}} is non empty set
FD . [q,Q] is set
A9 \/ FD is Relation-like FS -defined FS -valued Element of bool [:FS,FS:]
dom (alpha FD) is Element of bool the carrier of L
"\/" (((alpha FD) .: {FS,f}),(EqRelLATT FS)) is Element of the carrier of (EqRelLATT FS)
{((alpha FD) . FS),((alpha FD) . f)} is non empty Element of bool the carrier of (EqRelLATT FS)
"\/" ({((alpha FD) . FS),((alpha FD) . f)},(EqRelLATT FS)) is Element of the carrier of (EqRelLATT FS)
((alpha FD) . FS) "\/" ((alpha FD) . f) is Element of the carrier of (EqRelLATT FS)
"\/" ({FS,f},L) is Element of the carrier of L
(alpha FD) . ("\/" ({FS,f},L)) is Element of the carrier of (EqRelLATT FS)
f is Relation-like the carrier of L -defined the carrier of (EqRelLATT FS) -valued Function-like quasi_total monotone meet-preserving join-preserving Element of bool [: the carrier of L, the carrier of (EqRelLATT FS):]
dom f is Element of bool the carrier of L
bool the carrier of L is non empty V271() set
bool [:FS,FS:] is non empty V271() set
Image f is non empty strict reflexive transitive antisymmetric full meet-inheriting join-inheriting with_suprema with_infima SubRelStr of EqRelLATT FS
rng f is Element of bool the carrier of (EqRelLATT FS)
bool the carrier of (EqRelLATT FS) is non empty V271() set
subrelstr (rng f) is strict reflexive transitive antisymmetric full SubRelStr of EqRelLATT FS
the carrier of (Image f) is non empty set
id FS is Relation-like FS -defined FS -valued Function-like one-to-one non empty total V72() V74() V75() V79() Element of bool [:FS,FS:]
{{ the carrier of L}} is non empty trivial V47(1) set
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
the Relation-like Function-like ( the carrier of L,L, BasicDF L) . (0 + 1) is set
FS is non empty set
[:FS,FS:] is non empty set
[:[:FS,FS:], the carrier of L:] is non empty set
bool [:[:FS,FS:], the carrier of L:] is non empty V271() set
FD is non empty set
[:FD,FD:] is non empty set
[:[:FD,FD:], the carrier of L:] is non empty set
bool [:[:FD,FD:], the carrier of L:] is non empty V271() set
f is Relation-like [:FS,FS:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:FS,FS:], the carrier of L:]
A9 is Relation-like [:FD,FD:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:FD,FD:], the carrier of L:]
[FS,f] is non empty V25() set
{FS,f} is non empty set
{FS} is non empty trivial V47(1) set
{{FS,f},{FS}} is non empty set
[FD,A9] is non empty V25() set
{FD,A9} is non empty set
{FD} is non empty trivial V47(1) set
{{FD,A9},{FD}} is non empty set
[: the carrier of L, the carrier of L, the carrier of L, the carrier of L:] is non empty set
( the carrier of L,L,(BasicDF L)) is non empty set
DistEsti (BasicDF L) is epsilon-transitive epsilon-connected ordinal V45() set
( the carrier of L,(DistEsti (BasicDF L))) is non empty set
[:( the carrier of L,L,(BasicDF L)),( the carrier of L,L,(BasicDF L)):] is non empty set
d9 is T-Sequence-like Relation-like [: the carrier of L, the carrier of L, the carrier of L, the carrier of L:] -valued Function-like QuadrSeq of BasicDF L
( the carrier of L,L,(BasicDF L),d9) is Relation-like [:( the carrier of L,L,(BasicDF L)),( the carrier of L,L,(BasicDF L)):] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:( the carrier of L,L,(BasicDF L)),( the carrier of L,L,(BasicDF L)):], the carrier of L:]
[:[:( the carrier of L,L,(BasicDF L)),( the carrier of L,L,(BasicDF L)):], the carrier of L:] is non empty set
bool [:[:( the carrier of L,L,(BasicDF L)),( the carrier of L,L,(BasicDF L)):], the carrier of L:] is non empty V271() set
( the carrier of L,L,(BasicDF L),d9,(DistEsti (BasicDF L))) is Relation-like [:( the carrier of L,(DistEsti (BasicDF L))),( the carrier of L,(DistEsti (BasicDF L))):] -defined the carrier of L -valued Function-like quasi_total Element of bool [:[:( the carrier of L,(DistEsti (BasicDF L))),( the carrier of L,(DistEsti (BasicDF L))):], the carrier of L:]
[:( the carrier of L,(DistEsti (BasicDF L))),( the carrier of L,(DistEsti (BasicDF L))):] is non empty set
[:[:( the carrier of L,(DistEsti (BasicDF L))),( the carrier of L,(DistEsti (BasicDF L))):], the carrier of L:] is non empty set
bool [:[:( the carrier of L,(DistEsti (BasicDF L))),( the carrier of L,(DistEsti (BasicDF L))):], the carrier of L:] is non empty V271() set
( the carrier of L,{}) is non empty set
( the carrier of L,L,(BasicDF L),d9,{}) is Element of [:( the carrier of L,{}),( the carrier of L,{}), the carrier of L, the carrier of L:]
[:( the carrier of L,{}),( the carrier of L,{}), the carrier of L, the carrier of L:] is non empty set
the Relation-like Function-like ( the carrier of L,L, BasicDF L) . 1 is set
( the Relation-like Function-like ( the carrier of L,L, BasicDF L) . 1) `2 is set
proj1 d9 is epsilon-transitive epsilon-connected ordinal set
d9 . {} is set
rng d9 is Element of bool [: the carrier of L, the carrier of L, the carrier of L, the carrier of L:]
bool [: the carrier of L, the carrier of L, the carrier of L, the carrier of L:] is non empty V271() set
{ [b<sub>1</sub>,b<sub>2</sub>,b<sub>3</sub>,b<sub>4</sub>] where b<sub>1</sub>, b<sub>2</sub>, b<sub>3</sub>, b<sub>4</sub> is Element of the carrier of L : (BasicDF L) . (b<sub>1</sub>,b<sub>2</sub>) <= b<sub>3</sub> "\/" b<sub>4</sub> } is set
dq9 is Element of the carrier of L
q is Element of the carrier of L
Q is Element of the carrier of L
u is Element of the carrier of L
[dq9,q,Q,u] is V25() V26() V27() Element of [: the carrier of L, the carrier of L, the carrier of L, the carrier of L:]
[dq9,q,Q] is V25() V26() set
[dq9,q] is non empty V25() set
{dq9,q} is non empty set
{dq9} is non empty trivial V47(1) set
{{dq9,q},{dq9}} is non empty set
[[dq9,q],Q] is non empty V25() set
{[dq9,q],Q} is non empty set
{[dq9,q]} is Function-like non empty trivial V47(1) set
{{[dq9,q],Q},{[dq9,q]}} is non empty set
[[dq9,q,Q],u] is non empty V25() set
{[dq9,q,Q],u} is non empty set
{[dq9,q,Q]} is non empty trivial V47(1) set
{{[dq9,q,Q],u},{[dq9,q,Q]}} is non empty set
(BasicDF L) . (dq9,q) is Element of the carrier of L
(BasicDF L) . [dq9,q] is set
Q "\/" u is Element of the carrier of L
f . u is Element of the carrier of (EqRelLATT FS)
v is Relation-like FS -defined FS -valued total V72() V74() V79() Element of bool [:FS,FS:]
Aq9 is Element of [: the carrier of L, the carrier of L, the carrier of L, the carrier of L:]
Aq9 `4_4 is Element of the carrier of L
[FD,A9] `2 is set
{{ the carrier of L},{{ the carrier of L}}} is non empty set
the carrier of L \/ {{ the carrier of L},{{ the carrier of L}}} is non empty set
( the Relation-like Function-like ( the carrier of L,L, BasicDF L) . 1) `1 is set
[FD,A9] `1 is set
( the carrier of L) is non empty set
(( the carrier of L,{})) is non empty set
{( the carrier of L,{})} is non empty trivial V47(1) set
{{( the carrier of L,{})}} is non empty trivial V47(1) set
{{( the carrier of L,{})},{{( the carrier of L,{})}}} is non empty set
( the carrier of L,{}) \/ {{( the carrier of L,{})},{{( the carrier of L,{})}}} is non empty set
( the carrier of L,(succ {})) is non empty set
[:( the carrier of L,{}),( the carrier of L,{}):] is non empty set
( the carrier of L,L,(BasicDF L),d9,{}) is Relation-like [:( the carrier of L,{}),( the carrier of L,{}):] -defined the carrier of L -valued Function-like quasi_total Element of bool [:[:( the carrier of L,{}),( the carrier of L,{}):], the carrier of L:]
[:[:( the carrier of L,{}),( the carrier of L,{}):], the carrier of L:] is non empty set
bool [:[:( the carrier of L,{}),( the carrier of L,{}):], the carrier of L:] is non empty V271() set
( the carrier of L,L,(BasicDF L),d9,(succ {})) is Relation-like [:( the carrier of L,(succ {})),( the carrier of L,(succ {})):] -defined the carrier of L -valued Function-like quasi_total Element of bool [:[:( the carrier of L,(succ {})),( the carrier of L,(succ {})):], the carrier of L:]
[:( the carrier of L,(succ {})),( the carrier of L,(succ {})):] is non empty set
[:[:( the carrier of L,(succ {})),( the carrier of L,(succ {})):], the carrier of L:] is non empty set
bool [:[:( the carrier of L,(succ {})),( the carrier of L,(succ {})):], the carrier of L:] is non empty V271() set
BiFun (( the carrier of L,L,(BasicDF L),d9,{}),( the carrier of L,{}),L) is Relation-like [:( the carrier of L,{}),( the carrier of L,{}):] -defined the carrier of L -valued Function-like quasi_total Element of bool [:[:( the carrier of L,{}),( the carrier of L,{}):], the carrier of L:]
(( the carrier of L,{}),L,(BiFun (( the carrier of L,L,(BasicDF L),d9,{}),( the carrier of L,{}),L)),( the carrier of L,L,(BasicDF L),d9,{})) is Relation-like [:(( the carrier of L,{})),(( the carrier of L,{})):] -defined the carrier of L -valued Function-like quasi_total Element of bool [:[:(( the carrier of L,{})),(( the carrier of L,{})):], the carrier of L:]
[:(( the carrier of L,{})),(( the carrier of L,{})):] is non empty set
[:[:(( the carrier of L,{})),(( the carrier of L,{})):], the carrier of L:] is non empty set
bool [:[:(( the carrier of L,{})),(( the carrier of L,{})):], the carrier of L:] is non empty V271() set
( the carrier of L,L,(BasicDF L),Aq9) is Relation-like [:( the carrier of L),( the carrier of L):] -defined the carrier of L -valued Function-like quasi_total Element of bool [:[:( the carrier of L),( the carrier of L):], the carrier of L:]
[:( the carrier of L),( the carrier of L):] is non empty set
[:[:( the carrier of L),( the carrier of L):], the carrier of L:] is non empty set
bool [:[:( the carrier of L),( the carrier of L):], the carrier of L:] is non empty V271() set
dom ( the carrier of L,L,(BasicDF L),Aq9) is Relation-like ( the carrier of L) -defined ( the carrier of L) -valued Element of bool [:( the carrier of L),( the carrier of L):]
bool [:( the carrier of L),( the carrier of L):] is non empty V271() set
[{ the carrier of L},{{ the carrier of L}}] is non empty V25() set
{{{ the carrier of L},{{ the carrier of L}}},{{ the carrier of L}}} is non empty set
a is Element of FS
b is Element of FS
FD . (a,b) is Element of the carrier of L
[a,b] is non empty V25() set
{a,b} is non empty set
{a} is non empty trivial V47(1) set
{{a,b},{a}} is non empty set
FD . [a,b] is set
( the carrier of L,L,(BasicDF L),Aq9) . ({ the carrier of L},{{ the carrier of L}}) is set
( the carrier of L,L,(BasicDF L),Aq9) . [{ the carrier of L},{{ the carrier of L}}] is set
Aq9 `1_4 is Element of the carrier of L
Aq9 `1 is set
(Aq9 `1) `1 is set
((Aq9 `1) `1) `1 is set
Aq9 `2_4 is Element of the carrier of L
((Aq9 `1) `1) `2 is set
(BasicDF L) . ((Aq9 `1_4),(Aq9 `2_4)) is Element of the carrier of L
[(Aq9 `1_4),(Aq9 `2_4)] is non empty V25() set
{(Aq9 `1_4),(Aq9 `2_4)} is non empty set
{(Aq9 `1_4)} is non empty trivial V47(1) set
{{(Aq9 `1_4),(Aq9 `2_4)},{(Aq9 `1_4)}} is non empty set
(BasicDF L) . [(Aq9 `1_4),(Aq9 `2_4)] is set
Aq9 `3_4 is Element of the carrier of L
(Aq9 `1) `2 is set
((BasicDF L) . ((Aq9 `1_4),(Aq9 `2_4))) "\/" (Aq9 `3_4) is Element of the carrier of L
(((BasicDF L) . ((Aq9 `1_4),(Aq9 `2_4))) "\/" (Aq9 `3_4)) "/\" (Aq9 `4_4) is Element of the carrier of L
FS is Relation-like FS -defined FS -valued total V72() V74() V79() Element of bool [:FS,FS:]
FS is Relation-like FS -defined FS -valued total V72() V74() V79() Element of bool [:FS,FS:]
f is set
{f} is non empty trivial V47(1) set
[:{f},{f}:] is non empty set
[f,f] is non empty V25() set
{f,f} is non empty set
{{f,f},{f}} is non empty set
{[f,f]} is Function-like non empty trivial V47(1) set
id {f} is Relation-like {f} -defined {f} -valued Function-like one-to-one non empty total V72() V74() V75() V79() Element of bool [:{f},{f}:]
bool [:{f},{f}:] is non empty V271() set
field FS is set
rng (BasicDF L) is Element of bool the carrier of L
FS is set
( the Relation-like Function-like ( the carrier of L,L, BasicDF L) . 0) `2 is set
[ the carrier of L,(BasicDF L)] `2 is set
f is set
(BasicDF L) . f is set
FD . f is set
dom (BasicDF L) is Relation-like the carrier of L -defined the carrier of L -valued Element of bool [: the carrier of L, the carrier of L:]
bool [: the carrier of L, the carrier of L:] is non empty V271() set
rng FD is Element of bool the carrier of L
FS is non empty non trivial set
EqRelLATT FS is non empty reflexive transitive antisymmetric lower-bounded upper-bounded V227() with_suprema with_infima V297() RelStr
the carrier of (EqRelLATT FS) is non empty set
[: the carrier of L, the carrier of (EqRelLATT FS):] is non empty set
bool [: the carrier of L, the carrier of (EqRelLATT FS):] is non empty V271() set
[:FS,FS:] is non empty set
bool [:FS,FS:] is non empty V271() set
id FS is Relation-like FS -defined FS -valued Function-like one-to-one non empty total V72() V74() V75() V79() Element of bool [:FS,FS:]
f is Relation-like the carrier of L -defined the carrier of (EqRelLATT FS) -valued Function-like quasi_total monotone meet-preserving join-preserving Element of bool [: the carrier of L, the carrier of (EqRelLATT FS):]
Image f is non empty strict reflexive transitive antisymmetric full meet-inheriting join-inheriting with_suprema with_infima SubRelStr of EqRelLATT FS
rng f is Element of bool the carrier of (EqRelLATT FS)
bool the carrier of (EqRelLATT FS) is non empty V271() set
subrelstr (rng f) is strict reflexive transitive antisymmetric full SubRelStr of EqRelLATT FS
the carrier of (Image f) is non empty set
type_of (Image f) is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
[:[:FS,FS:], the carrier of L:] is non empty set
bool [:[:FS,FS:], the carrier of L:] is non empty V271() set
A9 is set
dom f is Element of bool the carrier of L
d9 is set
f . d9 is set
Aq9 is Element of the carrier of L
f . Aq9 is Element of the carrier of (EqRelLATT FS)
FD is Relation-like [:FS,FS:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:FS,FS:], the carrier of L:]
dq9 is Relation-like FS -defined FS -valued total V72() V74() V79() Element of bool [:FS,FS:]
A9 is Relation-like FS -defined FS -valued total V72() V74() V79() Element of bool [:FS,FS:]
d9 is Relation-like FS -defined FS -valued total V72() V74() V79() Element of bool [:FS,FS:]
Aq9 is set
dq9 is set
[Aq9,dq9] is non empty V25() set
{Aq9,dq9} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,dq9},{Aq9}} is non empty set
A9 "\/" d9 is Relation-like FS -defined FS -valued total V72() V74() V79() Element of bool [:FS,FS:]
{{ the carrier of L}} is non empty trivial V47(1) set
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() ext-real V38() V40() V45() Element of NAT
the Relation-like Function-like ( the carrier of L,L, BasicDF L) . (0 + 1) is set
A9 is non empty set
[:A9,A9:] is non empty set
[:[:A9,A9:], the carrier of L:] is non empty set
bool [:[:A9,A9:], the carrier of L:] is non empty V271() set
Aq9 is non empty set
[:Aq9,Aq9:] is non empty set
[:[:Aq9,Aq9:], the carrier of L:] is non empty set
bool [:[:Aq9,Aq9:], the carrier of L:] is non empty V271() set
d9 is Relation-like [:A9,A9:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:A9,A9:], the carrier of L:]
dq9 is Relation-like [:Aq9,Aq9:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:Aq9,Aq9:], the carrier of L:]
[A9,d9] is non empty V25() set
{A9,d9} is non empty set
{A9} is non empty trivial V47(1) set
{{A9,d9},{A9}} is non empty set
[Aq9,dq9] is non empty V25() set
{Aq9,dq9} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,dq9},{Aq9}} is non empty set
[: the carrier of L, the carrier of L, the carrier of L, the carrier of L:] is non empty set
( the carrier of L,L,(BasicDF L)) is non empty set
DistEsti (BasicDF L) is epsilon-transitive epsilon-connected ordinal V45() set
( the carrier of L,(DistEsti (BasicDF L))) is non empty set
[:( the carrier of L,L,(BasicDF L)),( the carrier of L,L,(BasicDF L)):] is non empty set
q is T-Sequence-like Relation-like [: the carrier of L, the carrier of L, the carrier of L, the carrier of L:] -valued Function-like QuadrSeq of BasicDF L
( the carrier of L,L,(BasicDF L),q) is Relation-like [:( the carrier of L,L,(BasicDF L)),( the carrier of L,L,(BasicDF L)):] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:( the carrier of L,L,(BasicDF L)),( the carrier of L,L,(BasicDF L)):], the carrier of L:]
[:[:( the carrier of L,L,(BasicDF L)),( the carrier of L,L,(BasicDF L)):], the carrier of L:] is non empty set
bool [:[:( the carrier of L,L,(BasicDF L)),( the carrier of L,L,(BasicDF L)):], the carrier of L:] is non empty V271() set
( the carrier of L,L,(BasicDF L),q,(DistEsti (BasicDF L))) is Relation-like [:( the carrier of L,(DistEsti (BasicDF L))),( the carrier of L,(DistEsti (BasicDF L))):] -defined the carrier of L -valued Function-like quasi_total Element of bool [:[:( the carrier of L,(DistEsti (BasicDF L))),( the carrier of L,(DistEsti (BasicDF L))):], the carrier of L:]
[:( the carrier of L,(DistEsti (BasicDF L))),( the carrier of L,(DistEsti (BasicDF L))):] is non empty set
[:[:( the carrier of L,(DistEsti (BasicDF L))),( the carrier of L,(DistEsti (BasicDF L))):], the carrier of L:] is non empty set
bool [:[:( the carrier of L,(DistEsti (BasicDF L))),( the carrier of L,(DistEsti (BasicDF L))):], the carrier of L:] is non empty V271() set
( the carrier of L,{}) is non empty set
( the carrier of L,L,(BasicDF L),q,{}) is Element of [:( the carrier of L,{}),( the carrier of L,{}), the carrier of L, the carrier of L:]
[:( the carrier of L,{}),( the carrier of L,{}), the carrier of L, the carrier of L:] is non empty set
the Relation-like Function-like ( the carrier of L,L, BasicDF L) . 1 is set
( the Relation-like Function-like ( the carrier of L,L, BasicDF L) . 1) `2 is set
proj1 q is epsilon-transitive epsilon-connected ordinal set
q . {} is set
rng q is Element of bool [: the carrier of L, the carrier of L, the carrier of L, the carrier of L:]
bool [: the carrier of L, the carrier of L, the carrier of L, the carrier of L:] is non empty V271() set
{ [b<sub>1</sub>,b<sub>2</sub>,b<sub>3</sub>,b<sub>4</sub>] where b<sub>1</sub>, b<sub>2</sub>, b<sub>3</sub>, b<sub>4</sub> is Element of the carrier of L : (BasicDF L) . (b<sub>1</sub>,b<sub>2</sub>) <= b<sub>3</sub> "\/" b<sub>4</sub> } is set
u is Element of the carrier of L
v is Element of the carrier of L
a is Element of the carrier of L
b is Element of the carrier of L
[u,v,a,b] is V25() V26() V27() Element of [: the carrier of L, the carrier of L, the carrier of L, the carrier of L:]
[u,v,a] is V25() V26() set
[u,v] is non empty V25() set
{u,v} is non empty set
{u} is non empty trivial V47(1) set
{{u,v},{u}} is non empty set
[[u,v],a] is non empty V25() set
{[u,v],a} is non empty set
{[u,v]} is Function-like non empty trivial V47(1) set
{{[u,v],a},{[u,v]}} is non empty set
[[u,v,a],b] is non empty V25() set
{[u,v,a],b} is non empty set
{[u,v,a]} is non empty trivial V47(1) set
{{[u,v,a],b},{[u,v,a]}} is non empty set
(BasicDF L) . (u,v) is Element of the carrier of L
(BasicDF L) . [u,v] is set
a "\/" b is Element of the carrier of L
f . b is Element of the carrier of (EqRelLATT FS)
FD is Relation-like [:FS,FS:] -defined the carrier of L -valued Function-like quasi_total symmetric zeroed u.t.i. Element of bool [:[:FS,FS:], the carrier of L:]
e is Relation-like FS -defined FS -valued total V72() V74() V79() Element of bool [:FS,FS:]
Q is Element of [: the carrier of L, the carrier of L, the carrier of L, the carrier of L:]
Q `4_4 is Element of the carrier of L
[Aq9,dq9] `2 is set
{{ the carrier of L},{{ the carrier of L}}} is non empty set
the carrier of L \/ {{ the carrier of L},{{ the carrier of L}}} is non empty set
( the Relation-like Function-like ( the carrier of L,L, BasicDF L) . 1) `1 is set
[Aq9,dq9] `1 is set
( the carrier of L) is non empty set
(( the carrier of L,{})) is non empty set
{( the carrier of L,{})} is non empty trivial V47(1) set
{{( the carrier of L,{})}} is non empty trivial V47(1) set
{{( the carrier of L,{})},{{( the carrier of L,{})}}} is non empty set
( the carrier of L,{}) \/ {{( the carrier of L,{})},{{( the carrier of L,{})}}} is non empty set
( the carrier of L,(succ {})) is non empty set
[:( the carrier of L,{}),( the carrier of L,{}):] is non empty set
( the carrier of L,L,(BasicDF L),q,{}) is Relation-like [:( the carrier of L,{}),( the carrier of L,{}):] -defined the carrier of L -valued Function-like quasi_total Element of bool [:[:( the carrier of L,{}),( the carrier of L,{}):], the carrier of L:]
[:[:( the carrier of L,{}),( the carrier of L,{}):], the carrier of L:] is non empty set
bool [:[:( the carrier of L,{}),( the carrier of L,{}):], the carrier of L:] is non empty V271() set
( the carrier of L,L,(BasicDF L),q,(succ {})) is Relation-like [:( the carrier of L,(succ {})),( the carrier of L,(succ {})):] -defined the carrier of L -valued Function-like quasi_total Element of bool [:[:( the carrier of L,(succ {})),( the carrier of L,(succ {})):], the carrier of L:]
[:( the carrier of L,(succ {})),( the carrier of L,(succ {})):] is non empty set
[:[:( the carrier of L,(succ {})),( the carrier of L,(succ {})):], the carrier of L:] is non empty set
bool [:[:( the carrier of L,(succ {})),( the carrier of L,(succ {})):], the carrier of L:] is non empty V271() set
BiFun (( the carrier of L,L,(BasicDF L),q,{}),( the carrier of L,{}),L) is Relation-like [:( the carrier of L,{}),( the carrier of L,{}):] -defined the carrier of L -valued Function-like quasi_total Element of bool [:[:( the carrier of L,{}),( the carrier of L,{}):], the carrier of L:]
(( the carrier of L,{}),L,(BiFun (( the carrier of L,L,(BasicDF L),q,{}),( the carrier of L,{}),L)),( the carrier of L,L,(BasicDF L),q,{})) is Relation-like [:(( the carrier of L,{})),(( the carrier of L,{})):] -defined the carrier of L -valued Function-like quasi_total Element of bool [:[:(( the carrier of L,{})),(( the carrier of L,{})):], the carrier of L:]
[:(( the carrier of L,{})),(( the carrier of L,{})):] is non empty set
[:[:(( the carrier of L,{})),(( the carrier of L,{})):], the carrier of L:] is non empty set
bool [:[:(( the carrier of L,{})),(( the carrier of L,{})):], the carrier of L:] is non empty V271() set
( the carrier of L,L,(BasicDF L),Q) is Relation-like [:( the carrier of L),( the carrier of L):] -defined the carrier of L -valued Function-like quasi_total Element of bool [:[:( the carrier of L),( the carrier of L):], the carrier of L:]
[:( the carrier of L),( the carrier of L):] is non empty set
[:[:( the carrier of L),( the carrier of L):], the carrier of L:] is non empty set
bool [:[:( the carrier of L),( the carrier of L):], the carrier of L:] is non empty V271() set
dom ( the carrier of L,L,(BasicDF L),Q) is Relation-like ( the carrier of L) -defined ( the carrier of L) -valued Element of bool [:( the carrier of L),( the carrier of L):]
bool [:( the carrier of L),( the carrier of L):] is non empty V271() set
[{ the carrier of L},{{ the carrier of L}}] is non empty V25() set
{{{ the carrier of L},{{ the carrier of L}}},{{ the carrier of L}}} is non empty set
W is Element of FS
V is Element of FS
FD . (W,V) is Element of the carrier of L
[W,V] is non empty V25() set
{W,V} is non empty set
{W} is non empty trivial V47(1) set
{{W,V},{W}} is non empty set
FD . [W,V] is set
( the carrier of L,L,(BasicDF L),Q) . ({ the carrier of L},{{ the carrier of L}}) is set
( the carrier of L,L,(BasicDF L),Q) . [{ the carrier of L},{{ the carrier of L}}] is set
Q `1_4 is Element of the carrier of L
Q `1 is set
(Q `1) `1 is set
((Q `1) `1) `1 is set
Q `2_4 is Element of the carrier of L
((Q `1) `1) `2 is set
(BasicDF L) . ((Q `1_4),(Q `2_4)) is Element of the carrier of L
[(Q `1_4),(Q `2_4)] is non empty V25() set
{(Q `1_4),(Q `2_4)} is non empty set
{(Q `1_4)} is non empty trivial V47(1) set
{{(Q `1_4),(Q `2_4)},{(Q `1_4)}} is non empty set
(BasicDF L) . [(Q `1_4),(Q `2_4)] is set
Q `3_4 is Element of the carrier of L
(Q `1) `2 is set
((BasicDF L) . ((Q `1_4),(Q `2_4))) "\/" (Q `3_4) is Element of the carrier of L
(((BasicDF L) . ((Q `1_4),(Q `2_4))) "\/" (Q `3_4)) "/\" (Q `4_4) is Element of the carrier of L
A9 is Relation-like FS -defined FS -valued total V72() V74() V79() Element of bool [:FS,FS:]
d9 is Relation-like FS -defined FS -valued total V72() V74() V79() Element of bool [:FS,FS:]
Aq9 is set
dq9 is set
[Aq9,dq9] is non empty V25() set
{Aq9,dq9} is non empty set
{Aq9} is non empty trivial V47(1) set
{{Aq9,dq9},{Aq9}} is non empty set
A9 "\/" d9 is Relation-like FS -defined FS -valued total V72() V74() V79() Element of bool [:FS,FS:]
A9 is Relation-like FS -defined FS -valued total V72() V74() V79() Element of bool [:FS,FS:]
L is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr
A is non empty reflexive transitive antisymmetric lower-bounded with_suprema with_infima RelStr